LIBRARY 

OF   THE 

UNIVERSITY  OF  CALIFORNIA. 

Deceived      V  JAN     11  1  393 .....  189 
^Accessions  No.  4-QQ5"3     .  Class  No, 


JOHN   WILEY  &   SONS, 

53  E.  Tenth  Street,  New  York, 

PUBLISH : 

THE  RAILROAD   SPIRAL. 

The  Theory  of  the  Compound  Transition  Curve  reduced 
to  Practical  Formulas  and  Rules  for  Application  in  Field 
Work,  with  Complete  Tables  of  Deflections  and  Ordinates 
for  five  hundred  Spirals.  By  Wm.  H.  Searles,  C.E.,  author 
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Pocket-book  form $1  50 

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and  containing  a  large  number  of  Useful  Tables,  Original 
and  Selected.  By  Wm.  H.  Searles,  C.E.,  late  Prof,  of 
Geodesy  at  Rensselasr  Polytechnic  Inst.,  Troy.  This  vol- 
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THE 

CIVIL   ENGINEER'S 
FIELD-BOOK: 

DESIGNED  FOR  THE  USE  OP  THE 

LOCATING    ENGINEER. 

CONTAINING 

TABLES   OF   ACTUAL   TANGENTS,    AND   ARCS    EXPRESSED   IN 
CHORDS  OF  100  FEET  FOR   EVERY  MINUTE  OF  INTER- 
SECTION, FROM  0°  TO    90°,  FROM  A  1°   CURVE 
TO  A  10°  CURVE,  INCLUSIVE; 

ALSO 

TABLES  OF  FORMULAE  APPLICABLE  TO  RAILROAD  CURVES 
AND  THE  LOCATION  OF  FROGS; 

TOGETHER  WITH 

RADII,  LONG  CHORDS,  GRADES,  NATURAL  TANGENTS,  NATURAL  SINES, 
NATURAL  VERSED  SINES,  NATURAL  EXTERNAL  SECANTS,  ETC. 


BY 

EDWAED   BUTTS, 

CIVIL    ENGINEER. 
SECOND  AND  REVISED  EDITION. 

NEW  YORK: 
WILEY  AND   SONS, 
TENTH  STREET 

.oor  west  of  Broadway. 


Copyright,  1886, 
By  JOHN  WILEY  &  SONS. 


PREFACE. 


IN  preparing  this  book  it  lias  been  the  author's  design  to 
present  a  volume  based  on  the  most  economic  principles  of 
field  engineering. 

Many  good  books  of  the  kind  are  in  print,  yet  none  of  them, 
it  is  believed,  have  presented  the  subject  to  the  full  extent  of 
a  labor-saving  medium. 

Considerable  time  is  spent  in  making  mathematical  field- 
calculations,  thereby  delaying  the  party  and  increasing  the 
expense  of  the  survey.  To  eliminate  many  of  the  errors  that 
occur  in, these  calculations,  and  advance  the  progress  of  field- 
operations,  extensive,  hitherto  unpublished,  tables  have  been 
added  to  this  work,  and  others  previously  published  have 
been  enlarged  to  prevent  the  field-work  extending  beyond 
their  bounds.  The  formulae  are  comparatively  arranged  in  a 
more  systematic  manner. 

The  work  of  computing  the  tables  has  been  thoroughly 
done,  and  it  is  believed  will  be  found  strictly  reliable. 

An  effort  has  been  made  to  make  the  problems  general,  and 
therefore  applicable  to  any  case  that  may  arise  in  a  long 
practice.  Throughout  the  work  each  problem  is  arranged 
with  reference  to  the  last  preceding  figure. 

Should  this  volume  prove  itself  an  assistant  to  the  field- 
engineer,  and  fill  the  space  for  which  it  is  designed,  the 
author's  wish  will  be  fully  realized.  E.  B. 

KANSAS  CITY,  Mo.,  August,  1885. 


TJHIVBBSITY 


CIVIL  ENGINEER'S  FIELD-BOOK. 


CURVE  FORMULAE  AND  PROBLEMS. 


\ 


ABBREVIATIONS. 

T  =  Tangent,  BA  or  BO. 
R  =  Radius,  AD  or  CD. 
J—  Intersection,  angle  FBCor  EBA. 
D  =  Deflection,  angle  for  100  ft.  chords,  BAa  or  BCe. 
d  =  Sub-deflection,   angle  for  any  chord   less  than  100  ft., 

B Af  or  BCg. 

E  =  External  Secant,  Be. 
M=  Middle  Ordinate,  Jc>. 
C  —  Chord,  or  Long  Chord,  any  chord  of  100  ft.  or  more, 

Aa  or  A  G. 

c  —  Sub-chord,  any  chord  less  than  100  ft.,  AforgC. 
A  =  Arc,  the  length  of  the  curve  in  chords  of  100  ft.,  AabcdeC. 


CIVIL  ENGINEER'S  FIELD-BOOK. 


TABLE  I. 
TO  FIND  THE  TANGENT. 


GIVEN. 

FORMULA. 

GIVEN. 

FORMULA. 

R,  I 

T 
T 
T 

—  R  tan  A7 

(7,7 
BJ,  AD,  AJ 

T 

T 
T 

C 

50  tan  |7 

2  cos  \I 
,,  tan  II 

sin  D 
=  E  cot  II 

vers  £7 
BJX  AD 
AJ 

TABLE  II. 
TO  FIND  THE  RADIUS. 


GIVEN. 

FORMULA. 

GIVEN. 

FORMULA. 

T,I 
D 

R 

R 
R 

T  cot  £7 

C,  7 

J7,  7 
AJ,  AB,  BJ 

R 
R 
R 

C 

50 

2  sin  £7 
M 

sin  D 
E 

vers  ^7 
A  J  X  AB 

exsec  £7 

BJ 

TABLE  III. 
TO  FIND  THE  DEFLECTION. 


GIVEN. 

FORMULA. 

GIVEN. 

FORMULA. 

GIVEN. 

FORMULA. 

R 

*">=*! 

r,  / 

50  tan  */ 

A,  I 

\I 

sin  D  —         y 

A 

TABLE   IV. 
TO  FIND  THE  EXTERNAL  SECANT. 


GIVEN. 

FORMULA. 

GIVEN. 

FORMULAE. 

R   I 

E  —  R  exsec  -^-7 

C  I 

^_  ^exsecU 

T  I 

E  —  T  tan  17 

7^Sln  U^ 

jz       M 

cos  ^  7 
E         ^^ 

' 

•    cos  £7 

' 

CUKYE   FORMULA    AND    PROBLEMS. 


TABLE  V. 
TO  FIND  THE  MIDDLE  ORDINATE. 


GIVEN. 

FORMULA. 

GIVEN. 

FORMULAE. 

*,/ 

M  -  R  vers  J  J 

0,7 

M  =  iC  tan  J7 

T,7 

MJF  nna  1  7" 

XV,   7 

7?     77* 

M=  R  -(Rcos^I) 

Hf             KE 

E,I 

M      R  +  E 

TABLE   VI. 
TO  FIND  THE  CHORD. 


GIVEN. 

FORMULA. 

GIVEN. 

FORMULA. 

x?,  7 

O  =  2R  sin  J7 

jftj 

0  =  2^coti7 

T  I 

sin  ^7 

' 

cosi 

' 

^"^exsec  |7 

TABLE  VII. 
TO  FIND  THE  INTERSECTION. 


GIVEN. 

FORMULAE. 

GIVEN. 

FORMULA. 

DA 

M 

A  ^ 

^  =  Too 

M,  R 

vers  £7  =  — 
xt 

T 

T,  f2 

tani/=^ 

E,R 

exsec  \I  =  — 

o 

X?,    C 

C,T 

cos  i/  =  -^ 

TO  FIND   THE  ARC. 
Problem  1. 

Given  the  1,  FBC  =  41°,  and  the  D,  BAa  =  2°,  to  find  the 
-4,  AabcdeC. 
Formula.  Example. 

^IAA  i^=  20°  30'  =  1230' 

:  -j)100  D  =  2°          =  T207"  =  10'  5 


Result,         yl  =  1025.00 


4  CIVIL  ENGINEER'S  FIELD-BOOK. 

TO  FIND   THE   SUB-DEFLECTIOK 
Problem  2. 

Given  the  c,  Af  —  75  ft.,  and  the  Dy  BAa  =  4°  18',  to  find 
the  d,  BAf. 

Formula.  Example. 

_  DC  D  =  4°  18'  =  258' 

"100  c=  75 

1290 

1806  Result, 

100.  I  19350.  I  193.50  -  3°  13' 30"  =  d. 


Problem  3. 

Many  sub-deflections  may  be  calculated  quickly  by  the  fol- 
lowing method:  Multiply  the  degree  of  the  given  curve  by 
0.3,  and  multiply  the  product  thus  obtained  by  the  length  of 
the  given  sub-chord,  and  then  reduce  the  second  product  one 
denomination;  the  result  will  be  the  required  sub-deflection. 

Given  the  c,  gC  —  30  ft.,  and  the  degree  of  curve  aDb  =  2°, 
to  find  the  d,  BCg. 

Example. 

Degree  of  curve  =  2° 
.3 
.6 

c  =     30. 

Second  product  —   18°  0 
Reduced  one  denomination  —  18'0  =  d. 
EXPLANATION. — When  it  is  required  to  run  a  curve  very 
accurately  the  above  formulae,  although  generally  used,  are 
not  correct.     This  will  be  readily  understood  by  considering 
that  the  shorter  the  chords  the  nearer  the   approach  to  the 
circumference  of  the  circle,  and  the  longer  the  chords  the 
nearer  the  approach  to  the  diameter  of  the  circle. 

The  base  of  most  field-work  and  calculations  is  one  hundred 
feet.  Therefore  when  a  chord  is  shorter  than  this  base  it 
should  be  proportionally  longer  than  would  be  indicated  in  a 
deflection  calculated  by  the  above  method,  and  vice  versa  when 
a  chord  is  longer  than  this  base. 

The  deflection  must  first  be  calculated  as  indicated  by  Prob- 
lem 2  or  3,  after  which  correct  the  sub  chord  by  the  following. 


CURVE   FORMULAE    AND    PROBLEMS.  5 

Problem  4. 

Given  the  d,  BAf  —  6°,  and  the  R,  AD  =  359.265,  to  find 
the  c,  Af. 

Formula.  Example. 

c  =  2Rsmd.  2R=  718.53 

d  =  6°    sin  0.10453 

215559 
359265 
287412 
71853 

Products  =          75.1079409 


vlv      C-    "d7/ 


Problem  5. 

Given  the  1,  FBC  =  45°,  and  the  11,  AD  =  637.275,  to  lay 
out  a  curve  by  ordinates  when  the  curve  begins  60  ft.  beyond 
a  station  and  ends  60  ft.  back  of  a  station. 

By  Table  I.  the  T,  BA  and  BC  =  R  tan  \I  =  263.97 

By  Table  III.  sin  D  =  -^  =  4°  30'. 


By  Problem  1,  A  =  ^100  =  500. 


Denote  BAa'  by  d. 
"      BAV    "    D'Ec. 

"      Aa'      "    c. 
"      AV       "    CEc. 
"      aa        "    o. 


Denote  a'Aa  by  x. 
"      VAb    "    x'Ec. 
"      Aa      "    y. 
f<      Ab      "   y'Ec. 
"      bb'        "    o'. 


CIVIL   ENGINEER  S    FIELD-BOOK. 


r 

By  Problem  2,  d  =  =^  =  1°48',  and  D'  =  d  +  D  =  1°  48' 
luu 

+  4°  30'  =  6°  18'. 

Then  x  =  \I  -  d  =  22°  30'  -  1°48'  =  20°  42',  and  x'  = 
\I  -  D'  =  22°  30'  -  6°  18'  =  16°  12'. 

By  Problem  4,  c  —  2R  sin  d  —  40.03,  and  C  —  139.86/&. 

To  find  yEc. 

Formula.  Example. 

y  =  ccosx.  #  =  20°  42'    cos  0.93544 

c=  4003 

280632 
374176 

Product  y  -  37.4456632 

To  find  oEc. 

Formula.  Example. 

o  =  c  sin  x.  x—  20°  42'     sin  0.35347 

c  —  40.03 


Product  o  = 


106041 
141388 

14.1494041 


Problem  6. 

Given  the  /,  FBC  =  45°,  and  the  nt  AD  =  637.275,  to  lay 
out  a  curve  from  points  on  the  tangents  AB  and  CB  when  the 


CURVE    FORMULA    AND    PROBLEMS.  7 

curve  begins  60  ft.  beyond  a  station  and  ends  60  ft.  back  of  a 
station. 
By  Table  I.  the  I\  BA  and  BC  =  R  tan  \I  =  263.96 

By  Table  III.  sin  D  =  ~  =  4°  30'. 
By  Problem  1,  A  =  —100  =  500. 

Denote  BAa  by  d.  Denote  Aa  by  c. 

"       BAb   "    D'.  "-      Ab    "    G. 

"       BAc   "    D".  "      Ac    "    C'. 

"       Aa'     "    #.  "      «#'    "    y. 

"     AV    "  xr.  "    w    "  y. 

"       ^4c'     <4    x".  "      cc'     "    y". 

By  Problem  2,  c?  =  ^  =  1°  48',  and  D'  =  d  +  D  =  1°  48' 

+  4°  30'  =  6°  18',  and  D"  =  d  +  2D  =  1°  48'  +  9°  =  10°  48'. 

By  Problem  4,  c  =  2R  sin  d  =  40.03,  and  G  =  139.86,  and 
C'  =  238.83 

To  find  x. 

Formula.  Example. 

x  =  ccosd.  d  =  r±8'    cos  0.99951 

e=  40.03 

299853 
399804 

Product  x  =  40.0103853 

Use  the  same  method  to  find  x'  and  x". 
To  find  y. 

Formula.  Example, 

y  —  c  sin  d.  d  =  1°  48'    sin  0.03141 

c~  40.03 

9423 
12564 


Product  y  =  1.2573423 

Use  the  same  method  to  find  y'  and  y". 
Then,  for  locating  the  other  half  of  the  curve,  begin  at  C 
and  run  towards  B,  using  the  same  formulae  as  given  above. 


CIVIL  ENGINEER'S  FIELD-BOOK. 


Problem  7. 

Given  the  R,  AD  =  1432.69  of  a  located  curve  AabcC,  it  is 
desired  to  run  another  curve  A'a'b'c'C'  parallel  to  it  at  a  given 
distance  of  A  A'  =  75  ft. 

The  chords  A  a,  ah  EC  are  100  ft.  long. 

Denote  the  chords  A  a',  a'b'Kc,  by  x. 

Denote  AD  by  R ,  then  R  =  AD  -  AA  =  1432.69  -  75 
=  1357.69 

By  Table  III.  sin  D  =  ~  =  2°. 
To  find  x. 

Formula.  Example. 

a  =  272' sin  U.         2  R' =  2715.38 

D  =  2°     sin  0.03490 

24438420 
1086152 
814614 


Product  x=          94.7667620 

If  it  is  desired  to  run  the  curve  A"a"b"c"C",  add  the  distance 
AA"  to  the  R,  AD,  and  use  the  above  method. 


CURVE   FORMULAE   AND   PROBLEMS. 


Problem  8. 

Given  the  R,  AD  —  2864.93,  to  locate  a  curve  when  the 
point  of  intersection  B  is  inaccessible. 

Make  the  offset  AN  —  12  ft.  =  a,  and  run  NR  parallel  to 
AG  intersecting  the  tangent  BU  at  P,  and  turn  the  angle 
RPH  =  OB  14  =  14°  =  I. 

By  Table  I.  the  T,  BA  and  BG  =  R  tan  ±1  =  351.76 

Denote  PO  by  x,  and  PB  by  z. 

Determine  the  unknown  sides  of  the  triangle  BPO  by  the 
following  formulae: 

To  find  x. 

Formula.  Example. 

x  =  a  cot  /.  /  =  14°    cot  4.01078 

a  =  12. 

802156 
401078 


Product  x  =  48.12936 

To  find  z. 
Formula.  Example. 

a  I—  14°~1    a  =    ["Quotient  z  = 


z  = 


sin  J    sin  0.24192  J  12.0000  [_49.60 
96768 

232320 

217728 


145920 


NO  -  AB  =  351.76,  and  NP(=  NO  +  0P'  =  351.76  + 
48.13)  —  399.89  from  P,  a  point  12  ft.  at  right  angles  to  the 
point  of  curve  A. 


10  CIVIL  ENGINEER'S  FIELD-BOOK. 

The  point  of  tangent  C  (=  BO  —  BP  =  351.76  -  49.60)  — 
302. 16  from  P. 

By  Table  III.  sin  D  =  ~  =  1°. 
{K 

By  Problem  1,  A  =  —100  =  700. 


Problem  9. 

Given  the  R,  AD  =  287.939,  and  the  distance  around  the 
curve,  AC  =  200  ft.,  to  locate  the  point  C  from  a  point  on  the 
tangent  A  G. 

The  R,  AD  being  that  of  a  20°  curve,  the  angle  FBC  — 
40°  =  /,  and  by  Table  VI.  the  chord  AC  =  2R  sin  |7  = 
196.962  =  C. 

Make  the  distance  AG  =  AC.  Then  invariably  the  angle 
AGGnudAGG  =  i/  =  10°. 

Calculate  the  distance  GC  =  x  by  the  following: 

Formula.  Example. 

L          20=  393.924 

±7  =  10°     cos  0.98481 

393924 
3151392 
1575696 
3151392 
3545316 


Product  x  =         387.94029444 


CURVE   FORMULAE   AND    PROBLEMS. 


11 


Problem  1O. 

Given  the  7?,  AD  =  1632.40,  to  locate  the  beginning  and 
end  of  a  curve  when  the  point  of  intersection  B  is  inaccessible. 
Continue  the  tangent  EA  to  JV,  also  the  tangent  HCto  P. 

Measure  the  distance  JVP  =  359.20  =  a,  and  turn  the  angle 
FPN  =  33°  43'  =  b,  and  the  angle  GNP  =  28°  35'  =  c;  then 
the  angle  GBP  =  b  +  c  =  33°  43'  +  28°  35'  =  62°  18'  =  7. 

By  Table  I.  the  I\  BA  and  BC  =  R  tan  ±1  =  986.67 

Denote  BN  by  x,  and  BP  by  z. 

Determine  the  unknown  sides  of  the  triangle  NBP  by  the 
following  formulae: 

To  find  x. 

Formula.  Example. 

asmb  b  —  33°  43'      sin  0.55509 

:    sin/  «  =  359.20 

1110180 
499581 
277545 
/  =  62°  18'"]  166527     _  ["Result  x  = 

sin  0. 88539 J 199. 3883280  L225. 19 
177078 

223103 
'    177078 


460252 
442695 

175578 
88539 

870390 


12  CIVIL  ENGINEER'S  FIELD-BOOK. 


To  find  z, 

Formula,  Example. 

_  a  sin  e  c  =  28°  35'      sin  0.47844 

~-~s^T  *=  359.20 

956880 
430596 


J  =  62°  18'~  143532         PResult  2  = 


'~| 


sin  0.  88539  171.  8556480  l94.  10 
88539 

833166 
796851 


363154 
354156 


88539 
14490 

NA  =  T  -  x  =  986.67  -  225.19  =  761.48,  the  distance 
from  N  to  the  point  of  curve  A. 

PC  =  T  -   z  =  986.67  -  194,10  =  792.57,  the  distance 
from  P  to  the  point  of  tangent  (7. 


Problem  1  1 . 

Given  the  /,  FBO  =  58°,  to  locate  a  curve  through  a  given 
point  1L 

Find  the  point  Q  on  the  tangent  J3A  where  the  angle  BGH 
=  K  =  29°. 

Measure  the  distance  Oil  =  40  ft.  =  a,  also  the  distance 
BO  =  500  ft.  =  b. 

Denote  OK  by  x,  and  HK\-y  y,  and  QA  by  z. 


CURVE    FORMULAE    AND    PROBLEMS. 


13 


Calculate  x  and  z  by  the  following  formula?: 
To  find  x. 

Formula.  Example, 

x  =  2b  cos  \T.  \I  —  29°     cos  0.87462 

2b  =  1000. 

Product  x  =  874.62000 

Then  y  =  x  -  a  =  874.62  -  40.  =  834.62 
To  find  z. 


Formula. 

z  = 


Example. 

y  =      834.62 
a  =  40. 


33384.80 


Result  z  — 
182.71 


28  I  233 
224 


362  I  984 
724 


3647  I  26080 
25529 


36541  I  55100 
36541 

The  tangent  BA  and  BC  =  b  +  z  =  500.  +  182.71  =  682.71 
By  Table  II.  the  11,  AD  =  Tcot  i/=  1231.64 


Problem  12. 

Given  the  /,  FBG  =  41°  36',  and  the  distance  CJ=  8.62  —  a, 
to  determine  how  far  toward  G,  A'  must  be  from  A  to  start 
the  curve  A'C',  which  is  similar  to  AC,  to  have  it  run  into  the 
tangent  C'K  parallel  to  Oil  at  the  given  distance  a. 


14  CIVIL  ENGINEER'S  FIELD-BOOK. 

Denote  the  distance  A  A'  by  x  and  calculate  it  by  the  following: 
Formula.  Example. 

a  I  —  41°  36'~1  a  —  ("Quotient  x  = 

~  sin  7         sin  0.66393 J  8.6200|_12.98 
66393 

198070 
132786 


652840 
597537 

553030 


Problem  13. 

Given  the  R,  AD  =  1432.69,  and  the  /,  FBO  =  62°  30',  of  a 
located  curve  AC  to  find  the  R\  AD'  of  another  curve  to  start 
from  the  same  point  A  and  end  in  the  tangent  C'K  parallel  to 
OH  at  a  given  distance  CC'  =  42.60  =  a. 

Denote  the  distance  DD'  by  x  and  calculate  it  by  the  fol- 
lowing. 
Formula.  Example. 

\a        \I—  31°  15'"]  \a  =   ["Quotient  x  = 

~  sin  i/      gin  o,51877j21.3000L41.05 

207508 

54920 

51877 


304300 
Then  R  =  R  +  x  =  1432.69  +  41.05  =  1473.74 


CURVE   FORMULAE   AND    PROBLEMS.  15 


Problem   14. 

Given  the  R,  AD  =  1910.03,  and  the  /,  FBC  =  31  30'  of  a 
located  curve  AC,  to  find  the  H' ;  AD'  of  another  curve  to 
start  from  the  same  point  A,  and  end  in  the  tangent  C'K,  par- 
allel to  GH&i  a  given  distance,  GO'  =  14  ft.  =  a. 

Denote  the  distance  DD'  by  x,  and  calculate  it  by  the  fol- 
lowing: 

Formula.  Example. 

a  I  =  31°  30'~|    a  =    ["Quotient  x  = 

vers  /'    vers  0.14736J14.0000L90.00 
133624 

73760 
73680 


x  =  — 


8000 
Then  R'  =  R  +  x  =  1910.08  4-  95.00  ==  2005.08 


COMPOUND  CURVES. 


Problem  15. 

Having  run  the  curve  A  C  with  the  R,  AD  =  955.366  and 
the  I,  FBC  —  54°  30',  it  is  desired  to  flatten  the  curve  at  each 
end,  a  distance  of  A  G  and  CH  =  150  ft.  with  a  radius  of  AD' 
and  CD'  =  1910.08  =  R'. 


16 


CIVIL  ENGINEER'S  FIELD-BOOK. 


Required  the  radius  GD"  and  IID"  =  r,  to  join  the  two 
curves  A  O  and  Gil  at  G  and  //. 

The  R',  AD',  and  CD'  being  that  of  a  3°  curve,  the  angle 
AD'G  =  4°  30',  also  CD'  II  =  4°  30'. 

The  angle  GD'U  =1-  (AD'G  +  CD'  11)  =  54°  30'  -  9° 
=  45°  30'  =  /'. 

Denote  R1  -  R  by  a;  then  a  =  1910.08-955.366  =  954.714. 

Denote  the  distance  D"D'  by  x,  and  calculate  it  by  the  fol- 
lowing: 

Formula.  Example. 

as'mil  a  =  954.714 

*  =  "sin  ±1'  I*  =  27°  15'  sin  0  45787 

6682998 
7637712 
6682998 
4773570 

iP  =  22°  45'  ~|  3818856         TResult  x  = 

sin  0.38671J437.13489918LH30.39 
38671 

50424 
38671 


117538 
116013 

152599 
116013 

365861 
Then  r  =  E'  —  x  =  1910.08  -  1130.39  ~  779.6 


CURVE    FORMULAE    AND    PROBLEMS. 


17 


Problem  1  6. 

Given  the  chord  AC'  =  600  ft.  =  O,  and  the  angle  BAG' 
=  45°,  and  the  angle  BO' A  —  67°  36',  to  find  the  radii  CD  and 
CD'  to  lay  out  the  compound  curve  AGO'. 

The  angle  GAG'  =  %BAC  =  -22°  30'  =  a,  and  the'  angle 
CO  A  =  $BC'A  =  33°  48'  =  b. 

The  angle  A  GC1  =  180°  -  (22°  30'  +  33°  48')  =  123°  42'  =  e. 

Denote  the  chord  A  G  by  x,  and  the  chord  CO'  by  y,  and  cal- 
culate the  two  sides,  x  and  yt  of  the  triangle  AGG'  by  the  fol- 
lowing formulae : 

To  find  x. 


Formula. 
C  sin  b 


x  = 


sm  e 


Example. 

b  =  33°  48' sin  0.55630 
C=  600. 

e  =  123°42H  333.78000  FResult  X  = 

8in0.83195>378°     [401.80 
100000 
83195 

?.68050 


18  CIVIL  ENGINEER'S  FIELD-BOOK. 

To  find  y. 
Formula.  Example. 


ff  sin  a         a  =  22°  30'  sin  0.38268 
~^T7~        0  =  600. 


e  =  123°  42r 
sin  0.83195 


229.60800 
166390 


"Result  y  = 
275.98 


632180 
582365 

498150 
415975 

821750 

748755 

729950 

The  angle  GAG'  =  %'BB' C  —  |/to  the  curve  AC,  and  sim- 
ilarly the  angle  GO  A  =  %GB» '0'  =  $1  to  the  curve  CO'. 
Having  thus  found  the  chords  A C,  and  CC'  the  R,  CD,  by 

Table  II.  =  --^—-r=  524.20,  and  the  R,  CD  =  248.05 
2  sm  |/ 


Problem  1  7. 

Given  the  angle  FBC'  =  112°  36',  and  the  distance  ^4J5 
=  600.870  =  a,  and  the  distance  C*-B  =  459.557  =  5,  to  find 
the  radii  CD  and  CD  to  lay  out  the  compound  curve  A  CC' . 

Denote  the  angle  BAG'  by  x,  and  the  angle  BC' A  by  y,  and 
the  distance  AC'  by  g. 

The  angle  ABC'  =  180°  -  112°  36'  =  67°  24'  =  c,  and  0 
+  #  =  112°  36' , 

Calculate  a?,  y,  and  2,  by  the  following  formulae: 

To  find  half  the  difference  between  x  and  y. 


tan  $(y  —  x)  = 


Formula, 
(a  —  b)  tan  $(x  +  y) 


CURVE   FORMULA   AND   PROBLEMS.  19 

Example. 

a  —  b=  141.313 
+  y)=  56°  18'  tan  1.49944 

565253 
565252 

1271817 
1271817 
565252 
a  +  b  =q  141313     ["Result  tan  tfy-a?)  = 

1060. 427J  211.89036472  L-19982  =  11°  18' 
3060427 

10584766 
9543843 


10409234 
9543843 

8653917 
8483416 


1705012 

Then  x  =  *(«  +  y)  -  l(y  -x)=  56°  18'  -  11°  18'  =  45° 
and  y  =  \(x  +  y)  +  \(y  -  x)  =  56°  18'  +  11°  18'  =  67°  36'. 
To  find  s. 

Formula. 

a 

z  = sin  c. 

sm  y 

Example. 

y  =  67°  86'"]    a  =  I"    a     = 

sin  y 
-649.90 


I     . 
sin  0.92455J  600.870  [j 


554730 

461400         c  =  67°  24'  sin  0  92321 
369820 


915800  129980 

194970 
129980 
584910 


Result  z  =  599.9941790 

Then  by  Problem  16,  the  chord  AC  =  401.20  and  the  chord 
CO  =  275.98 

By  Table  II.  the  Rt  CD  =       .*\r=  524.20,  and  the  J?, 
OD'  =  248.05. 


CIVIL  EKGIKEEK'S  FIELD-BOOK. 


REVERSED  CURVES. 


Problem  1  8. 

Given  the  angle  CrAF  =  20°  =  a,  and  the  distance  AC' 
=  400  ft.  =  C,  to  find  the  R,  CD  and  CD'  to  join  the*  two  paral- 
lel lines  AF and  EG'  with  the  reversed  curve  ACG'. 


Formula. 

R=_$c_ 

sin  a 


Example. 
a  =  20°~|  i(7  =  ["Quotient. 

sin  0.34202J  100.000  [_292. 380 
68404 

315960 

307818 


81420 
68404 

130160 
102606 

275540 


Problem  19. 

Given  the  angle  C'AF=  3°  31'  =  a,  and  the  distance  AE 
—  14  ft.  =  d,  to  find  the  R,  CD  and  CD'  to  join  the  two  par- 
allel lines  ,4^ and  EG'  with  the  reversed  curve  ACG' . 

Calculate  the  distance  AC'  =  C  by  the  following: 


CURVE  FORMULAE  AND  PROBLEMS. 


Formula.  Example. 

_  d_^     a  —  3°  31H  d  —  ("Quotient.  C  = 

~  siu  a    sin  0. 06134 J  1 4.000  [_228. 236 
12268 

17320 
12268 


50520 
49072 

14480 
12268 

22120 

18402 

37180 
Then  by  Problem  18,  the  R,  CD  and  CD'  =  ~-  =  930.208 


Problem  2O. 

Given  the  distance  AF  —  196.11  =  b,  and  the  distance  AE 
=  14  ft.  =  dy  to  find  the  R,  CD  and  CD'  to  join  the  two  par- 
allel lines  J.^7and  EC'  with  the  reversed  curve  AGO'. 

Calculate  the  angle  C' AF  =  a  by  the  following: 
Formula.  Example. 

d  b  =~\    d  =    ("Quotient,  tan  a  = 

tan  a  =  r 

196. 11 J  14.0000  L-07139  =  4°  05' 
137277 

27230 
19611 


76190 

58833 

173570 

Then  by  Problem  19  the  distance  AC'  =  ~ 196.605 

sin  a 

And  by  Problem  18  the  R,  CD  and  CD  =  4-^~  =  690.230 

bin  a 


CIVIL  ENGINEER'S  FIELD-BOOK. 


Problem  21. 

Given  the  R,  CD  and   CD  =  819.02  and  the  angle  C'AF 
=  3°  15'  =  a,  to  find  the  distance  AF  =.  b. 

Formula.  Example. 

b  =  2R  sin  2a.         2R  =  1638.04 

2a  =  6°  30'  sin  0.11320 

3276080 
491412 
163804 
163804 

Product  b  =  185.4261280 


Ei 


Problem  22. 

Given  the  angle  C'AF=  3°  45'  =  |J,  and  the  R',  CD  = 
941.60,  and  the  distance  AE  =  14  ft.  =  d,  to  find  the  R,  CD' 
of  the  curve  CC'  to  join  the  tangent  J£Cr,  which  is  parallel  to 
AF  at  the  given  distance,  and  complete  the  reversed  curve 
ACC'. 

Denote  AC  by  (7,  and  AC'  by  C",  and  CC'  by  C. 

Calculate  C'  and  C"  by  the  following  formulae: 

To  find  C'. 

Formula.  Example. 

C'  =  2R'  sin  !/.      2R  =  1883.20 

i/    =  3°  45'  sin  0.06540 

7532800 
941600 
1129920 

Product  C'  =          123.1612800 


CURVE   FORMULA   AND    PROBLEMS. 


To  find  C". 
Formula. 

c"  =  -J-, , 

sin 


Example. 
i/=  3°  45' I  d  =   ["Quotient.     C"  = 

sin  0.06540J  14.000  [_214.067 
13080 

9200 
6540 

26GOO 
26160 


44000 
39240 

47600 
Then  C  =  C"  -  C1  =  214.067  -  123.161  =  90.906 


Having  Urns  found  C  by  Table  II.  R  = 


sin 


.=  695.0 


Problem  23. 

Given  the  /,  OBF  =  14°  32',  and  tlie  distance  BB'  =  548.5 
rr  a,  and  7',  GB'JI  =  10°  30,  to  find  the  ^,  CT)  and  CD'  to 
join  the  two  lines  EB  and  I?'//  with  the  reversed  curve  ACC'. 


24 


CIVIL   EITGINEEU'S   FIELD-BOOK. 


Formula, 
a 


tan  i/  +  tan 

Example. 

7°  21'  tan  0.12899 
5°  15'  tan  0.09189 


tan 


1   a  =  fResult. 
8    548.50 


taniT  =    .22088    548.50    2483.24 
J  441 76 L 


106740 

88352 

183880 
176704 


66264 

54960 
44L76 

107840 


Problem  24. 

Given  the  R,  AD  =  1661.0  and  the  R',  AD'  =  941.6  and 
the  R",  CD"  =  235  4,  and  the  distance  Aa  and  eC'  =  20  ft.  = 
d,  to  join  the  two  parallel  curves  Ae  and  aG'  with  the  re- 
versed curve  AGG'. 

Required  the  /',  ADD",  and  the  /",  D'D'G',  to  determine 
the  length  of  the  curve  AG,  and  the  length  of  the  curve  GG'. 

Find  all  the  sides  of  the  triangle  DD'D"  by  the  following 
method:  The  distance 

D'D"  =  R'  +  R"    =  941.6  +  235.4  =  1177.0  =  a, 
and      D'D  =  R  +  d  -  R"  =  1661.0  +  20.  -  235.4  = 

1445.6  =  b, 
and      DD'  =  R  +  R  =  1661.0  +  941.6  =  2602.6  =  c. 

Ma  _i_  b  _|_  C)  =  2612.6  =  s. 


CURVE    FORMULA    AND    PROBLEMS. 


Then  calculate  /'  and  /"  by  the  following  formulae: 
To  find  /'. 

Formula. 


sin  ±1'  — 


($  —  a)  (s  —  c) 


n(s  —  a}  (s  —  c)  = 
14356.0000 


ac 
306326.02J 


122530408 


Example. 

Quotient  = 
.0046865101 
6]   36 


r- 
|_ 


i- 

sin 
|_    = 


Result, 
r/'  =  .06846 
3°  55' 30" 


210295920 
183795612 

128 

1086 
1024 

265003080 
245060816 

1364 

6251 
5456 

/'  =  7°  51' 


199422640 

183795612 


13686  1  79501 


To  find  /". 

.Formula. 

.          _  sin  I'c 


156270280 
153163010__ 

•31072700" 
30632602 

44009SOO 


Example. 

T  =  7°  51'    sin  0.13658 
c   =  2602.6 

81948 
27316 
81948 
27316 

b  —   "1355.4631 08 ["Result,  sin  I"  = 
1445.6    [28912         [^24589= 
66343 

57824 

85191 

72280 


129110 
115648 

134628 


CIVIL  ENGINEER'S  FIELD-BOOK. 


FROG  PROBLEMS. 

ABBREVIATIONS. 


N  =  Frog  number. 
D  =  Degree  of  curve. 
C  =  Chord,  AC. 
F  =  Frog  angle,  HEG. 
L  =  Distance,  JE. 


S  =  Length  of  switch-rail. 

R  =  Radius,  AD. 

T  —  Tangent,  BA. 

I  =  Intersection,  FBG. 

G  =  Gauge  of  track,  JK. 


Problem  25. 

Given  the  frog  measurements  EN  =  8.55  =  a,  and  IIG 
0.95  =  bt  to  find  the  frog  number  N. 

Formula.  Example. 

—  _a  b  ="|  a  —  ("Quotient.    N  — 

~  *"  0.95J8.55L9. 

8.55 


Problem  26. 

Given  the  frog  measurements  EN  =  8.55  =  a,  and  IIG 
0.95  =  &,  to  find  the  F,  II KG. 

Formula.  Example. 

±F--  a  =~H&  =  FQuotient,  tan  \F  = 

~  a  8. 55 JO. 4750 L. 05555  =  3°  10'  47" 

4275 

4750 


CURVE   FORMULA   AND   PROBLEMS.  27 

Problem  27. 

Given  the  frog  number  N,  —  9,  to  find  Hie  Ft  IIEG. 
Formula.  Example. 


0.50  N  =~]         ["Quotient,  tan  %F  = 

N  9  J  0. 50  L  05555  =  3°  10'  47" 


45 
50 


Problem  28. 

Given  the  It,  AD  =  150.656,  and  the  G,  JK  =  4.708,  and 
the  L,  JE  =  37.664,  to  find  the  F,  IIEG. 

Formula. 
L 


tan  F  = 


Example. 
R  —  \G  =~|  Z  =    ["Quotient,  tan  ^  = 

148. 302  J  37.6640  L.  25397  =  14°  15' 
296604 

800360 
741510 


588500 
444906_ 

1435940 
1334718 

1012220 


28  CIVIL  ENGINEER'S  FIELD-BOOK. 


Problem  29. 

Given  the  R,  AD  =  150.656,  and  the  F,  HEG  =  14°  15',  to 
find  the  C,  AC. 

'Formula. 
C  =  211  sin  $F. 

Example. 

2R  =  301.312 

$F=  7°  07'  30"    sin  0.124035 

1506560 

903936 
1205248 
602624 
301312 


Product  C  =  37.373233920 


Problem  SO. 

Given  the   F,  HKQ-  =  14°  15',  and  the  It,  AD  =  150.656, 
and  the  G,  JK  =  4.708  to  find  the  L,  JE. 

Formula. 
L  =  (ll-  i#)  tan  F. 

Example. 

E  -  |#  =  148.302 

F  =  14°  15'     tan  0.25397 

1038114 
1334718 
444906 
741510 
296604 


Product  L  =  37.66425894 


Problem  31 . 

Given  the  G,  JK  —  4.708,  and  the  frog  number  N~  =  4,  to 
find  the  L,  JE. 

Formula.  Example. 

L  =  2GN.  2G  =        9.416 

N=      4 

Product  L  =      37.664 


CURVE   FORMULAE   AND    PROBLEMS. 


Problem  32. 

Given  the  L,  JE  =  37.664  to  find  the  length  of  the  switch- 
rail  8. 
Formula.  Example. 

_    L  ~~|  L  =  ["Quotient.     8  = 

~3-36  3.36J37.664L11.209 

336 

406 
336 


704 
672 


3200 
The  above  formula  is  for  a  gauge  of  4.708;  for  a  three-foot 

gauge.    S  =    - 


TO  FIND   THE   TANGENT   Oil  RADIUS. 

To  find  the  T,  BA  or  BC,  or  the  R,  AD.  The  F,  BEG  = 
.FJW7  =  7.  Then  by  Table  I.  T  =  R  tan  \I,  and  by  Table 
II.  R-  TcotiL 


Problem  33. 

Given  the  R,  AD  =  762.696,  and  the    G,  JK -  4.708,  to 
find  the  F,  Q-K11  of  the  middle  frog  in  a  three-throw  switch. 

Formula. 
vers  ±F  = 


30  CIVIL  ENGINEER'S  FIELD-BOOK. 


Example. 
IQ)  =-|  G  =  ("Quotient,  vers  +F  = 

1530. 1J  4.7080 1_.  003076  =  4°  29' 45" 
45903 


117700 
107107 

105930 


Problem  34. 

Given  the  R,  AD  =  762.696,  and  the  F,  IIEG  =  8°  59'  30", 
to  find  the  distance  AE  =  I. 

Formula. 

I  =  It  tan  \F. 

Example. 

B  =  762.696 

$F  =  4°  29'  45"     tan  0.078628 

6101568 
1525392 
4576176 
6101568 

5338872 


Product  I  = 


59.9(5926  L088 


Problem  35. 

To  find  the  frog  angle  when  the  main  track  is  curving  in  the 
same  direction  as  the  proposed  turnout. 

Given  the  curve  of  the  main  track,  AF  =  5°,  and  the  curve 
of  the  turnout  AL  =  9°  30'.  Subtracting  the  lesser  curve  from 


CURVE   FORMULA    AND    PROBLEMS.  31 

the  greater,  we  have  a  departure  of  4°  30',  with  a  relative 
radius  of  1273.57  =  R  '. 
Then  given  R1  =  1273.57,  and  the  G,  JK  =  4.708,  to  find 

the  F,  IIEG. 

Formula. 


Example. 
R'  +  ±Q  =n     G  =    ["Quotient,  vers  F  = 

1275.  924  J  4.708000  L  00368  =  4°  55' 

3827772 

8802280 
7655544 

11467360 


Problem  36. 

Given  the  R,  AD'  =  603.805,  and  the  R'<  AD  =  1146.28,  and 
the  Ft  IIEG  =  4°  55',  and  the  G,  JK  =  4.708,  to  find  the 
chord  AC=  C. 

By  the  following  method  solve  the  required  parts  of  the 
triangle  EDD': 

The  distance 
DD'  =  R  -  R  =  1146.28  -  603.805  =  542.475  =  a. 

The  distance 
D'/S  =  7?  +  \G  =  603.805  +  2.354  =  606.159  =  b. 

To  find  the  angle  EDD  =  I'. 


Formula. 
.     T,       b  sin  F        b 

Example. 
=                  606.159 
=  4°  55'    sin  0.08571 

a            F 

606159 
4243113 
3030795 

4849272 

a  -      51.95388789    Result,  sin  /'  = 
542.475  j  4883275       |_.09577  =  5°29'44" 

3131137 
2712375 

4187628 
3797325 

3903039 


32 


CIVIL   ENGINEER  S   FIELD-BOOK. 


Then  the  angle  AD' C  =  I'  +  F  =  5°  29' 44"  +  4°  55'  = 
10°  24' 44"  =  /. 
By  Table  VI.  C  =  2It  siii  I/  =  109.58. 


Problem  37. 

To  locate  a  frog  when  the  main  track  is  curving  in  a  direc- 
tion opposite  to  that  of  the  proposed  turnout. 

Given  the  curve  of  the  main  track  AF  =  3°,  and  the  curve 
of  the  proposed  turnout  AL  —  9°,  and  the  G,  JK  =  4.708 

Adding  the  lesser  curve  to  the  greater,  we  have  a'  departure 
of  12°  with  a  relative  radius  of  478.339  =  R'. 

To  find  the  Ft  HEG. 

Formula. 


Example. 
$Q  =  n    G  =    Pvers.  F  = 

480.693  J  4.708000  L  00979  =  8°  01'  30" 
4326237 

3817630 
3364851 

4527790 
4326237 


2015530 

Then  relatively  the  angle  CD' A  =  6°  01'  08"  =  /. 
Then,  given  the  R,  AD'  =  637.275,  and  the  /,  ADC  =  6° 
01'  08",  to  find  the  chord  A  C  =  C. 
By  Table  VI.  C  =  2E  sin  \I  =  66.91 


CURVE   FORMULAE    AND    PROBLEMS. 


M 
o 


W 
o 


.       CO 

I! 


<l      CO 

EH     O 

O 


§ 


Q 

S 


1 


2 


t-  O 


I  SJ  i~  :r  cs  o  co 

|   O      -O      •      •      • 

I  ?•*  !<2  r1  o  en  JH 


C^S^^ 
^3  O  i  ,  <X  O»  00 


*°  Jg  °°  g  »  S 


O    rt  O^TFriO 
W         I-H 


51-1  t_T_<O 
O    CO  »-ilO 


i 


feco 

!-<=> 


N 


Is 


^- 

^j  00  ^  QC  OS  0 


c?  ?  £ 

' 


05 


CIVIL  ENGINEER'S  FIELD-BOOK. 


TABLE   IX. 
RIGHT   TRIANGLES. 


TO  FIND  A. 


GIVEN. 

FORMULAE. 

GIVEN. 

FORMULAE. 

5 

6,  c 

tan  A  —  - 

c,  b 

cot  A  —  - 

c 

b 

6,  a 

SinA=l 

c,  a 

cos  A  =  - 

a 

TO  FIND  B. 


6,c 
6,  a 

cot  B  -—  - 

cos  J5  =  - 
a 

c,  6 
c,  a 

tan  B      b 

sin  B  =.- 
a 

TO  FIND  a. 

A,b 
A,c 

6 

.B,  6 

b 

~  sin  A 
~  cos  ^[ 

cos  1? 
c 

~sin  B 

TO   FIND  b. 

A,c 
A,  a 

b  =  c  tan  ^4 
6  =  a  sin  ^l 

5,  a 
B,  c 

b  —  a  cos  J5 
5  =  c  cot  £ 

TO  FIND  c. 

A,  a 

c  =  a  cos  .4 
c  =  b  cot  ^4 

B,a 

c  =  a  sin  5 
c  =  b  tan  5 

CURVE   FORMULAE   AND   PROBLEMS. 


35 


TABLE  X. 
OBLIQUE  TRIANGLES. 


TO  FIND  a,  ft,  c. 

TO  FIND  A, 

B,  C. 

GIVEN. 

FORMULAE. 

GIVEN. 

FORMULAE. 

A,  ft,  C 
A,B,c 
A,B,b 

a 
ft 
c 

ft  sin  C 

a,  ft,  C 
A,  6,  c 
-4,  a,  ft 

sin^L 
sm£ 
sin  C 

ft  sin  C 

sin  A 
c  sin  A 

a 
c  sin  .4 

sinB 
ft  sin  B 

ft 
a  sin  .4 

sin  .4 

ft 

TO   FIND  A,B,C. 


GIVEN. 

FORMULA. 

a,  c,  s 
a,  ft,  s 
ft,  c,  s 

/(s  -  a)  (s  - 

c) 

an  ^       |/             ac 

„•  i  p       A*  —  a)  (s  —  k) 

^/            aft 

-in  ,c_    .  As-b)(s- 

c) 

Y             be 

36 


CIVIL  ENGINEER'S  FIELD-BOOK. 


TABLE  XI. 
LONG  CHORDS,  DEFLECTIONS,  AND  ORDINATES. 


CURVE. 

LONG  CHORDS. 

DEFLEC- 
TIONS. 

ORDI- 

NATES. 

200 
ft. 

300 
ft. 

4OO 
ft. 

500 
ft. 

GOO 
ft. 

599.733 

700 
ft. 

|j 

H  go 

Chord. 

25. 

50. 

1° 

199.992 

299.970 

399.924 

499.848 

699.574 

.873 

1.745 

.164 

.218 

2° 

199.970 

299.878 

399.695 

499.391 

598.934 

698.295 

1.745 

3.490 

.327 

.436 

3° 

199.931 

299.726 

399.315 

498.630 

597.604 

696.168 

2.618 

5.235 

.491 

.655 

4° 

199.878 

299.513 

398.782 

497.566 

595  744 

693.196 

3.490 

6.980 

.655 

.873 

5° 

199.810 

299.239 

398.099 

496.201 

593.358 

689.386 

4.362 

8.724 

,818 

1.091 

6° 

199.726 

298.904 

397.264 

494.534 

590.449 

684.745 

5.234 

10.467 

.982 

1.309 

7° 

199.627 

298.509 

396.278 

492.568 

587.021 

679.285 

6.105 

12.210 

1.146 

1.528 

8° 

199.513 

298.054 

395.142 

490.306 

583.081 

673.015 

6.976 

13.951 

1.310 

1.746 

9° 

199.383 

297.538 

393.857 

487.749 

578.633 

665.950 

7.846 

15.692 

1.474 

1.965 

10° 

199.239 

296.962 

392.424 

484.900 

573  686 

658.105 

8.716 

17.431 

1.638 

2.183 

11* 

199.079 

296.325 

390.843 

481.762 

568.245 

649.496 

9.585 

19.169 

1.802 

2.402 

13° 

198.904 

295.629 

389.116 

478.338 

562.321 

640.142 

10.453 

20.906 

1.967 

2.620 

13° 

198.714 

294.874 

387.243 

474.633 

555.921 

630.062 

11.320 

22.641 

2.131 

2.839 

14° 

198.509 

294.059 

385.225 

470.649 

549.056 

619  278 

12.187 

24.374 

2.296 

3.058 

15° 

198.289 

293.185 

383.065 

466.390 

541.736 

607.812 

13.053 

26.105 

2.461 

3.277 

16° 

198054 

292.252 

380.763 

461.862 

533  972 

595.688 

13.917 

27.835 

2.625 

3.496 

17° 

197.803 

291.261 

37'8.320 

457.069 

525.776 

582.933  14.781 

29.562 

2.791 

3.716 

18° 

197.538 

290.211 

375.739 

452.015 

517.160 

569.571  15.643 

31.287 

2.956 

3.935 

19° 

197.256 

289.104 

373.021 

446.706 

508.139 

555.634  16.505 

33.010 

3.121 

4.155 

30° 

196.962 

287.939 

370.167 

441.147 

498.724 

541.147  17.365 

34.730 

3.287 

4.374 

CURVE   FORMULA   AND   PROBLEMS. 

TABLE  XII. 
RADII. 


37 


M 

0° 

Curve. 

1°           3°     1      3°     |      4° 
Curve.  Curve.  Curve.  Curve. 

5° 
Curve. 

6° 

Curve. 

7° 
Curve. 

8° 
Curve, 

9° 

Curve. 

O 

5729.65  2864.93  1910.08  1432.69  1146.28 

955.366 

819.020 

716.779 

637.275 

1 

343775.  5635.72  2841.26  1899.53  1426.  74;  1142.  47 

952.722 

817.077 

715.291 

636.099 

3 

171887. 

5544  83  2817.97  1889.09  1420.85  1138.69 

950.093 

815.144 

713.810 

634.928 

3 

114592. 

5456.82  2795.06  1878.77  1415.01 

1134.94 

947.478 

813.238 

712.335 

633.761 

4 

85943.7 

5371.56  2772  53  1868.56  1409  21 

1131.21 

944.877 

811.303 

710.865 

632.599 

5 

68754.9 

5288.92  2750.35  1858.47  1403.46 

1127.50 

942.291 

809.397 

709.402 

631.440 

6 

57295.8 

5208  .  79  2728  .  52  1  848  .  48  1  397  .  76 

1123.82 

939  719 

807.499 

707.945 

630.286 

7 

49110.7 

5131.05  2707.04  1838.59  1392.10 

1120.16 

937.161 

805.611 

706.493 

629.136 

8 

-12971.8  5055.59  2685.89  1828.82  1386.49 

1116.52 

934.616 

803.731 

705.048 

627.991 

9 

38197.2 

4982.332665.08^819.141380.92 

1112.91 

932.086 

801.860 

703.609 

626.849 

1O 

34377.5 

4911.  is'2644.  58  1809.57  1375.40 

1109.33 

929.569 

799.997 

702.175 

625.712 

11 

31252.3 

4841.98  2624.39  1800.10  1369.92 

1105.76 

927.066 

798.144 

700.748 

624.579 

13 

28647.8 

4774.74  2604.51  1790.73  1364.49 

1102.22 

924.576 

796.299 

699.326 

623.450 

13 

26444.2 

4709  .  33  2584  .  93  1  781  .  45  1359  .  1  0 

1098.70 

922.100 

794  462 

697.910 

622.325 

14 

24555.4 

4645.69  2565.65  1772.27  1353.75 

1095.20 

J19.637 

792.634 

696.499 

621.203 

15 

22918.3 

4583.75  2546.64  1763.18  1348.45 

1091.73 

917.187 

790.814 

695.095 

620.087 

16 

21485.9 

4523.44  2527.92  1754.19  1343.15  1088.28 

914.750 

789.003 

693.696 

618.974 

17 

20222.1 

4464.70  2509.47  1745  26  1337.65  1084.85 

912.326 

787.210 

692.302 

617.865 

18 

19098.6 

4407.46  2491.29  1736.48  1332.77  1081.44 

909.915 

785.405 

690.914 

616.760 

19 

18093.4 

4351.67  2473.  371727.  75  j  1327.  63 

1078.05 

907.517 

783.618 

689.532 

615.660 

30 

17188.8 

4297  .  28  2455  .  70  1  719  .  1.2  1322  .  53 

1074.68 

905.131 

781.840 

688.156 

P.14.563 

31 

16370.2 

4244.23  2438.29  1710.56  1317.46  1071.34 

902.758 

780.069 

686.785 

613.470 

33 

15626.1 

4192.47  2421.12  1702.10  1312.  4311068.01 

900.397 

778.307 

685.419 

612.380 

33 

14946.7 

4141.96  2404.19  1693.72  1307.45 

1064.71 

898.048 

776.552 

684.059 

611.295 

34 

14323.6 

4092.66  2387.50  1685.42  1302.50 

1061.43 

895.712 

774.806 

682.704 

610.214 

35 

13751.04044.51  2371.04  1677.201297.58 

1058.16 

893.388 

773.067 

681.354 

609.136 

36 

13222.113997.49  2354.80  1669.06  1292.71 

1054.92 

891.076 

771.336 

680.010 

608.062 

37 

12732.4 

3951.54  2338.78  1661.00  1287.87 

1051.70 

H88.776 

769.613 

678.671 

606.992 

38 

12277.7 

3906.54  2322.98  1653.01  1283.07 

1048.48 

886.488 

767.897 

677.338 

605.926 

39 

11854.3 

3862.74  2307.39  1645.11  1278.30 

1045.31 

884.211 

766.190 

676.008 

604.864 

3O 

11459.2 

3819.83  2292.01  1637.28  1273.57 

1042.14 

881  946 

764.489 

674.686 

603.805 

31 

11089.6 

3777.85  2276.84  1629.52  1268.87 

1039.00 

879.693 

762.797 

673.369 

602.750 

33 

10743.0 

3736.79  2261.86  1621.84  1264.21 

1035.87 

877.451 

761.112 

672  056 

601.698 

33 

10417.5 

3696.61  2247.08  1614.22  1259.58 

1032.76 

875.221 

759.434 

670.748 

600.651 

34 

101  Il.li3o57.  29  '2232.  49  1606.68  1254.98 

1029.67 

873  002 

757.764 

669.446 

599.607 

35 

9822  18  3618.802218.09  1599.21  1250.42 

1026.60 

S70.795 

756.101 

668.148 

598.567 

36 

9549.34  3581  .10  2203.87  1591.81  1245.89 

1023.55 

868.598 

754.445 

666.856 

597.530 

37 

9291.293544.19  2189.84  .1584.48  1241.40 

1020.51 

866.412 

752.796 

665.568 

596.497 

38 

9046.75  3508.02  2175.98  1577.21  1236.94  1017.49 

864  238 

751.155 

664.286 

595.467 

39 

8814.78 

3472.592162.30  1570.01  1232.  51  11014.50 

8G2.0V5 

749.521 

663.008 

594.441 

j 

40 

8594.41 

3437  .  87  2148  .  79  1562  .  88  1  228  .  1  1  '  101  1  .  51 

S59.922 

747.894 

661.736 

593.419 

41 

8384.80  3403.83  2135  44  1555.81  1223.74  1008.55 

857.780 

746.274 

660.468 

592.400 

43 

8185.16  3370.46  2122.26  1548.80  1219.40  1005.60 

855.648 

744.661 

659.20:. 

591.384 

43 

7994.81:3337.74  2109.24  1541.86  1215.30  1002.67 

853.527 

743.055 

657.947 

590.372 

44 

78  1  3  .  1  1  3305  .  65  2096  39  1  534  .  98  1  2  10  .  82  999  .  762 

851.417 

741.456 

656  694 

589.364 

45 

7639  .  49  3274  .  1  7  2083  .  68  1  528  .  16  1  206  .  57  996  .  867 

849.317 

739.864 

655.446 

588  359 

46 

7473.42  3243.29  -,'071.  13  1521.40  1202.36  993.988 

847.228 

738.279 

654.202 

587.357 

47 

7314.41  3212.982058.73  1514.70  1198.17991.126 

845.148 

736.701  652.963 

586.359 

48 

7162.03  3183.23  2046.48  1508.06  1194.  01  '988.  280 

843.080 

735.129651.729 

585.364 

49 

7015.87  3154.  03!2034.  37  1501.48  1189.88  985.451 

841.021 

733.564 

650.499 

584.373 

50 

6875.55  3125.36  2022.  41  '1494.95  1185.78  982.638 

838.972 

732.005 

649.274 

583.385 

51 

6740.74  3097.20  2010.59  1488.481181.71  979.840 

836.933 

730.454648.054 

582.400 

53 

66  1  1  .  12  3069  55  1  998  .  90  1482  .  07  1  1  77  .  66  977  .  060 

834.904 

728.909646.838 

581.419 

53 

6486.38  3042.39  1987.35  1475.71  1173.65  974.294 

832.885 

727.  370  '645.  627 

580.441 

54 

6366.263015.71  1915.93  1469.  41  '1169.  66  971.544 

830.876 

725  838644.420 

579.466 

55 

6250.51  2989.48  1964.64  1463.16  1165.70  968.810 

828.876 

724  312643.218 

578.494 

56 

6138.90  2963.  7  1  1953.  48  1456.96  1161.76  966.091 

826.886 

722.79*642.021 

577.526 

57 

61  >31  .  20  2938  39  1  942  .  4  4  1450  .  8  1  1  1  57  .  85  903  .  387 

824.905 

721.280640.828 

576.561 

58  !  5927.  2-2  2013.49  1931  .53  1444.72  1153.97  960.698 

822.934 

719.774639.639 

575.599 

59  58-.'G  .  76  2889  .  01  |  1920  .  75,  1438  .68  1150.  1  1  958.  025 

820.973 

718.273638.455 

574.641 

CIVIL  ENGINEER'S  FIELD-BOOK. 


TABLE  XII.—  RADII  -Continued. 


M 

10° 

Curve. 

11° 

Curve. 

Curve 

13° 

Curve. 

14° 

Curve. 

15° 

Curve. 

Curve. 

17° 
Curve. 

18° 

Curve. 

19° 

Curve. 

o~ 

573.686 

521.671 

478.339441.684 

410.275 

383  065  1359.  265  338.  273 

319.623 

302.943 

1 

572.734 

520.885 

477.678441.120 

409  790  382  .  64  \»  358  .  893  337  .  945 

319.330 

302.680 

2 

571.784 

520.100 

477.018440.559 

409.  306  382.  220  !  358.  523 

337.616 

319.037 

302.417 

3 

570.839 

219.318 

476  361 

439.999 

408.823 

381.  799  1358.153  337  289 

318.745 

302.155 

4 

569.896 

518.539 

475.705 

439.440 

408.341 

381.380357.784336.962 

318.453 

301.893 

5 

568.957 

517.761 

475.052 

438.882 

407.860 

380.961 

357.415 

336.636 

318.162 

301.632 

6 

568.020 

516.986 

474.400 

438.326 

407.380 

380.543357.048336.310 

317.871 

301.371 

7 

567.087 

516.214 

473.750 

437.772 

406.902 

380.125356.681 

335.985 

317.581 

301.111 

8 

566.156 

515.443 

473.102 

437.219 

406.424 

379  .  709  356  .  31  5  335  .  660  317.  292 

300.851 

9 

565.229 

514.675 

472.455 

436.667 

405.948 

379.294355.950 

335.337 

317.003 

300.592 

10 

564.305 

513.909 

471.810 

436.117 

405.473 

378.880355.585 

335.013 

316.715 

300.333 

11 

563.384 

513.146 

471.167 

435  568 

404.998 

378.466355.222 

334.  691  1316.  427 

300.074 

12 
13 

562.466 
561.551 

512.385 
511.626 

470.526 

469  887 

435.020 
434.474 

404.526 
404.055 

378  .  054  ;  354  .  859  334  .  369  1  3  1  6  .  1  39 
377.642  351  496  334.048  315.853 

299.816 
299.559 

14 

560.638 

510.869 

469.249 

433  929 

403.583 

377.231 

354.135 

333.727 

315.566 

299.302 

15 

559.729 

510.115 

4G8.613 

433.385 

403.114 

376.821 

353.774333.407 

315.281 

299.045 

16 

558.823 

509  363 

467.978 

432.844 

402.645 

376.412 

8:8.414 

333.088 

314.993 

298.789 

17 

557.920 

508.613 

467.346 

432.300 

402.178 

376.004 

353.  054  1332.  769 

314.711 

298.533 

18 

557.019 

507.865 

466  715 

431.764 

401.712 

375.597 

352.696 

332.451  314  426 

298  278 

19 

556.122 

507.120 

466.086 

431.226 

401.246 

375.191  352.338  332.133  314.143 

298.023 

20 

555.227 

506.376 

465.459 

430.690 

400.782 

374.786351.981 

331.816313.860 

297.768 

21 

554.336 

505.635 

464.833:430.154 

400.319  374.381  351,  625  331  .  500  313.577 

297.514 

22 

553.447 

504.896464.209429.620 

399  857 

373.977351.269 

331.184313.295 

297.260 

23 

552.561 

504.159463.586429.088 

399.396 

373  575350.914 

330.869313.013 

297.007 

24 

551.678 

503.425 

462.966428.557 

398  .  937  373  .  1  73  350  .  560  330  .  555  31  2  .  732 

296.755 

25 

550.800 

502  692 

462.347428.026 

398.4781372.772 

350.207 

330.241 

312.452 

296.502 

26 

549.920 

501.962461.729427.498 

398.020372.372 

349.854 

329.928 

312.172 

296.250 

27 

549.046 

501.233461.114426.971 

397.564 

371.972 

349.  502:329.  615  311.  892 

295.999 

28 

548.174 

500.507 

460.500426.445 

397.108 

371.574 

349.150329.303 

311.613 

295.748 

29 

547.305 

499.783 

459.887425.920 

396.653 

371.176 

348.800 

328.991 

311.335 

295.497 

30 

546.438 

499.061 

459.276 

425  396 

396.200 

370.780 

348.450 

328.689 

311  056 

295.247 

31 

545.575 

498.342 

458.667424.874 

395.747 

370.384 

348.101 

328.370 

310.779 

294  998 

32 

544.714 

497.624 

458.060424.354 

395.296 

369.989 

347.752328.061 

310.502 

294.748 

33 

543.856 

496  908 

457.454423.834 

394.841 

369.595 

347.405327.751 

310.225 

294.500 

34 

543  001 

496.195 

456.850423.316 

394.396 

369.202 

347.057 

327.443309.949 

294  251 

35 

542.148 

495.483 

4.r;6.247422.799 

393.948 

368.809 

346.  71  li  327.  135 

309  614 

294.003 

36 

541  298 

494.774 

455.646422  283 

393.501 

368.418 

346  365 

326.828 

309.399 

293  756 

37 

540.451 

494.066 

455.047421.769 

393.054 

368  027 

346.021 

326.521 

309.124 

293.509 

38 

539.606 

493.361 

454.449421.256 

392.609 

367.637 

845,676 

326.215 

308.850 

293.262 

39 

538.764 

492.657 

453.853420.743392.165 

367.248 

345.333 

325.909 

308.577 

293.015 

40 

537.924 

49!  .956 

453.259420.233:391.722 

366.859 

344.990325.604 

303  303 

292.770 

41 

537.088 

491.257 

452.664  419.723 

391.280 

366.472:344.647 

325  530308.031 

292.524 

43 

536.253 

490.559 

452.073:419.215 

390.838 

366.0851344.306 

324.996:307.759 

292.279 

43 
44 

535.422 
534.593 

489.864 
489.171 

451.482418.708 
450.894  418  203 

390.398 
389.959 

365  .  691  343  .  965  324  .  692  307  .  487 
365  .315343.  625  324  .  390  307  .216 

292.034 
291.790 

45 

533.767 

488.479 

450.307417.698 

389.521 

364.931 

343.285 

324.088306.945 

291.546 

46 

532.943 

487.790 

449.722417.195 

389.084 

364  547 

342.947 

323.786306.675 

291.303 

47 

532.120 

487.103 

449.138416.693 

388.647 

364.165 

342.609 

323.485306.405 

291.060 

48 

531.303 

486.417 

448.556416.192 

388.212363.783 

342.271 

323.184  306.136 

290.818 

49 

530.487 

485.733 

447.975415.692 

387.778363.402 

341.934 

322.885305.868 

290.575 

50 

529.673 

485.051 

447.395j415.194 

387.34.' 

3G3.022 

341.598 

322.585 

305  599 

290.334 

51 

528.862 

484.372 

446  818414.697 

386.912 

362.643341.263 

322.237  305.332 

290.092 

5*3 

528.053 

483.694 

446.241 

414.201 

386.481 

362.264 

340.928 

821.989:305.064 

289.851 

53 

527.247 

483.018 

445.666 

413.706386.050 

361.887 

340  594 

321.  691  1304  797 

289.611 

54 

526.443 

482.344 

445.093 

413.212385  621 

361.510 

340.  2GO 

321.394304.531 

289.371 

55 

525.642 

481.671 

444.521 

412.720385.193 

361.134 

339.928 

321.097:304.265 

289.131 

56 

524.843 

481.001 

443.951 

412.229384.765 

360.758339.595 

320.801  304.000 

288.892 

57 

524.046 

480.333 

443.382 

411.739384.339 

360.  384!  339  265 

320.506303.735 

288.653 

58 

523.252 

479.666 

442  814 

411.250383.913 

360.010338.933 

320.211  303.470 

288.414 

59 

522.461 

479.001 

442.248 

410.762383.488 

359.637338.603 

319.916  303.206 

288.176 

CURVE    FORMULAE    AND    PROBLEMS. 


39 


TABLE   XIII. 
GRADES. 


Grade 
per 
100  ft. 

Rise 
per 
Mile. 

Grade 
per 
100  ft. 

Rise 

per 
Mile. 

Grade 
per 
100  ft. 

Rise 
Mite. 

Grade 
per 
100  ft. 

Rise 
per 
Mile. 

.05 

2.640 

.59 

31.152 

1.13 

59  664 

1.67 

88.176 

.06 

8.168 

.60 

31.680 

1.14 

60.192 

1.68 

88.704 

.07 

3.696 

.61 

32.208 

1.15 

60.720 

1.69 

89.232 

.08 

4.224 

.62 

32.736 

1.16 

61.248 

1.70 

89.760 

.09 

4.752 

.63 

33.264 

17 

61.776 

1.71 

90.288 

.10 

5.280  i 

.64 

33  792 

.18 

62.304 

1.72 

90.816 

.11 

5.808 

.65 

34.320 

.19 

62.832 

1.73 

91.344 

.12 

6.336 

.66 

34.848 

.20 

63.360 

1.74 

91.872 

,w 

6.864 

.67 

35  376 

.21 

63  888 

1.75 

92.400 

.14 

7.392 

.68 

35.904 

.22 

64.416 

1.76 

92.928 

.15 

7.920  ! 

.69 

36.432 

.23 

64.944 

1.77 

93.456 

.16 

8.448  | 

.70 

36.960 

24 

65.472 

1  78 

93.984 

.17 

8.976  j 

.71 

37.488 

.25 

6G.OOO 

1.79 

94.512 

.18 

9.504 

.72 

38.016 

.26 

66.528 

1.80 

95.040 

.19 

10.032 

.73 

38.544 

.27 

67.056 

1.81 

95.568 

.20 

10  560 

74 

39  072 

.28 

67.584 

1.82 

96  096 

.21 

11.088 

.75 

39.600 

.29 

68.112 

1.83 

96  624 

.22 

11.616 

.70 

40.128 

.30 

68.640 

1.84 

97.152 

!23 

12.144 

.77 

40.656 

31 

69  168 

1  85 

97.680 

.24 

12.672 

.78 

41.184 

32 

69.696 

1.86 

98.208 

.25 

13  200 

.79 

41.712 

33 

70.224 

1.87 

98.736 

.26 

13.728 

.80 

42.240 

.31 

70.752 

1.88 

99.264 

.27 

14  256 

.81 

42.768 

35 

71.280 

1.89 

99.792 

.28 

14.784 

.8-3 

43.296 

.36 

71.803 

1.90 

100.320 

.29 

15.312 

.83 

43.824 

.37 

72.333 

1.91 

100.848 

.30 

15.840  ! 

.81 

44.352 

38 

72.864 

1.92 

101.376 

.31 

16.368  1 

.85 

44.880 

.39 

73.392 

1.93 

101.904 

.32 

16  896 

.86 

45.408 

.40 

73.92) 

1.94 

102.432 

.33 

17.421 

.87 

45.936 

.41 

74.448 

1.95 

102.960 

.34 

17.952 

.88 

46.464 

.42 

74.976 

1.96 

103.488 

.35 

18.480 

.89 

46.992 

.43 

75.504 

1.97 

104.016 

.36 

19.008 

.90 

47.520  1 

.44 

76.032 

1  98 

104.514 

.37 

19.536 

.91 

48.048 

.45 

76.560 

1.99 

105.072 

.38 

20.064 

.92 

48.576 

.46 

77.088 

2  oa 

105.600 

.39 

20.592 

.93 

49.104 

.47 

77.616 

2.10 

110.880 

.40 

21.120 

.94 

49.632 

.48 

78.144 

2.20 

116.160 

.41 

21.648 

.95 

50.160 

.49 

78.672 

2.30 

121.440 

.42 

22  176 

.96 

50.688 

.50 

79  200 

2.40 

126.720 

.43 

22.704 

.97 

51.216 

.51 

79.728 

2.50 

132  000 

.44 

23.232 

.98 

51.744 

.52 

80.256 

2.60 

137.280 

.45 

23.760 

.99 

52.272 

.53 

80  784 

2.70 

142.560 

.46 

24.288 

.00 

52.800 

.54 

81.312 

2.80 

147.840 

.47 

24.816 

.01 

53.328 

.55 

81.840 

2.90 

153  120 

.48 

25.344 

.02 

53.856 

.56 

82.3(38 

3.00 

158.400 

.49 

25  872 

.03 

54.384 

.57 

82.896 

3.10 

163.6SO 

.50 

26.400 

.04 

54.912 

.58 

83.424 

3.20 

168.960 

.51 

26.928 

.05 

55.440 

59 

83.952 

3.30 

174.240 

.52 

27.456 

.06 

55.968 

.60 

84.480 

3.40 

179.520 

.53 

27.984 

.07 

56.496 

.61 

85.008 

3.50 

184.800 

.54 

28.512 

.08 

57.024 

.62 

85.536 

3.60 

190.0SO 

.55 

29.040 

.09 

57.552 

63 

86  064 

3.70 

195.360 

.56 

29.568 

.10 

58.080 

.64 

86  592 

3.80 

200.640 

.57 

30.096 

1  11 

58.608 

.65 

87.120 

3.90 

205.920 

.58 

30.624 

1.12 

59.136 

.66 

87.648 

4.00 

211.200 

40  CIVIL  ENGINEER'S  FIELD-BOOK. 

EXPLANATION   OF  TABLE  XIV. 


MINUTES  EXPRESSED  IN  DECIMALS. 

In  the  third  column,  under  the  heading  of  "  1°  Curve,  Arc," 
will  be  found  the  minutes  given  in  the  first  column  under 
**0°,"  expressed  in  decimals  of  a  degree,  by  simply  putting 
the  decimal  point  two  places  to  the  left.  For  example: 

6'  =  .10    and    54'  =  .90 

Proof:  6'  +  54'  =  1°,  and  .10  +  .90  =  1.00  -  1°. 
In  like  manner  all  arcs  to  a  one  degree  curve  are  expressions 
of  their  intersections  decimally. 


TO  FIND  THE  TANGENT. 

Given  the  /,  FBC  —  42°  38',  and  the  degree  of  curve  AC  = 
5°,  to  find  the  T,  BA  and  BC. 

Find  the  number  corresponding  to  the  number  of  whole 
degrees  in  the  given  /,  at  the  top  of  the  left  or  right  hand 
column,  after  which  descend  the  column  until  the  correspond- 
ing minutes  in  the  given  I  is  reached,  then  on  the  same  line 
to  the  right  or  left  under  the  heading  "  5°  Curve,  Tan.,"  will 
be  found  the  required  T  =  447.301 


Problem  38. 

Given  the  /,  FBC  =  24°  50',  and  the  degree  of  curve  AC  ~ 
4°  12',  to  find  the  l\  BA  and  BC. 
Select  the  tan.  to  the  given  /  from  the  curve  column  corre- 


CURVE   FORMULAE   AND    PROBLEMS.  41 

spending  to  the  number  of  whole  degrees  in  the  given  curve. 
Multiply  this  by  the  number  of  whole  degrees  in  the  given 
curve,  and  divide  the  product  by  the  given  curve  expressed 
decimally. 

Example. 

1=  24°  50'.     4°  Curve,  Tan.  =  315.435 
Number  of  whole  degrees  =  4 


Given  curve  =  4°  12'  =  4.20 


1261.740 
1260 


^Result,  T  — 


1740 
1680 

600 


TO   FIND  THE  ARC. 

Given  the  /,  FBO  =  56°  40',  and  the  degree  of  curve  AC  = 
9°,  to  find  the  A,  AfabcC. 

Find  the  number  corresponding  to  the  number  of  whole  de- 
grees in  the  given  /at  the  top  of  the  left  or  right  hand  column, 
after  which  descend  the  column  until  the  corresponding 
minutes  in  the  given  1  is  reached,  then  on  the  same  line  to  the 
right  or  left  under  the  heading  "  9°  Curve,  Arc"  will  be  found 
the  required  A  =  629.630 


Problem  39. 

Given  the  /,  FBG  =  96°  18',  and  the  degree  of  curve  AC  = 
2°  15',  to  find  the  A,  AfabcC. 

To  the  number  of  whole  degrees  in  the  given  J  affix  the 
fractional  part  expressed  decimally;  also  to  the  number  of 
whole  degrees  in  the  given  curve  affix  the  fractional  part  ex- 
pressed decimally,  and  divide  the  former  by  the  latter.  The 
quotient  will  be  the  required  A. 

Example. 
Given  curve  =~]  J  =  96°  18'  —  ("Quotient,  A  = 


en  curve  =~"| 

3 15'  =  2.25J 


2°  15'  =  2.25  J        96.30        [J2.SQ  =  4280  ft. 
900 

630 
450 

1800 


42  CIVIL   ENGINEERS   FIELD-BOOK. 


TO  FIND   THE   SUB-DEFLECTION. 

Given  the  c,  Af  =  90  ft.,  and  the  degree  of  curve  AC  =  5°, 
to  find  the  d,  BAf. 

Take  half  the  given  c  —  45,  and  find  the  number  correspond- 
ing to  it  in  the  column  headed  "  5°  Curve,  Arc."  Then  in  the 
upper  right  or  left  hand  corner  of  the  table  will  be  found  the 
degrees,  beneath  which  on  a  line  with  the  corresponding  num- 
ber will  be  found  the  minutes  of  the  required  d. 

Thus  the  d,  BAf  =  2°  15'. 


Problem  4O. 

Given  the  C,  Af  =  60  ft.,  and  the  degree  of  curve  AC  =  4° 
30',  to  find  the  d,  BAf. 

Multiply  the  degree  of  the  given  curve  expressed  decimally 
by  half  the  given  c,  and  find  the  number  corresponding  to  it 
in  the  column  headed  "1°  Curve,  Arc."  Then  in  the  top 
right  or  left  hand  corner  of  the  table  will  be  found  the  degrees 
beneath  which  on  a  line  with  the  corresponding  number  will 
be  found  the  minutes  of  the  required  d. 

Example. 

Given  curve  —  4°  30'  =      4.5 

|c  = 30 

Product  135.0  =  l°21'  =  d. 


TO  FIND  THE  INTERSECTION. 

GIVEN  THE   CURVE  AND  ARC. 

Given  the  degree  of  the  curve  AC  —  10°,  and  the  A,  AfabcG 
=  485.000,  to  find  the  /,  FBG. 

Find  the  number  corresponding  to  the  given  A  in  the 
column  headed  "10°  Curve,  Arc."  Then  in  the  upper  right 
or  left  hand  corner  of  the  table  will  be  found  the  degrees,  be- 
neath which  on  a  line  with  the  corresponding  number  will  be 
found  the  minutes  of  the  required  /  =  48°  30', 


CURVE    FORMULAE    AK  I)    PROBLEMS.  43 

GIVEN  THE  CURVE  AND   TANGENT. 

Given  the  degree  of  the  curve  AC  =  7°,  and  the  T,  BA  and 
BC  —  171.601,  to  find  the  7,  FBG. 

Find  the  number  corresponding  to  the  given  Tin  the  column 
headed  "7°  Curve,  Tan."  Then  in  the  upper  right  or  left 
hand  corner  of  the  table  will  be  found  the  degrees,  beneath 
which  on  a  line  witL  the  corresponding  number  will  be  found 
the  minutes  of  the  required  I  =  23°  40'. 


TO  FIND   THE  DEGREE  OF  CURVE. 

GtVEN  THE  INTERSECTION  AND   TANGENT. 

Given  the  /,  FBC=  37°  33',  and  the  T,  BA  and  BG=  195.02, 
to  find  the  degree  of  the  curve  AC. 

Find  .the  number  corresponding  to  the  number  of  whole 
degrees  in  the  given  /  at  the  top  of  the  left  or  right  hand 
column,  after  which  descend  the  column  until  the  correspond- 
ing minutes  in  the  given  /  is  reached;  then  on  the  same -line 
to  the  right  or  left  seek  a  number  under  the  heading  ''Tan." 
corresponding  to  the  given  T\  at  the  top  of  the  column  in  which 
the  corresponding  number  is  found  will  be  found  the  required 
degree  of  curve  =  10°. 

GIVEN  THE  INTERSECTION  AND   ARC. 

Given  the  /,  FBC  —  42°  18',  and  the  A,  AfabcC=  528.750, 
to  find  the  degree  of  the  curve  AC. 

Find  the  number  corresponding  to  the  number  of  whole 
degrees  in  the  given  /at  the  top  of  the  left  or  right  hand  col- 
umn, after  which  descend  the  column  until  the  corresponding 
minutes  in  the  given  /is  reached;  then  on  the  same  line  to  the 
right  or  left  seek  a  number  under  the  heading  "  Arc"  corre- 
sponding to  the  given  A ;  at  the  top  of  the  column  in  which 
the  corresponding  number  is  found  will  be  found  the  required 
degree  of  curve  =  8°. 


TABLE  XIV. 

ACTUAL   TANGENTS,    AND   ARCS   EXPRESSED    IN   CHORDS   OF 

100  FEET  FOR  EVERY  MINUTE  OF  INTERSECTION, 

FROM  0°  TO  90°,  FROM  A  1°  CURVE  TO 

A  10°  CURVE,  INCLUSIVE. 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


0° 
M. 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

1 

.830799 

1.66667 

.415415 

.833333 

.276962 

.555556 

.207740 

.416667 

.166211 

.333333 

2 

1.66160 

3.33333 

.  830830 

1.6666? 

.553923 

1.11111 

.415480 

.833333 

.332421 

.600007 

3 

2.49240 

5.00000 

1.24624 

2.50000 

.830885 

1.66667  .623220 

1.25000 

.498032 

1.00000 

4 

3.32320 

6.66667 

1.66166 

3.33333 

1.10785 

2.22222  .830960 

1.66607 

.664842 

1.33:J33 

5 

4.15400 

8.33333 

2.07707 

4.16667 

1.38481 

2.777781.0:3870 

2.08333 

.83105:3 

1  .  60007 

6 

4.98480 

10.0000 

2.49249 

5.00000 

1.66177 

3  333331.24644 

2.50000 

.  997264 

2.00000 

7 

5.81559 

11.6667 

2.90790 

5.83:333 

1.93873 

3.888891.45418 

2.91667 

1.16347 

2.33:333 

8 

6.64639 

13.3333 

3.32332 

6.66667 

2.21569 

4.44444  1.60192 

3.33333 

1.32968 

2.60007 

9 

7.47719 

15.000(3 

3.73873 

7.50000 

2.49265 

5.00000  1.80900 

3.75000 

1.49590 

3.00000 

10  18.30799 

16.6667 

4.15415 

8.33333 

2.7G962 

5.55556  2  07740 

4.16667 

1.66211 

3.33333 

11  9.16744 

18..  3333 

4.58389 

9.16667 

3.05613 

6.11111 

2.29230 

4.58333 

1.83405 

3.66667 

13 

10.0269 

20.0000 

5.01363 

10.0000 

3.34264 

6.66667 

2.50721 

5.00000 

2.00599 

4.00000 

13 

10.8577 

21.6667 

5.42904 

10.&333 

3.61960 

7.222222.71495 

5.41667 

2.17220 

4.33:333 

14 

11.6885 

23.3333 

5.84446 

11.6667 

3.89656 

7.777782.92269 

5.83333 

2.3:3841 

4.66607 

15 

12  5193 

25.0000 

6.25987 

12.5000 

4.17352 

8.333333.13043 

6.25000 

2.50462 

5.00000 

16 

is.asoi 

26.6667 

6.67529 

13.33J33 

4.45049 

8.  88889  '3.  3381  7 

6.66067 

2.67083 

5.333:33 

17 

14  '.1809 

28.3:333 

7.09070 

14.1667 

4  72745 

9.44444  3.54591 

7.083:33 

2.83704 

5  C0667 

18 

15.0117 

30.0000 

7.50612 

15.0000 

5.00441 

10.00003  75365 

7.50000 

3.00325 

6.00000 

19 

15.8425 

31.6667 

7.92153 

15.8333 

5.28137 

10.55563.96139 

7.91667 

3.16946 

6.33333 

2O 

16.6733 

a3.  3333 

8.33695 

16.6667 

5.55833 

11.11114.16913 

8.33a33 

3.33567 

6.66667 

21 

17.5041 

35.0000 

8.75236 

17.5000 

5.83529 

11.6667 

4.37687 

8.75000 

3.50189 

7.00000 

22 

18.a349 

36.6667 

9.16778 

18.3333 

6.11226 

12.22224.58461 

9.16667 

3.66810 

7.33333 

23 

19.1657 

38.333:3 

9.58319 

19.1667 

6.38922 

12.77784.79235 

9.58333 

3.83431 

7.66067 

24 

19.9965 

40.0000 

9.99861 

20.0000 

6.66618 

13.33335.00009 

10.0000 

4.00052 

8.00000 

25 

20.8273 

41.6667 

10.4140 

20.8333 

6.94314 

13.88895.20783 

10.4167 

4.16673 

8.33333 

26 

21.6581 

43.33-13 

10.8294 

21.6667 

7.22010 

14.44445.41557 

10.8333 

4.33294 

8.66607 

27 

22.4889 

45.0000 

11.2449 

22.5000 

7.49706 

15.00005.62331 

11.2500 

4.49915 

9.00000 

28 

23.3197 

46.6667 

11.6603 

23.a333 

7.77403 

15.5556 

5.83105 

11.6667 

4  66536 

9.33333 

29 

24.1505 

48.3333 

12.0757 

24.1667 

8.05099 

16.1111 

6.0:3879 

12.0833 

4.83157 

9.66667 

30 

24.9813 

50.0000 

12.4911 

25.0000 

8.32795 

16.6667 

6.24653 

12.5000 

4.99778 

10.0000 

31 

25.8121 

51.6667 

12.9065 

25.8333 

8.60491 

17.2222 

6.45427 

12.9167 

5.16399 

10.3333 

33 

26  6429 

53.3333 

13.3219 

26.6667 

8.88187 

17.7778  6  66201 

13.3333 

5.3:3020 

10.6667 

33 

27.5023 

55.0000 

13.7517 

27.5HOO 

9.16S38 

18.33-336.87691 

13.7500 

5.50214 

11.0000 

34 

28.3618 

56.6667 

14.1814 

28.3333 

J.  45  490 

18.88897.09182 

14.1667 

5.67409 

11.3333 

35 

29.1926 

58.3333 

14.5968 

29.1667 

9.73186 

19.4444 

7.29956 

14  5833 

5.84030 

11.6667 

36 

30.0234 

60.0000 

15.0122 

30.0000 

10.0088 

20.0000 

7.50730 

15.0000 

6.00651 

12  0000 

37 

30.8542 

61.6667 

15.4276 

30.8333 

10.2858 

20.55567.71504 

15.4167 

6.17272 

12.3333 

38 
39 

31.6850 
32.5158 

63.3333 
65.0000 

15.8431 
16.2585 

31.6667 
32.5000 

10  5627 
10.8397 

21.1111  7.92278 
21.66678.13052 

15.8333 

16.2500 

6  33893 
6.50514 

12.6667 
13.0000 

4O 

33.3466 

66.6667 

16.6739 

33.3333 

11.1167 

22.22228.33826 

16.6667 

6.67135 

13.3:333 

41 

34.1774 

68.3333 

17.0893 

34.1667 

11.3936 

22.7778 

8.54600 

17.0833 

6.83756 

13.6667 

43 

35.0082 

70.0000 

17.5047 

a5.oooo 

11.6706 

23.33338.75374 

17.5000 

7.00377 

14.0000 

43 

35.8390 

71.6667 

17.9201 

35.8333 

11  9476 

23.88898.96148 

17.9167 

7.16998 

14.3333 

44 

36.6698 

73  33:33 

18.3356 

36.6667 

12.2245 

24.44449.16922 

18.3333 

7.33619 

14.6667 

45 

37.5006 

75.0000 

18.7510 

37.5000 

12.5015 

25.0000,9.37096 

18.7500 

7.50240 

15.0000 

46 

38.3314 

76.6667 

19.1664 

38  3333 

12.7784 

25.55569.58470 

19.1667 

7.66861 

15.3333 

47  39.1622 

78.3333 

19.5818 

39.1667 

13.0554 

26.1111  9.79244 

19.5833 

7.83482 

15.6607 

48  139.9930 

80.0000 

19.9972 

40.0000 

13  3324 

26.6667110.0002 

20.0000 

8.00103 

16.0000 

49  40.8238 

81.6667 

20  4126 

40.8333 

13  6093 

27.222210.2079 

20.4167 

8.16725 

16.3333 

5O 

41.6546 

83.3333 

20.8280 

41.6667 

13.8863 

27.777810.4157 

20.8333 

8.33346 

16.6667 

51 

42  4&54 

85.0000 

21.2435 

42.5000 

14.1632 

28.3333 

10.6234 

21.2500 

8.49967 

17.0000 

53  43.3162 

86.6667 

21.6589 

43.3333 

14.4402 

28.  8889!  10.  8311 

21.6667 

8.66588 

17.3333 

53  144.1470 

88.3:333 

22.0743 

44  1667 

14.717229  4444)  11.  0389 

22.0833 

8.83209 

17  6667 

54  !44  9778 

90.0000 

22.4897 

45  0000 

14.  9941  !  30.  0000  11.  2466 

22.5000 

8.99830 

18.0000 

55  45.837291.6667 

22.9194 

45.8333 

15.280630.555611.4615 

22.9167 

9.17024 

18.3:333 

56  46.696693.3338 

23.3492 

46.6667 

15.5672 

31.1111 

11  6764 

23.3333 

9.34218 

18.6007 

57  :  47.  5274  !  95.  0000 

23.7646 

47.5000 

15.8441 

31  6667 

11.  8842  123.7500 

9.50839 

19.0000 

58  48.3582,96.6667 

24.180048.3333 

16.  1211  132.  2222  12.0919  24.1667 

9.07400 

19.33:33 

59  49.1890,98.3333 

24.5954 

49.1667  16.  3980,32.77781  12.  2996 

24.58:33 

9.84081119.6667 

46 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

O« 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

.138529 

.277778 

.118758 

.238095 

.103933 

208333 

.092404 

.185185 

.083185 

.166667 

1 

.27705? 

.555556 

.237516 

.476190 

.207866 

.416667 

.184808 

.370370 

.166370 

.333333 

2 

.415580 

.833333 

.356274 

.714285 

.311799 

.625000 

.277212 

.555556 

.249555 

.500000 

3 

.554115 

1.11111 

.475032 

.952380 

.415732 

.833333 

369617 

.740741 

.332740 

.666667 

4 

.692643 

1.38889 

.593789 

1.19048 

.519666 

.04167 

.462021 

.925926 

.415925 

.833333 

5 

.831172 

1.66667 

.712547 

1  .42856 

.623599 

.25000 

.554425 

1.11111 

.499110 

1.00000 

6 

,969701 

1.94444 

.831305 

1.66667 

.727532 

.45833 

.646829 

1.29630 

.582295 

1.16667 

7 

1.10823 

2.22222 

.950063 

1.90476 

.831465 

.66667 

.739233 

1.48148 

.665480 

1.33333 

8 

1.24676 

2.500001.06882 

2.14286 

.935398 

.87500 

.831637 

1.66667 

.748665 

1.50000 

9 

1.38529 

2.77778 

1.18758 

2.38095 

1.03933 

2.08333 

.924041 

1.85185 

.831851 

1.66667 

10 

1.52859 

3.05556 

1.31043 

2.61905 

1.14685 

2.29167 

1.01963 

2.03704 

.917904 

1.83333 

11 

1.67190 

3.  33333  1  1.43329 

2.85714 

1.2543? 

2.50000 

1.11522 

2.22222 

1.00396 

2.00000 

12 

1.81043 

3.61111 

1.55204 

3.09524 

1.35830 

2.70833 

1.20763 

2.40741 

1.08714 

2.16667 

13 

1.94895 

3.88889 

1.67080 

3.33333 

1.46223 

2.91667 

1.30003 

2.59259 

1.17033 

2.33333 

14 

2.08748 

4.16667 

1.78956 

3.  57143 

1.56616 

3.12500 

1.39243 

2.77778 

1.25351 

2.50000 

15 

2.22601 

4.44444 

1.90832 

3.80952 

1.67010 

3.33333 

1.48484 

2.96296 

1.33670 

2.6666? 

16 

2.36454 

4.72222 

2.02707 

4.04762 

1.77403 

3.54167 

1.57724 

3.14815 

1.41988 

2.83333 

17 

2.50307 

5.00000 

2.14583 

4.28556 

1  .87796 

3.75000 

1.66905 

3.33333 

1.50307 

3.00000 

18 

2.64160 

5.27778 

2.26459 

4.52381 

1.981903.95833 

1.76205 

3.51&52 

1  .58625 

3.16667 

19 

2.78013 

S.  55556 

2.38335 

4.70190 

2.08583 

4.16667 

1.85446 

3.70370 

1.66944 

3.33333 

20 

2.91866 

5.83333 

2.50211 

5.00000 

2.18976 

4.37500 

1.94686 

3.88889 

1.75262 

3.50000 

21 

305718 

6.11111 

2.62086 

5.23810 

2  293704.58333 

2.03920 

4.07407 

1.83581 

3.66667 

22 

3.19571 

6.38889 

2.73962 

5.47619 

2.39763 

4.79167 

g.  13167 

4.25926 

1.91899 

3.83333 

23 

3.33424 

6.6666? 

2.85838 

5.71429 

2.50156 

5.00000 

2.2240? 

4.44444 

2.00218 

4.00000 

24 

3.47277 

6.94444 

2.97714 

5.95238 

2.60550|5  20833 

2.31648 

4.62963 

2.08536 

4.1666? 

25 

3.61130 

7.22222 

3.09590 

6.19048 

2.709435.416(7 

2.40888 

4.81481 

2.16855 

4.33333 

26 

3.74983 

7.50000 

3.21465 

6.42856 

2.81336  5.62500 

2.50128 

5.00000 

2.25173 

4.50000 

27 

3.88836 

7.77778 

3.33341 

6.6666? 

2.917295.83333 

2.59369 

5.18518 

2.33492 

4.66667 

28 

4.02688 

8.05556 

3.45217 

6.90476 

3.021236.04167 

2.68609 

5.37037 

2.41810 

4.83333 

29 

4.16541 

8.33333 

3.57093 

7.14286 

3.  12516 

6.25000 

2.77850 

5.55556 

2.50129 

5.00000 

3O 

4.30394 

8.61111 

3.68969 

7.38095 

3.22909 

6.45833 

2.87090 

5.74074 

2.58447 

5.16667 

31 

4.44247 

8.88889 

3.80844 

7.61905 

3.33303 

6.66667 

2.96331 

5.92593 

2.66766 

5.33333 

32 

4.58578 

9.16667 

3.93130 

7.85714 

3.44054 

6.87500 

3.05890 

6.11111 

2.75371 

5.50000 

33 

4.72908 

9.44444 

4.05415 

8.09524 

3,54806 

7.08333 

3.15449 

6.29630 

2.83977 

5.6666? 

34 

4.86761 

9.72222 

4.17291 

8.33333 

3.65199 

7.29167 

3.24689 

6.48148 

2.92295 

5.83333 

35 

5.00614 

10.0000 

4.29166 

8.57143 

3.75593 

7.50000 

3.33929 

6.66667 

3.00614 

6.00000 

36 

5.14467 

10.2778 

4.41042 

8.80952 

3.85986 

7.70833 

3.43170 

6.&5185 

3.08932 

6.16667 

37 

5.28320 

10.5556 

4.52918 

9.04762 

3.96379 

7.91667 

3.52410 

7.03704 

3.17251 

6.33333 

38 

5.42172 

10.8333 

4.64794 

9.28556 

4.0677'3 

8.12500 

3.61651 

7.22222 

3.25569 

6.50000 

39 

5.56025 

11.1111 

4.76670 

9.52381 

4.17166 

8.33333 

3.70891 

7.40741 

3.33888 

6.66667 

4O 

5.69878 

11.3889 

4.88545 

9.76190 

4.27559 

8.54167 

3.80132 

7.59259 

3.42206 

6.83333 

41 

5.83731 

11.6667 

5.00421 

10.0000 

4.37953 

8.75000 

3.89372 

7.77778 

3.50525 

7.00000 

42 

5.97584 

11.9444 

5.12297 

10.2381 

4.48346 

8.95833 

3.98612 

7.96296 

3.58843 

7.16667 

43 

6.11437 

12.2222 

5.24173 

10.4762 

4.58739 

9.1666? 

4.07853 

8.14815 

3.67162 

7.33333 

44 

6.25290 

12.5000 

5.36049 

10.7143 

4.69133 

9.37500 

4.17093 

8.3&S33 

3.75480 

7.50000 

45 

6.39143 

12.7778 

5.47924 

10.9524 

4.79526 

9.58333 

4.26334 

8.51852 

3.83799 

7.6666? 

46 

6.52995 

13.05565.59800 

11.1905 

4.8991919.79167 

4.35574 

8  70370 

3.92117 

7.83333 

47 

6.66848 

13.  3333  !  5.  716  ,"6 

11.4286 

5.00312 

10.0000 

4.44814 

8.88889 

4.00436 

8.00000 

48 

6.80701 

13.6111  5.83552 

11.6667 

5.10706 

10.2083 

4.54055 

9.07407 

4.08754 

8.16667 

49 

6.94554 

13.8889 

5.95428 

11.9048 

5.21099 

10.4167 

4.63295 

9.25926 

4.17073 

8.33333 

5O 

7.08407 

14.1667 

6.07303 

12.1429 

5.31492 

10.6250 

4.72536 

9.44444 

4.25391 

8.50000 

51 

7.22260 

14.44446.19179 

12.3810 

5.41886 

10.8333 

4.81776 

9.62963 

4.33710 

8.60667 

52 

7.36113 

14.72226.31055 

12.6191 

5.52279 

11.0417 

4.91017 

9.81481 

4.42028 

8.83333 

53 

7.49965 

15.00006.42931 

12.8571 

5.62672 

11.2500 

5.00257 

10.0000 

4.5034? 

9.00000 

54 

7.64296 

15.27786.55216 

13.0952 

5.73424 

11.4583 

5.09816 

10.1852 

4.58952 

9.1066? 

55 

7.78627 

15.55566.67501 

13.3333 

5.S417'611.666? 

5.19375 

10.3704 

4.  67557 

9.33333 

56 

7.92479 

15.  8333  '6.  79377 

13.5714 

5.9456911.8750 

5.28615 

10.5556 

4.75876 

9.50000 

57 

8.  06&321  16.  1111:6.  91253 

13.8095 

6.04962  12.0833 

5.37856 

10.7407 

4.84194 

9.66067 

58 

8.20185  16.3889:7.03129 

14.0476 

6.15356  12.  291715.  47096 

10.9259 

4.92513 

9.83333, 

59 

TABLE   XIV. — ACTUAL   TANGEKTS,    ETC. 


1° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

50.0000 

Tan. 

Arc. 

Tan. 

Arc. 

25.0000 

Tan. 

Arc. 

O 

50.0198  100.00025.0108 

16.6750 

33.3333 

12.5074 

10.0070 

20.0000 

1 

50.8500  101.667 

25.4263 

50.8333 

16.9520!  33.  8889 

12.7151 

25.4167 

10.173220.3333 

2 

51.6814  103.333 

25.8417 

51.6667 

17.2289134.4444 

12.9229 

2.').  8333  10.  3394 

20.6667 

3 

52.5122105.000'26.2571 

52.5000 

17.5059:35.0000 

13.1306 

26.2500  10.5057 

21.0000 

4 

53.3130 

106.667 

26.6725 

53.3333 

17.782835.5556 

13.3383 

26.666710.6719 

21.3333 

5 

54.1738 

108.333 

27.0879 

54.1667 

18.059836.1111 

13.5461 

27.0833  10.83S1 

21.6667 

6 

55.0046illO.000 

27.50:33 

55.0000 

18.3368 

36.6667 

13.7538 

27.5000  11.0013 

22.0000 

7 

55.8354111.667 

27.9187 

55.8333 

18.613737.2222 

13.9616 

27.9167 

11.1705 

22.3333 

8 

56.6662  113.333 

28.3342 

56.6667 

18.8907 

37.7778 

14.1693 

28.3333  11.3367 

22.6667 

9 

57.4970 

115.000 

28.7496 

57.5000 

19.1677 

38.3333 

14.3770 

28.7500  11.5029 

23.0000 

10 

58.3278 

116.667 

29.1650 

58.3333 

19.4446 

38.8889 

14.584829.1667 

11.6691  23  3333 

11 

59.1586 

118.333 

29.5804 

59.1667 

19.7216 

39.4444 

14.792529.5S33 

11.835323.6667 

18 

59  .  9894  i  1  20  .  000  29  .  9958 

60.0000 

19.9985 

40.0000 

15.000330.0000 

12.0016!  24.  0000 

13 

60.8202 

121.667 

30.4112 

60.8333 

20.2755 

40.5556 

15.2080 

80.4167 

12.167824.3333 

14 

61.6510 

123.33330.8266 

61.6667 

20.5525 

41.1111 

15.4157 

30.8333 

12.3340 

24.6667 

15 

62.4818 

125.000 

31.2421 

62.5000 

20.8294 

41.6667 

15.6235 

31.2500 

12.5002 

25.0000 

16 

63.3126 

1  26.  667  !  31.  6575 

63.3333 

21.1064 

42.2222 

15.8312 

31.6667 

12.6664 

25.3333 

17 

64.1721 

128.333 

32.0872 

64.1667 

21.3929 

42.7778 

16.0461 

32.0833  12.8383 

25.6667 

18 

65.0315 

130.000 

32.5170 

65.00JO 

21.6794 

43.3333 

16.2610 

32.5000 

13.0103 

26.0000 

19 

65.8623 

131.667 

32.9324 

65.8333 

21.9564 

43.8889 

16.4688 

32.9167 

13.1765 

26.3333 

30 

66.6931 

133.333 

33.3478 

66.6667 

22.2333 

44.4444 

16.6765 

33.3333 

13.3427 

26.6667 

21 

67.5239 

135.000 

33.7632 

67.5000 

22.5103 

45.0000 

16.884--J 

33.7500 

13.5089 

27.0000 

22 

68.3547 

136.  667134.1786 

68.3333 

22.7873 

45.5556 

17.0920 

34.1667 

13.6751 

27.3333 

23 

69.1855 

138.  333  '34.  59  10 

69.1667 

23.0642 

46.1111 

17.2997 

34.5833 

13.8413 

27.6667 

24 

70.0163 

140.00035.0094 

70.0000 

23.3412 

46.6667 

17.5075 

35.0000 

14.0075 

28.0000 

25 

70.8471 

141'.  667 

3.-).  4249 

70.8333 

23.6181 

47.2222 

17.7152 

35.4167 

14.1738 

«8.  3333 

36 

71.6779 

143.33335.8403 

71.6667 

23.8951 

47.7778 

17.9230 

35.8333 

14.3400 

28.6667 

21 

72.5087 

145.00036.2557 

72.5000 

24.1721 

48.3333 

18.1307 

36.2500 

14.5062 

29.00CO 

28 

73.3395 

146.667 

36.6711 

73.3333 

24.4490 

48.8889 

18.3384 

36.6667 

14.6724 

29.3333 

29 

74.1703 

148.333 

37.0865 

74.1667 

24.7260 

49.4144 

18.5462 

37.0833 

14.8386 

29.6667 

30 

75.0011 

150.000 

37.5019 

75.0000 

25.0029 

50.0000 

18.7539 

37.5000 

15.0048 

30.0000 

31 

75.8319 

151.  667  3  r.  91  73 

75.8333 

25.2799 

50.5556 

18.961737.9167 

15.171030.8333 

32 

76.6627 

1  53.  333  ;  33.  3328 

76.6667 

25.5569 

51.1111 

19.1694 

38.3333 

15.3372 

30.6667 

33 

77.4935 

155.00038.7482 

77.5000 

25.8338 

51.6667 

19.3771 

38.7500 

15.5034 

31.0000 

34 

78.3243 

156.667 

39.1636 

78.3333 

26.1108 

52.2222 

19.5849 

39  1667 

15.6696 

31.3333 

35 
36 

79.1551 
79.9859 

158.33339.5790 
160.00039.9944 

79.1667 
80.0000 

26.3878 
26.6647 

52.7778 
53.3333 

19.7926 
20.0004 

39.583315.8359 
40.000016.0021 

31.6667 
32.0000 

37 

80.8167 

161.66740.4098 

80.8333 

26.9417 

53.8889 

20.2081 

40.416716.1683 

32.3333 

38 

81.6475 

163.333 

40.8253 

81.6667 

27.2186 

54.4444 

20.4158 

40.8333 

16.3345 

32.6667 

39 

82.5070 

165.000 

41.2550 

82.5000 

27.5052 

55.0000 

20.6307 

41.2500 

16.5064 

33.0000 

4O 

83.3664 

166.667 

41.6847 

83.3333 

27.7917 

55.5556 

20.8456 

41.6667 

16.6784 

33.3333 

41 

84.1972 

168.33342.1001 

84.1667 

28.0686 

56.1111 

21.0534 

42.0833 

16.8446 

33.6667 

4  a 

85.0280 

170.000 

42.5156 

85.0000 

28.3456 

56.6667 

21.2611 

42.5000 

17.0108 

34.0000 

43 

85.8588 

171.667 

42.9310 

85.8333 

28.6225 

57.2222 

21.4689 

42.9167 

17.1770 

34.3333 

44 

86  6896 

173.333 

43.3464 

86.6667 

28.8995 

57.7778 

21.6766 

43.3333 

17.3432 

34.0667 

45 

87.5204 

175.000 

43.761887.5000 

29.1765 

58.3333 

21.8843 

43.7500 

17.5094 

35.0000 

46 

88.3512 

176.667 

44.1772 

88.3333 

29.4534 

58.8889 

22.0921 

44.1667 

17.6756 

35.3333 

47 

89.1820 

178.33344.592689.1667 

29.7304 

59.4444 

22.2998 

44.5833 

17.8418 

35.C667 

48 

90.0128 

180.000 

45.  0081  190.0000 

30.0074 

60.0000 

22.5076 

45.0000 

18.0081 

36.0000 

49 

90.8436 

181.667 

45.4235:90.8333 

30.2843 

60.5556 

22.7153 

45.4167 

18.174336.3333 

50 

91.6744 

183.333 

45.838991.6667 

30.5613 

61.1111 

22.9230 

45.8333 

18.340536.6667 

51 

92.5052 

185.000 

46.2543 

92.5000 

30.8382 

61.6667 

23.1308 

46.2500 

18.506737.0000 

52 

93.3360 

186.667 

46.669793.3333 

31.1152 

62.2222 

23.3385 

46.6667 

18.  6729  '37.  3333 

53 

94.1668 

188,333 

47.0851  94.1667 

31.3922 

62.7778 

23.5463 

47.0833 

18.8391;  37.  6667 

54 

94.9976 

190.000  47.5005  95.0000 

31.6691 

63.3333 

23.754047.5000 

1  9.  0053  :  38.  0000 

55 

95.8284 

191.667 

47.916095.8333 

31.9461 

63.8889 

23.9617 

47.9167 

19.171538.3333 

56 

96.6592 

193.333 

48.331496.6667 

32.2230 

64.4444 

24.1695 

48.3333  19.337738.6667 

57 

97.4900 

1  95  .  000  48  .  7468  '  97  .  5000 

32.  5000  j  65.  0000 

24  .  3772  48  .  7500:  1  9  .  5040  39  .  0000 

58 

98.3208 

196.667 

49.162298.3333 

33.7770 

65.5556 

24  .  5850  49  .  1  667  i  1  9  .  6702  39  .  33S3 

59 

99.1802 

198.33349.591999.1667 

33.0635 

66.1111 

24.7999  49.5833  19.8421  39.6667 

48 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

1° 

Tan.      Arc. 

Tan. 

7715004 

Arc. 

14.2856 

Tan. 
6.25749 

Arc. 

12.5000 

Tan. 

Arc. 

Tan.      Arc. 

M. 

8.34038  16.6667 

5.56337 

11.1111 

5.00831  10.0000 

8.47891  16.9444 

7.26880  14.5238 

6.36142 

12.7083 

5.65577 

11.2963 

5.0915010.1667 

1 

8.61744  17.2222 

7.387'56  14.7619 

6.46536 

12.9167 

5.74818 

11.4815 

5.17468  10.3333 

8.75597  17.5000 

7.50632  15.0000 

6.56929 

13.1250 

5.84058 

11.6667 

5.25787  10.5000 

3 

8.89449 

17.7778 

7.62508  15.2381 

6.67322 

13.3333 

5.93298 

11.8519 

5.3410510.6667 

4 

9.03302 

18.0556 

7.743*3  15.4762 

6.77715 

13.5417 

6.02539 

12.0370 

5.42424  10.8333 

5 

9.17155 

18.3333 

7.86259  15.7143 

6.88109 

13.7500 

6.11779 

12.2222 

5.5074211.0000 

6 

9.31008 

18.6111 

7.98135  15.9524 

6.98502 

13.9583 

6.21020 

12.4074 

5.59061  11.1667 

7 

9.44861 

18.8889 

8.10011  16.1905 

7.08895 

14.1667 

6.30260 

12.5926 

5.6737911.3333 

8 

9.58714 

19.1667 

8.21887 

16.4286 

7.19289 

14.3750 

6.39500 

12.7778 

5.75698  11.5000 

9 

9.72567 

19.4444 

8.33762 

16.6667 

7.29682 

14.5833 

6.48741 

12.9630 

5.8401611.6667 

1O 

9.86420 

19.7222 

8.45638  16.9048 

7.40075 

14.7917 

6.57981 

13.1482 

5.92335  11.8333 

11 

10.0027 

20.0000 

8.57514  17.1429 

7.50469 

15.0000 

6.67222 

13.3333 

6.00653 

12.0000 

13 

10.141320.2778 

8.69390 

17.3810 

7.60862 

15.2083 

6.76462 

13.5185 

6.08972 

12.1667 

13 

10.  2798  120.5556 

8.81266  17.6191 

7.71255 

15.4167 

6.85703 

13.7037 

6.17290 

12.3333 

14 

10.4183120.8333 

8.93141  17.8571 

7.81649 

15.6250 

6.94943 

13.8889 

6.25609 

12.5000 

15 

10.5568 

21.1111 

9.05017118.0952 

7.92042 

15.8333 

7.04183 

14.0741 

6.33927 

12.6667 

16 

10.7001 

21.3889 

9.1730218.3333 

8.02794 

16.0417 

7.13742 

14.2593 

6.42533 

12.8333 

17 

10.8434 

21.6667 

9.29588J18.5714 

8.13545 

16.2500 

7.23301 

14.4444 

6.51138 

13.0000 

18 

10.9820 

21.9444 

9.41463 

18.8095 

8.23939 

16.4583 

7.32542 

14.6296 

6.59457 

13.1667 

19 

11.1205 

22.2222 

9.53339  19.0476 

8.34332 

16.6667 

7.41782 

14.8148 

6.67775 

13.3S33 

2O 

11.2590 

22.5000 

9.65215  19.2856 

8.44725 

16.8750 

7.51023 

15.0000 

6.76094 

13.5000 

21 

11.3976 

22.7778 

9.77091119.5238 

8.55119 

17.0833 

7.60263 

15.1852 

6.84412 

13.6667 

22 

11.5361 

23.0556 

9.88967119.7619 

8.65512 

17.2917 

7.69504 

15.3704 

6.92731 

13.8333 

23 

11.6746 

23.3833 

10.008420.0000 

8.75905 

17.5000 

7.78744 

15.5556 

7.01049 

14.0000 

24 

11.8132 

23.6111 

10.1272 

20.2381 

8.86298 

17.7083 

7.87984 

15.7407 

7.09368 

14.1667 

25 

11.9517 

23.8889 

10.2459 

20.4762 

8.96692 

17.9167 

7.97225 

15.9259 

7.17686 

14.3333 

26 

12.0902 

24.1667 

10.3647 

20.7143 

9.07X185 

18.1250 

8.06465 

16.1111 

7.26005 

14.5000 

27 

12.2287 

24.4444 

10.4835 

20.9524 

9.17478 

18.3333 

8.15706 

16.2963 

7.34323 

14.6667 

28 

12.3673 

24.7222 

10.6022 

21.1905 

9.27872 

18.5417 

8.24946 

16.4815 

7.42642 

14.8333 

29 

12.5058 

25.0000 

10.7210 

21.4286 

9.38265 

18.7500 

8.34186 

16.6667 

7.50960 

15.0000 

30 

12.6443 

25.2778 

10.8397 

21.6667 

9.48658 

18.9583 

8.43427 

16.8519 

7.59279 

15.1667 

31 

12.7829 

25.5556 

10.9585 

21.9048 

9.59052 

19.1667 

8.52667 

17.0370 

7.67597 

15.3333 

32 

12.9214 

25.8383 

11.0772 

22.1429 

9.69445 

19.3750 

8.61908 

17.2222 

7.75916 

15.5000 

33 

13.0599 

26.1111 

11.1960 

22.3810 

9.79838 

19.5833 

8.71148 

17.4074 

7.84234 

15.6667 

34 

13.1984 

26.3889 

11.3148 

22.6191 

9.90232 

19.7917 

8.80389 

17.5926 

7.92553 

15.8333 

35 

13.3370 

26.6667 

11.4335 

22.8571 

10.0062 

20.0000 

8.89629 

17.7778 

8.00871 

16.0000 

36 

13.4755 

26.9444 

11.552323.0952 

10.1102 

20.2083 

8.98869 

17.9630 

8.09190 

16.1667 

37 

13.6140 

27.2222 

11.671023.3383 

10.2141 

20.4167 

9.08110 

IS.  1482 

8.17508 

16.3333 

38 

13.7573 

27.5000 

11.793923.5714 

10.3216 

20.6250 

9.17669 

18.3338 

8.26114 

16.5000 

39 

13.9006 

27.7778 

11.916723.8095 

10.4291 

20.8333 

9.27228 

18.5185 

8.34719 

16.6667 

4O 

14.0392 

28.0556 

12.035524.0476 

10.5331 

21.0417 

9.36468 

18.7037 

8.43037 

16.8333 

41 

14.1777 

28.3333 

12.154324.2856 

10.6370 

21.2500 

9.45709 

18.8889 

8.51356 

17.0000 

42 

14.3162 

28.6111 

12.  2730  124.5238 

10.7409 

21.4583 

9.54949 

19.0741 

8.59674 

17.1667 

43 

14.4547 

28.8889 

12.391824.7619 

10.8449 

21.6667 

9.64190 

19.2593 

8.67993 

17.3333 

44 

14.5983 

29.1667 

12.510525.000<> 

10.9488 

21.8750 

9.73430 

19.4444 

8.76311 

17.5000 

45 

14.7318 

29.4444 

12.629325.2381 

11.0527 

22.0833 

9.82670 

19.6296 

8.84630 

17.6667 

46 

14.  8703:29.7222 

12.748025.4762 

11.1567 

22.2917 

9.91911 

19.8148 

8.92948 

17.8333 

47 

15.008930.0000 

12.866825.7143 

11.2606 

22.5000 

10.0115 

20.0000 

9.01267 

18.0000 

48 

15.1474j30.2778 

12.985625.9524 

11.3645 

22.7083 

10.1039 

20.1852 

9.09585 

18.1667 

49 

15.  2859  '30.  5556 

13.104326.1905 

11.4685 

22.9167 

10.1963 

20.3704 

9.17904 

18.3333 

5O 

15.4244130.8333 

13.2231 

26.4286 

11.5724 

23.1250 

10.2887 

20.5556 

9.26223 

18.5000 

51 

15.563031.1111 

13.341826.6667 

11.676323.3333 

10.3811 

20.7407 

9.34541 

18.6667 

52 

15.701531.3889 

13.460626.9048 

11.780323.5417 

10.4735 

20.9259 

9.42860 

18.8333 

53 

15.840031.6667 

13.579427.1429 

11.8842s23.7'500 

10.5659 

21.1111 

9.51178 

19.0000 

54 

15.978631.9444 

13.6981  27.3810 

11.9881123.9583 

10.6583 

21.2963 

9.59497 

19.1667 

55 

16.1171  32.  2222J13.  81  69  27.  6191 

12.0921  24.1667 

10.7507 

21.4815 

9.67815 

19.3333 

56 

16.  2556  !  32.  5000 

13.935627.8571 

12.196024.3750 

10.8431 

21.6667 

9.76134 

19.5000 

57 

16.3941  32.7778 

14.0544  28.0952 

12.299924.5833 

10.9356 

21.8519 

9.84452 

19  6667 

58 

16.537533.0556 

14.177228.3333 

12.407524.7917 

11.0311 

22.0370 

9.93057 

19.8333 

59 

49 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


2° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.      Arc. 

Tan. 

Arc. 

~1F 

l6o~7040 

200.000 

50.0217 

100.000 

33.350066.6667 

25.014850.0000 

20.0140 

40.0000 

i 

100.870 

201  .  667 

50.4371 

100.833 

33  627067.2222 

25.222550.4167 

20.1803 

40.3333 

3 

101.701 

203.333 

50.8525 

101.667 

33.903967.7778 

25.430250.8333 

20.3405 

40.0067 

3 

103.53-2 

205.000 

51.2679 

102.500 

34.  180968.3333 

25.638051.2500 

20.5127 

41.0000 

4 

103.363 

206.667 

51.6833 

103.333 

•34.457808.8889 

25.8457 

51.6667 

20.6789 

41.3333 

5 

101.194 

208.333 

52.0988 

104.107 

34.734869.4444 

26.0535 

52.0833 

20.8451 

41.6667 

6 

105.021 

210.000 

52.5142 

105.000 

35.0118:70.0000 

20.2012 

52.5000 

21.0113 

42.0000 

7 

105.855 

211.667 

52.9296 

105.833 

35.  2887  70.  5556 

26.4089 

52.9107 

21.1775 

42.3333 

8 

100.  G8G 

213.333 

53.8450 

106.G-.i7 

r>.  5657  71.1  111 

20.6767 

53.3333 

21.3437 

42.6667 

9 

107.517 

215.000 

53.7604 

107.500 

35.8427 

71.6667 

20.8844 

53.75UU 

21.5099 

43.0000 

1O 

108.348 

216.667 

54.1758 

108.333 

36.119672.2222 

27.0922 

54.1667 

21.6762 

43.3333 

11 

109.178 

218.333 

54.5912 

109.167 

3(3.3960  72.7778 

tf.aMKJ 

54.5833 

21.842443.0007 

12 

110  009 

220.000 

•)5.0067 

110.000 

36.07:35 

73.3333 

27.5070 

55.0000 

22.0080 

44.0000 

13 

110.810 

221.667 

55.4221 

110.833 

36.9505 

7.3.8889 

27.7154 

55.4167 

22.1748 

44.3333 

14 

111.671 

223.333 

>5.8'375 

111.667 

37.2275 

7'4.4444 

27.9231 

55.8333 

22.341044.6667 

15 

112.502 

225.000 

56.2529 

112.500 

37.50H 

75.0000 

28.1309 

56.2500 

•22.5072 

45.0000 

16 

113.332 

226.667 

56.6633 

113.333 

37.7814 

75.5550 

28.3380 

56.6007 

22.673445.3333 

17 

114.163 

228.333 

57.0837 

114.  107 

38.0583 

76.1111 

28.5403 

57.0833 

22.8396 

45.0007 

18 

114.994 

230.000 

57.4991 

115.000 

33.3353 

76.GOG7 

28.7'541 

57.5-000 

38.006846.0UOO 

19 

115.825 

231.667 

57.9146 

115.833 

38.6123 

7?  222'; 

28.9018 

57.9167 

23.1721 

40.3333 

20 

116.656 

233  333 

58.3300 

116.887 

38.8892 

77.7778 

29.1696 

58.3333 

23.3383 

46.6667 

31 

117.515 

235.000 

58  .  7597 

117.500 

39.1757 

78.3333 

29.3345 

53.7  500 

23.5102 

47.0000 

22 

118.375 

236  667 

59.1895 

118.333 

39.4623 

78.8839 

29.5994 

59.1667 

23.  G821  47.3333 

23 

119.205 

238.333 

59.6049 

119.167 

39.7392 

79.4414 

29.8071 

59.5833 

23.8484 

47.0667 

24 

120.036 

240.000 

60.0203 

120.000 

40.0102 

80.0000 

30.0119 

60.0000 

24.014048.0000 

25 

120.867 

241.667 

60.4357 

120.833 

40.2931 

80.5556 

•30.2226 

60.4167 

24.1808 

48.3333 

26 

121.698 

243.333 

60.8511 

121.667 

40.5701 

81.1111 

30.4303 

60.8333 

24.347048.0007 

27 

122.529 

245.000 

61.2665 

122.500 

40  8471 

81.6667 

30.6381 

61.2500 

24.5132 

49.0000 

28 

123.359 

246.667 

61.6819 

123.333 

41.1240 

82.  22,  '2 

30.8158 

61.6667 

24.0794 

49.3333 

39 

124.190 

248.333 

62.0974 

124.167 

41.4010 

82.7778 

•31.0536 

62.0833 

24.8456 

49.6067 

30 

125.021 

250.000 

62.5128 

125.000 

41.6779 

83.3333 

31.2613 

62.5000 

25  0118 

50.0000 

31 

125.852 

251.667 

62.9282 

125.833 

41.9549 

83.8889 

31.4690 

62.9107 

25.1780 

50.3333 

32 

126.683 

253.333 

63.3436 

126.667 

42.2319 

84.4444 

'31.6768 

63.3333 

25.3443 

50.6607 

33 

127.513 

255.000 

63.7590 

127.500 

42.5088 

85.0000 

31.8845 

63.7500 

25.510551.0000 

34 

1  28.344 

256.667 

64.1744 

128.&33 

42.7858 

85.5556 

32.0923 

64.1667 

25.G7'67 

51.3333 

35 

129.175 

258.333 

64.5898 

129.167 

43.0628 

86.1111 

32.3000 

64.5833 

25.8429 

51  .  6667 

36 

130.006 

260.000 

65.0053 

130.000 

43.3397 

86.6607 

32.5077 

65.0000 

•20.0091  52.0000 

37 

130.837 

261.667 

65.4207 

130.833 

43.6167 

87.2222 

32.7155 

65.4107 

20.1753 

52.3333 

38 

131.667 

263.333 

65.8361 

131.667 

43.8936 

87.7778 

32.9232 

65.8333 

•26.3415 

52.0(567 

39 

132.527 

265.000 

66.2658 

132.500 

44.1802 

88.3333 

33.1381 

66.2500 

26.5135 

53.0000 

40 

133.386 

266.667 

66.6956 

133.333 

44.466788.8889 

33.3530 

06.6667 

26.6854 

53.3333 

41 

134.217 

268.333 

67.1110 

131.167 

44.7436:89.4444 

33.5608 

67.08:33 

26.8516 

53.  (5007 

42 

135.048 

270.000 

67.5264 

135.000 

45.020G  90.0000 

33.7085 

67.5000 

27.0178 

54.0000 

43 

135.879 

271.667 

67.9418 

135.833 

45.29:590.5550 

33.9702 

67.9167 

27.184054.3333 

44 

136.709 

273.333 

68.3572 

13;>.  667 

45.574591.1111 

34.1840 

68.3333 

27.3502 

54  .  6(567 

45 

137.510 

275.000 

68.7726 

137.500 

45.851591.6607 

34.3917 

68.7500 

27.5165 

55  0000 

46 

138.371 

276.667 

69.1881 

138.333 

46.128492.2222 

34.5995 

09.1667 

'27.082755.3333 

47 

139.202 

278.333 

69.6035 

139.167 

16.4054  92.7778 

34.8072 

69.5833 

27.8489 

55.0067 

48 

140.033 

280.000 

70.0189 

140.000 

46.082493.3333 

35-0149 

70.0000 

28.0151 

56.0000 

49 

140.863 

281.667 

70.4313 

140.833 

16  959393.H889 

35.2227 

70.4167 

28.1813 

56.3333 

5O 

141.694283.333 

70.8497141.007 

17.2363 

94.4444 

35.4304 

70.8333 

28.3475 

56.6667 

51 

142.525285.000 

71.2651  142.500 

47.5132 

95.0000 

85.638-2 

71.250028.5187 

57  0000 

52 

143.356286.667 

71.6805  143.333 

47.7902 

95.5556 

35.8459 

71.66K7 

28.  (5799  57.  3333 

53 

144.18728S.333 

72.0960  144.167 

48.0672 

96.1111 

36.0536 

72.0833 

28.8461 

57.6667 

54 

145.017290.000 

72.5114  145.000 

4H.3441 

96.6667 

36.2614 

72.5000 

29.  01  23  !  58.  0000 

55 

145.  84  8  201.007 

72.  9268  H  5.  833 

48.6211 

07.2222 

36.4691 

72.916729.1780 

58.3333 

56 

146.679293.333 

73.3422  146.067 

48.8980 

97.7778 

36.6709 

73.3333  29.3448  58.6607 

57 

147.  510  S95.  000 

73.7576  147.500 

49.1750 

98  3333 

36.8846 

73.750029.5110 

59.0000 

58 

148.341  296.6'V? 

74.1730  148.383 

49  .  4520  !  98  .  8889  37  .  0923  74  .  1  667  29  .  6772 

59.3383 

59 

149.200298.333 

74.6028  149.167 

49.  73^5  199.4444  137.  3072  >  74.  5833  29.8491  59.6667 

50 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

2° 

Tan.       Arc. 

Tan.      Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

16.080888.3333 

14.3001  28.5714 

12.5150 

25.0000 

11.1207 

22.2222 

10.0100 

20.0000 

(f 

16.81  93  33  .6111  14.416838.  8095 

1:3.0189 

25.2083 

11.2191 

22.4074 

10.  QMS 

20.1607 

i 

It).  95:  8  33.8889  14.5370  29.0470 

12.7228 

#3.4107 

11.3115 

22.5926 

10.1830 

20.8333 

1  7  .  0963  34  .  1  607  j  14  .  0504  ^9  .  2850 

12.8208 

25.0250 

11.4039 

22.7778 

10.2002 

20.5000 

3 

17.  8349.34.  44441  14.  7T51  89.5:338 

12.9307 

25.8333 

11.4904 

88.9030 

10.3494 

20.6607 

4 

17.373484.7222 

14.893929.7019 

13.0340 

20.041*; 

11.5888 

23.1482 

10.4326 

20.8333 

5 

17.511935.0000 

15.012030.0000 

13.1380 

20.2500 

11.0812 

23.8333 

10.5157 

21.0000 

G 

17.65U5;85.8778 

15.131430.2381 

13.2425 

20.4583 

11.7736 

23.5185 

10.5989 

21.16G7 

7 

17.789035.5550 

15.XJ50230.4702 

13.3404 

20.0607 

11.8600 

23.7037 

10.6821 

21.3333 

£ 

17.9275 

35.8333 

15.308930.7143 

13.4504 

20.8750 

11.9584 

23.8889 

10.7653 

21.5000 

i) 

18.0600 

36.1111 

15.487730.9524 

13.5543 

27.0833 

12.0508 

24.0741 

10.8485 

21.6667 

10 

18.SJ046l36.S889 

15.600431.1905 

13.6582 

27.2917 

12.1432 

24.2593 

10.9317 

21.83:33 

11 

18.3431  30.0007 

15.725231.4280 

13.7622 

27.5000 

12.2356 

24.4444 

11.0148 

22.0CCO 

12 

18.481030.9444 

15.843931.6067 

13.8061 

27.7083 

12.328024.6290 

11.0980 

22.1607 

13 

18.020237.2222 

15.902731.9048 

13.9700 

27.9167 

12.4204  24.8148 

11.1812 

22.3333 

14 

18.7587 

37.5000 

10.081532.1429 

14.0740 

28.1250 

12.5128 

25.0000 

11.2644 

22  5000 

15 

18.8972 

37  .  7778 

16.200232.3810 

14.177'9 

28.3333 

12.6052 

25.1852 

11.3470 

22.6667 

16 

19.035738.0550 

10.319032.6190 

14.2818 

28.5417 

12.6976 

25.37'04 

11.4308 

22.8333 

17 

19.174338.3333 

16.437732.8571 

14.3858 

28.7500 

12.7900 

25.5556 

11.5140 

23.00CO 

18 

19.3128 

38.6111 

16.556533.0952 

14.4897 

28.9583 

12.8824 

25.7407 

11.5971 

23.1067 

19 

19.4513 

38.8889 

16.675233.3333 

14.5930 

29.1667 

12.9748 

25.9259 

11.6803 

23.3333 

20 

19.5940 

39.1607 

16.7981  33.5714 

14.7012 

29.3750 

13.0704 

26.1111 

11.7004 

23.5000 

21 

19.7379 

39.4444 

16.921033.8095 

14.8087 

29.5833 

13.1660 

26.2963 

11.8524 

23.6667 

22 

19.8705 

39.7222 

17.039734.0470 

14.9126 

29.7917 

13.2584 

26.4815 

11.9356 

23.8333 

23 

20.0150 

40.0000 

17.158534.2856 

15.0165 

30.0000 

13.3508 

20.6667 

12.0188 

24.0000 

24 

20.1535 

40.2778 

17.277234.5238 

15.1205;30.2083 

13.4432 

26.8519 

12.1020 

24.1667 

25 

20.2921 

40.5550 

17.396034.7619 

15.  2244130.  4167 

13.5356 

27.0370 

12.1852 

24.3333 

26 

20.4300 

40.8333 

17.514735.0000 

15.  3283  130.6250 

13.6280 

27.222-; 

12.2684 

84.5000 

27 

20.5091 

41.1111 

17.033535.2381 

15.4323 

30.8333 

13.7204 

27.4074 

12.3515 

24.6667 

28 

20.7070 

41.3889 

17.752335.4762 

15.5362 

31.0417 

13.8128 

27.5926 

12.4347 

24.8333 

29 

20.8-162 

41.6667 

17.871035.7143 

15.6401 

31.2500 

13.9052 

27  .  7778 

12.5179 

•25.0000 

80 

20.98-17 

41.9444 

17.989835.9524 

15.7441 

31.4583 

13.9976 

27.9030 

12.0011 

•J5.1GG7 

31 

21.1232 

42.2222 

18.108536.1905 

15.8480 

31.6667 

14.0900 

28.1482 

12.6843 

85.8333 

32 

21.2618 

42.5000 

18.227330.4280 

15.9519 

31.8750 

14.1824 

28.3333 

12.7675 

25.5000 

33 

21.4003 

42.7778 

18.346036.6667 

16.0559 

32.0833 

14.2748 

28.5185 

12.8507 

25.6667 

34 

21.5388 

43.0556 

18.464836.9048 

16.1598 

32.2917 

14.3673 

28.7C37 

12.9338 

25.8333 

35 

21.6773 

43.3333 

18.583637.1429 

16.2037 

32.5000 

14.4597 

28.8880 

18.0170 

26.0000 

36 

21.8159 

43.6111 

18.702337.3810 

16.3077 

3-'.  7083 

14.5521 

89.0741 

13.1002 

26.1667 

37 

21.9544 

43.8889 

18.8211  37.6190 

16.4710 

32.9167 

14.6445 

29.2593 

13.1F34 

26.3333 

88 

22.0977 

44.1667 

18.943937.8C71 

16.5791 

33.1250 

14.7401 

29.4444 

13.2694 

26.5000 

39 

22.2410 

44.4444 

19.0668  38.'  0952 

16.0866 

33.3333 

14.8356 

29.6296 

13.3555 

26.6G67 

40 

22.  3795|  44.  7222 

19.185538.3333 

16.7906 

33.5417 

14.9280 

29.  814  e; 

13.4387 

26.8333 

41 

22.5181:45.0000 

19.304338.5714 

16.8945 

33.7500 

15.0205 

30.0000 

13.5219 

27.0000 

42 

22.6566:45.2778 

19.4231  38.8095 

16.9984 

33.9583 

15.1129 

30.1S52 

13.6051 

27.1G67 

43 

22.7951  45.5556 

19.541839.0476 

17.1024 

34.1667 

15.2053 

30.8704 

13.6882 

27.3333 

44 

22  933745.8333 

19.660639.2856 

17.2063 

34.3750 

15.2977 

30.5556 

13.7714 

27.5000 

45 

23.072246.1111 

19.779339.5228 

7.3102 

31.5833 

15.3901 

30.7407 

13.8546 

27.6G67 

46 

23.210746.3880 

19.8981  39.7619 

7.4142 

31.7917 

15.4825 

30.9259 

13.937'8 

27.F333 

47 

23.319246.0067 

20.016840.0000 

7.5181 

35.0000 

15.5749 

31.1111 

14.0210 

28.0000 

48 

23.487840.9444 

20.135640.2381 

7.6220 

35.2083 

15.6673 

31.2963 

14.1042 

28.1C67 

49 

23.6263 

47.2222 

20.254440.4762 

7.72f>0 

35.4167 

15.7597 

31.4815 

14.?  874 

88.3333 

50 

28.764$ 

47.5000 

20.3731  40.7143 

7.8299 

35.6250 

15.8521 

31.C667 

14.2705 

28.5000 

51 

23.9031 

47.7778 

20.491940.9524 

7.9338 

35.8333 

15.9445 

31.8519 

14.3537 

28.6667 

52 

24.0419 

-18.0556 

20.610641.1005 

18.0378 

36.0417 

16.036932.0370 

14.4369 

28.8333 

53 

24.  ISO-! 

48.3333 

20.729441.4286 

IS.  1417 

36  2500 

16.1293 

32  2222 

14.5201 

29.0000 

54 

24.  31  SO 

48.6111 

20.848241.0667 

18.2456 

36.4583 

16.2217 

32  .'4074 

14.6033 

29.1G67 

55 

24.4575 

48.8889 

20.966941.9048 

18.3406 

30.6067 

16.3141 

32.5926 

14.6865 

29.3333 

56 

24.5900  49.1667 

21.085742.1429 

18.4535 

36.8750 

16.4065 

32.7778 

14.7696 

29.5000 

57 

24.7315 

49.444-1 

21.204442.3810 

18.5574 

37.0833 

16.4989 

32.9630 

14.8598 

29.6667 

58 

24.8778 

49.7222 

21.327342.6190 

18.0650 

37.2917 

16.5945 

33.1482 

14.9389 

29.8333 

59 

51 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


3° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tail.  I    Arc. 

Tan.      Arc. 

Tan. 

Arc. 

O 

50.060 

oo.uoo 

75.0325 

150.000 

0.0250  100.  000  ,37.  5222;  75.  0000  30.0211 

60.0000 

1 

50.890 

01.667 

75.4479 

150.8:33 

0.3020  1UO.  556;  37.  7299  75.4167  30.187:-) 

60.3333 

2 

51.721 

03.33375.8633 

151.667 

0.5789 

10  1  .  1  1  1  37  .  9376  ;  7  o  .  833:3  30  .  8535 

60.6667 

3 

52.552 

05.000 

6.2788 

52.500 

0.8559 

101.667  38.1454  76.2500  30.5197 

61.0000 

4 

53.383 

06.667 

6.6942 

153.333 

1.1328 

102.22238  3531 

76.666730.6859 

61.3333 

5 

51.214 

08.333 

7.1090 

154.167 

ol.4098 

102.778 

38.5609 

77.083330.8521 

61  6607 

6 

55.044 

10.000 

7.5250 

155.000 

ol.6868 

103.333 

38.7686 

77.500031.0183 

62.0000 

i 

55.875 

11.667 

"7.9404 

155.833 

ol.9637 

103.889 

38.9763 

77.916731.1845 

62.3332 

8 

56.706 

13.333 

"8.3558 

156.667 

o2.2407 

104.444 

39.1841 

78.3:33331.3508 

62.6667 

9 

57.537 

315.000 

"8.7713 

157.500 

o2.5176 

105.000 

39.3918 

78.750031.5170 

63.0000 

1O 

58.368 

316.667 

79.1867 

158.333 

52.7946 

105.556 

39.5996 

79.166731.6832 

63.3333 

11 

59.198 

318.333 

"9.6021 

159.167 

53.0716 

106.111 

39.8073 

79.  5833  '31.  8494 

03.6667 

12 

60.029 

320.000 

80.0175 

160.000 

53.3485 

106.667 

40.0150 

80.000032.0156 

04.0000 

13 

60.860 

321.667 

80.4329 

160.833 

>3.6255 

107.222 

40.2228 

80.410732.1818 

64.3333 

14 

161.691 

323.333 

80.8483 

161.667 

53.9025 

107.778 

40.4305 

80.8333:32.3480 

64.6667 

15 

162.522 

325.000 

81.2637 

162.500 

54.1794 

108.333 

40.6383 

81.250083.5142 

65.0000 

16 

163.352 

326.667 

81.6792 

163.333 

54.4564 

108.889 

40.846081.666732.6804 

65.3333 

17 

164.212 

328.333 

82.1089 

164.167 

54.7429 

109.444 

41.0609 

82.  0833  ^2.8524 

65.6667 

18 

165.071 

330.000 

82.5386 

165.000 

55.0294 

110.000 

41.2758 

82.500033.0243 

06.0000 

19 

165.902 

331.667 

82.9540 

165.833 

55.3064 

110.556 

41.4835 

82.9167 

33.1905 

66.3333 

2O 

166.733 

333.333 

83.3695 

166.667 

55.5833 

111.111 

41.6913 

83.3333 

33.3567 

66.6667 

21 

167.564 

335.000 

83.7849 

167.500 

55.8603 

111.667 

41.8990 

83.7500 

33.5230 

67.0000 

22 

168.394 

336.667 

84.2003 

168.333 

56.1373 

112.222 

42.1068 

84.1667 

33.6892 

67.3333 

23 

169.225 

338.333 

84.6157 

169.167 

56.4142 

112.778 

42.3145 

84.5833 

33.8554 

67.6667 

24 

170.056 

340.000 

85.0311 

170.000 

56.6912 

113.333 

42.5222 

85.0000 

34.0216 

68.0000 

25 

170.887 

341.667 

85.4465 

170.833 

56.9681 

113.889 

42.7300 

85.4167 

34.1878 

68.3333 

26 

27 

171.718 
172.548 

343.333 

345.000 

85.8620 
86.2774 

171.667 
172.500 

57.2451 
57.5221 

114.444 

115.000 

42.9377 
43.1455 

85.833334.354068.6667 
86.250034.520269.0000 

28 

173.379 

346.667 

86.6928 

173.333 

57.7990 

115.556 

43.3532 

86.6667 

34.6864  69.3333 

29 

174.210 

348.333 

87.1082 

174.167 

58.0760 

116.111 

43.5609 

87.0833 

34.8526 

69.6667 

3O 

175.041 

350.000 

87.5236 

175.000 

58.3529 

116.667 

43.7687 

87.500035.0189 

70.0000 

31 

175.872 

351.667 

87.9-390 

175.833 

58.6299 

117.222 

43.9764 

87.  9  167  ,35.1851  j  70.  3333 

32 

176.702 

353.333 

88.3544 

176.667 

58.  9069!  117.  778 

44.1842 

88.333335.351370.6667 

33 

177.562 

355.000 

88.7842 

177.500 

59.1934  118.333 

44.3991 

88  .  7500  35  .  5232  71  .  0000 

34 

178.421 

356.667 

89.2139 

178.333 

59.4799  118.889 

44.6140 

89.166735.6952 

71.33:33 

35 

179.252 

358.333 

89.  6293  1179.1  67 

59.7569  119.444 

44.8217 

89.583335.8614 

71  .  6667 

36 

180.083 

360.000 

90.0447 

180.000 

60.0338120.000 

45.0294 

90.000036.0276 

72.0000 

37 

180.914 

361.667 

90.4602 

180.833 

60.3108 

120.556 

45.2372 

90.416736.1938 

72.3333 

38 

181.744 

363.333 

90.8756 

181.66" 

60.5877 

121  .111 

45.4449 

90.833336.3600 

72.6667 

39 

182.575 

365.000 

91.2910 

182.500 

60.8647 

121.667 

45.6527 

91  .  2500 

36.5262 

73.0000 

4O 

183.406 

366.667 

91.7064 

183.3a3 

61.1417 

122.222 

45.8604 

91  .  6667 

36.6924 

73.3333 

41 

184.23" 

368.333 

92  1218 

184.16" 

61.4186 

122.778 

46.0681 

92.0833 

36.8588 

73.6667 

42 

185.068 

370.000 

92.5372 

185.000 

61.6956 

123.333 

46.2759 

92.5000 

37.0248 

74.0000 

43 

185.898 

371.667 

92.9527 

185.83.' 

61.9725 

123.889 

46.4836 

92.9167 

37.1911 

74.3333 

44 

186.729 

373.333 

93.3681 

186.66~ 

62.2495 

124.444 

46.691493.3333 

37.3573 

74.6667 

45 

187.560 

375.000 

93.7835 

187.500 

62.5265 

125.000 

46.8991  93.7500 

37.5235 

75.0000 

46 

188.39 

376.667 

94.1989 

188.333 

62.8034 

125.556 

47.106894.1667 

37.6897 

75.3333 

47 

189.222 

378.  as: 

94.6143 

189.16" 

63.0804  126.111 

47.3146  94.5833 

37.8559 

75.6667 

48 

190.05'. 

380.000 

95.0297 

190.00 

63.3574  126.667 

47.5223 

95.0000 

38.0221 

76.0000 

49 

190.883 

831.  .66? 

95.  4451  |  190.  833 

63.63431127.222 

47.7301 

95.4167 

38.1883 

76.3333 

50 

191.714 

383.333 

95.8606 

191.  66r 

63.9113 

127.77? 

47.937895.833338.3545 

76  .6667 

51 

192.574 

38=).  000 

96.2903 

192.50C 

64.1978 

128.333 

18.152796.250038.5265 

77.0000 

52 

193.43: 

386.66" 

96.7200  193.33' 

64.484:-] 

128.88S 

48  .  3676  96  .  6667  38  .  698  4 

77.3333 

53 

194.264 

388.333 

97.1355  194.16~ 

64.7613 

129.444 

48.575497.083338.8646 

77.6667 

54 

195.095 

390.000 

97.5509195.000 

65.0382 

130.000 

48.7831  97.5000,39.0308 

78.0000 

55 

185.935 

391.667 

97.96^3 

195.83: 

65.3152 

130.556 

48.990897.9167  39.1970 

78.3333 

56 

196.756 

393.333 

98.3817  196.66" 

65.5921 

131.111 

4  9  .  1  986  98  .  3333  39  .  3(533  78  .  6667 

rj  * 

197.587 

395.000 

98.7971 

197.500 

65.8691 

131.667 

49  .  4063  98  .  7500  39  .  5295  1  79  .  0000 

5£ 

198.418 

396  667 

99.2125  198.333 

66.1461 

132.222 

49  .  61  41  i  99  .  1  667  39  .  6957  79  .  3333 

59 

199.249 

398.333 

99.6279,199.16' 

6(5.4230 

132.778  49.8218  99.5833  39.8619|79.6667 

TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve, 

1O°  Curve. 

3° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.       Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

25.0211,50.0000 

21.4501 

42.8571 

18.7725:37.5000 

16.0901 

33.3333 

15.0249 

W.Ot'OO 

O 

25.159750.2778 

21.568943.0952 

18.876437.7083 

16.7825 

33.5185 

15.1081 

30.1667 

1 

25.298250.5556 

21.087043.3333 

18'.  9803  37  9107 

16.8749 

33.7037 

15.1913 

30.3333 

2 

25.4367,50.8333 

-21.800443.5714 

19.084338.1250 

16.9673 

33.8889 

15.2745 

30.5000 

3 

25  575351.1111 

-21.925243.8095 

19.188238.3333 

17.0597 

34.0741 

15.3577 

30.6667 

4 

25.713851.3889 

22.043944.0170 

19.  2921!  38.  5417 

17.1521 

34.2593 

15.4409 

30.8333 

5 

25.852351.6667 

22.162744.2850 

19.396138.7500 

17.2445 

34.4444 

15.5241 

31.0000 

6 

25.990851.9444 

22.2814 

44.5238 

19.500038.9583 

17.3369 

34.6296 

15.0072 

31.1007 

7 

26.129452.2222 

22.4002 

44.7619 

19.603939  1667 

17.4293 

34.8148 

15.6904 

31.3333 

8 

26.2679 

52  5000 

22.5190 

45.0000 

19.7079 

39.3750 

17.5217 

35.0000 

15.7736 

31.5000 

9 

26.4064 

52.7778 

22.6377 

45.2381 

19.8118 

39.5833 

17.6141 

35.1852 

15.8568 

31.6667 

1O 

26.5450 

53.0556 

22.7565 

45.4762 

19.915739.7917 

17.7065 

35.3704 

15.9400 

31.8333 

11 

26.6835 

53.3333 

22.8752 

45.7143 

20.  0197  140.0000 

17.7990 

35.5550 

16.0232 

32.0000 

12 

26.8220 

53.6111 

2-2.9940 

45.9524 

20.123640.2083 

17.8914 

35.7407 

16.1063 

32.1007 

13 

26.9605 

53.8889 

23.1127 

46.1905 

20.2275 

40.4107 

17.9838 

35.9259 

16.1895 

32.3333 

14 

27.0991 

54.1667 

23.2315 

46.4286 

20.3315 

40.0250 

18.0762 

36.1111 

16.27'27 

32.5000 

15 

27  237'6 

54.4444 

23.3503 

46.6607 

20.4354 

40.8333 

18.1080 

36.2963 

16.3559 

32.0007 

16 

27^3809 

54.7222 

23.4731 

46.9048 

20.5429 

41.0417 

18.2642 

30.4815 

16.4420 

32.8333 

17 

27.5242 

55.0000 

23.5960 

47.1429 

20.6504 

41.25CO 

18.3597 

36.6667 

10.5280 

33.0000 

18 

27.6627 

55.277* 

23.7147 

47.3810 

20.7544 

41.4583 

18.4522 

36.8519 

16.6112 

33.1667 

19 

27.8013 

55.5556 

23.8335 

47.6190 

20.8583 

41.6667 

18.5446 

37.0370 

16.6944 

33.3333 

2O 

27.9398 

55.8333 

23.9522 

47.8571 

•20.9622 

41.8750 

18.6370 

37.2222 

16.777'6 

33.5000 

21 

28.0783 

56.1111 

24.0710 

48.0952 

21.0662 

42.0833 

18.7294 

37.4074 

10.8007 

83.0007 

22 

28.2169 

56.3889 

24.1898 

48.3323 

21.1701 

42.2917 

18.8218 

37.5926 

16.9439 

33>3£3 

23 

28.3554 

56.0667 

•24.3085 

48.5714 

21.2740 

42.5000 

18.9142 

37.7778 

".0271 

34.0000 

24 

28.4939 

56.9444 

24.4273 

48.8095 

21.3780 

42.7083 

19.0066 

37.9630 

1".1103 

34.1007 

25 

28.6324 

57.2222 

24  5460 

49.0476 

21.4819 

42.9167 

19.0990 

38.1482 

17.1935 

34.3333 

26 

28.7710 

57.5000 

24.0648 

49.2850 

21.5858 

43.1250 

19.1914 

38.3333 

"  2707 

34.5000 

27 

28.9095 

57.7778 

24.7835 

49.5238 

21.6898 

43.3333 

19.2838 

38.5185 

"^3599 

34.G6C7 

28 

29.0480 

58.0556 

24.9023 

49.7619 

21.7937 

43.5417 

19.3762 

38.7037 

17.4430 

34.8333 

29 

29.1866 

58.3333 

25.0211 

50.0COO 

21.8976 

43.7500 

19.4686 

38.8889 

".5262 

35.0000 

30 

29.3-251 

58.0111 

25.1398 

50.2381 

22.0016 

43.9583 

19.5610 

39.0741 

".6094 

35.1667 

31 

29.4630 

58.8889 

25.2586 

50.47'62 

22.1055 

44.1667 

19.6534 

39.2593 

".6920 

35.3333 

32 

29.0069 

59.1667 

25.3814 

50.7143 

22.2130 

44.3750 

19.7490 

39.4444 

".7787 

35.5000 

33 

29.7502 

59.4444 

25:5043 

50.9524 

22.3205 

44.5833 

19.8446 

39.6296 

".8047 

35.6607 

34 

29.8888 

59.7222 

25.6230 

51.1905 

22.4245 

44.7917 

19.9370 

39.8148 

".9479 

35.8333 

35 

30.0273 

00.0000 

25.7418 

51.4286 

22.5?84 

45.0000 

20.0294 

40.0000 

18.0311 

30.0000 

36 

30.1658 

60.2778 

25.8006 

51.6667 

22.6323 

45.2083 

20.1218 

40.1852 

18.1143 

30.1007 

37 

30.3043 

60.5556 

25.9793 

51.9048 

22.7363 

45.4167 

20.2142 

40.3704 

18.1974 

30.3333 

38 

30.4429 

60.8333 

26.0981 

52.1429 

22.8402 

45.6250 

20.3066 

40.5556 

18.2806 

36.5000 

39 

30.5814 

61.1111 

26.2168 

5-2.3810 

22.9441 

45.8333 

20.3990 

40.7407 

18.3638 

36.6667 

40 

30.7199 

61.3889 

26.3356 

52.6190 

23.0481 

46.0417 

20.4914 

40.9259 

18.4470 

36.8333 

41 

30.8585 

61.6667 

•26.4543 

52.8571 

23.1520 

46.2500 

20.5838 

41.1111 

18.5302 

37.0000 

42 

30.9970 

61.9444 

26.5731 

53.0952 

23.2559 

46.4583 

20.6762 

41.2963 

18.6134 

37.1007 

43 

31.1355 

62.2222 

26.6919 

53.3333 

23.3599 

46.6667 

20.7686 

41.4815 

18.6966 

37.3333 

44 

31.2740 

62.5000 

26.8106 

53.5714 

23.4638 

46.8750 

20.8610 

41.6667 

18.7797 

37.5000 

45 

31.4126 

62.7778 

26.9294 

53.8095 

23.5677 

47.0833 

20.9534 

41.8519 

18.8629 

37.0007 

46 

31.5511 

03.0556 

•27.0481 

54.0476 

23.6717 

47.2917 

21.0458 

42.0370 

18.9461 

37.8333 

47 

31.6896 

63.3333 

27.1669 

54.2856 

23.7756 

47.5000 

21.1382 

42.2222 

19.0293 

38.0000 

48 

31.8282 

63.6111 

27.2857 

54.5238 

23.8795 

47.7083 

21.2307 

42.4074 

19.1125 

38.1067 

49 

31.9667 

63.8889 

27.4044 

54.7619 

23.9835 

47.9167 

21.3231 

42.5926 

19.1957 

38.3333 

50 

32.1100 

64.1667 

27.527'3 

55.0000 

24.0910 

48.1-250 

21.4186 

42.7778 

19.2817 

38.5000 

51 

32.253304.4444 

27.6501 

55.2381 

24.1985 

48.3333 

21.5142 

42.9630 

19.3678 

38.6607 

52 

32.3018  04.7222 

27.7089 

55.4762 

24.3024 

48.5417 

21.6066 

43.1482 

19.4510 

38.8S33 

53 

32.530305.0000 

27.8870 

55.7143 

24.4064 

48.7500 

21.6990 

43.3333 

19.5341 

39.0000 

54 

32.00S9G5.2778 

•28.0004 

55.9524 

24.5103 

48.95H3 

21.7914 

43.5185 

19.0173 

39.1607   55 

3-3.  8074,65.  555fi 

•28.1251 

50.1905 

24.6142 

49.1667 

21.8839 

43.7037 

19.7005 

39.333*  56 

3-2.9)59  05.8333 

•28.2-139 

56.4280 

24.7182 

49.3750 

21.9763 

43.8889 

19.7837 

39.5000  57 

38.0845l66.llll 

28.36-27 

50.00(57 

24.8221 

49.5833 

22.0087 

44.0741 

19.8069 

39.0007  58 

33.223066.3889 

28.4814 

56.9048 

24.9260 

49.7917 

22.1611 

44.2593 

19.9501 

39.8333,  59 

53 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


40 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Are. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

200.079400.000 

100.043200.000 

66.7000  133.3:33 

50.0295 

100.00040.0281 

80.0000 

1 

200.910401.667 

100.459200.833 

66.9770  133.889 

50.2373 

100.41740.1943 

80.3333 

3 

201.  741'  403.  333 

100.874 

201.667 

67.2539  134.444  50.4450  100.  833!  40.  3605 

80.0007 

3 

302.572405.000 

101.290 

202.500 

67  .  5309  1  35  .  000  50  .  6528 

101.25040.5207 

81.0000 

4 

203.403406.667 

101  .705 

203.333 

67  8078 

135.556  50.8605  101  .667140.6929 

81.3333 

5 

204.233408.333 

102.120 

204.167 

08.0848 

136.  11  1)51.  0682 

102.083 

40.8592 

81.6667 

G 

205.064410.000 

102.536 

205.000 

68.3618 

136  667:51.2760102.500 

41.025482.0000 

7 

205.924411.667 

102.966 

205.833 

08.6483 

137.222!51.4909 

102  917 

41.1073 

82.3333 

8 

206  783413  333 

103  395 

206.667 

68  9348 

137.  778!  51.  7  058 

103.333 

41.3692 

82.0007 

9 

207.614 

415.000 

1U3.811 

207.500 

69.2117 

138.333 

51.9135 

103.750 

41.535583.0000 

1O 

208.445 

416.667 

104.226 

208.333 

69.4887 

138.889 

52.1213 

104.167 

41.7017 

83  3333 

11 

209.275418  333 

104.612 

209.167 

69.1657 

139.444 

52.3290 

104.583 

41.8679 

83  6667 

13 

210.106420.000 

105.057 

210.000 

70.0426 

140000 

52.5307 

105.000 

42.0341  84  0000 

13 

210.937 

421.667 

105  472 

210.833 

70.3196 

140.556 

52.7445 

105  417 

42.2003 

84.3333 

14 

211.768423.333 

105.888 

211.667 

70.5960 

141.111 

53.9522 

105.833 

42.36455 

84.0007 

15 

212.599425.000 

1  00.303 

212.500 

70  8735 

141.667 

53.  1600!  106.  250 

42.532785.0000 

16 

213.  4291426.  667 

106.719 

213  333 

71.1505 

142.222 

53  3077 

106.667 

42.698985.3333 

17 

214.260428.333 

107.134 

214.167 

71.4274 

142  778 

53.5754 

107.083 

42.8051 

85.0007 

18 
10 

215.091  430.000 
215.922431.667 

107.549 
107.965 

215.000 
215.833 

71.7044 
71.9814 

143.333 

143.889 

53.7832 
53.9909 

107.500 
107.917 

43.0314 
43.1976 

86.0000 
86.3333 

30 

216  753 

433.333 

108.380 

216.667 

72.2583 

144.444 

54.1987 

108.333 

43.3038 

86.6607 

31 

217.583435.000 

108.796 

217.500 

72.5353 

145.000 

54.4064 

108.750 

43.5300 

87.0000 

33 

218.  4141430.6*57 

109.211 

218.333 

72.8122 

145.556 

54.6141 

109.107 

43.690287.3333 

33 

219.274  438.333 

109.641 

219.167 

73.09SS 

140  111 

54.  82901  109.  583 

43  8681 

87.0007 

34 

220.133 

440.000 

110.071 

220.000 

73.3853 

146.667 

55.0439 

110.000 

44.0401 

88  00(50 

35 
36 

220.1)64 
221.795 

441.667 
443.  333 

110.486 
110.901 

220.  833 
221.667 

73.6022 
73.9392 

147.222 

147.778 

55.2517  110.417 
55.4594  110.833 

44.2003 
44.3725 

88.3333 
83.6667 

37 

222.626 

445.000 

111.317 

222.500 

74.2162 

148.333 

55.6672,111.250 

44.5387 

89.0000 

38 

223.456 

446.067 

111.732 

223.313 

74.4931 

148.889 

55.8749 

111.667 

44.7019 

89.3333 

39 

224.287 

448.3-13 

112.148 

224.167 

74.7701 

149.444 

56.0827 

112.083 

44.8711 

89.0007 

30 

225.118 

450.000 

112.563 

225.000 

75.0470 

150  000 

56.2904 

112.500 

45.0373 

90.0000 

31 

225.949 

451.667 

112.979 

225.883 

75.3240 

150.556 

56.4981 

112  917 

45.2036 

90.3333 

33 

226.780 

453.333 

113  394 

226.667 

75.6010 

151.111 

56.7059 

113.333 

45.3698 

90.0007 

33 

227.610 

455.000 

113.809 

227.500 

75.8779 

151.667 

56.9136 

113.750 

45.5360 

91.0000 

34 

228.441 

456.667 

114.225 

228.333 

76.1549 

152.222 

57.1214 

114.167 

45.7022 

91.3333 

35 

2-29.272 

458.333 

114.640 

229.167 

76.4319 

152.778 

57.3291 

114.583 

45.  8684  1  91.  660  / 

36 

230.103 

4GO.OOO 

115.056 

230.000 

76.7088 

153.333 

57.5308 

115.000 

46  0346 

92.0000 

37 

230.962461.667 

115.485 

230.833 

76  9953 

153.889 

57.7517 

115.417 

46.2065 

92.3333 

38 

23  1.822  '463.  333 

115.915 

231.667 

77.2818 

154.444 

57.9006 

115.833 

46.3785 

92.6067 

39 

232.652 

465.000 

116.330 

232.500 

77.5588 

155.000 

58.1744 

116.250 

46.5447 

93.0000 

4O 

233.483 

466.667 

116.746 

233.333 

77.8358 

155.556 

58.3821 

116.667 

46.7109 

93.3333 

41 

234.314468.333 

117.161 

234.167 

78.1127 

156.111 

58.5899  117.083 

46.8771 

93.6007 

43 
43 

235.145470.000 
235.976|  471.  667 

117.577 
117.992 

235.000 
2a5.  833 

78.3897 
78.6666 

156.667 

157.222 

58.7976117.500 
59.  0053!  117.  917 

47.043394.0000 
47.2095194.3333 

44 

236.806473.333 

118.408 

236.667 

78.9436 

157.778 

59.2131 

118.333 

47.3758 

94.0007 

45 

237.  637  i  475.  000 

118.823 

237.500 

79.2206 

158.333 

59.  4208|  118.  750 

47.5420:95.0000 

46 

238.468476.667 

119.233 

238.333 

79  4975 

158.889 

59.6286 

119.167 

47.7082 

95.3333 

47 

239.299478.333 

119.654 

239.167 

79.7745 

159.444 

59.8363119.583 

47.  8744  195.6607 

48 

240.130480.000 

120.069 

240.000 

80.0515 

160.000 

60.0440 

120.000 

48.0406 

96.0000 

49 

240.  960  481.  C67 

120.485 

240.  833 

80.3284 

100.556 

60.2518 

120.417 

48.2068j96.3333 

50 

241.791 

483.333 

120.900 

241.667 

80  6054 

161.111 

60.4595 

120.833 

48.3730  96  6007 

51 

242.651 

485.000 

121.330 

242.500 

80.8019 

101.6(37 

60.  6744  1121.250 

48.545097.0000 

53 

•343.510 

486.667 

121.760 

243.333 

81.1784 

102.222 

60.8893 

121.667 

48.7109 

1)7.3333 

53 

.'44.341 

488.333 

122.175 

244.107 

HI.  4651 

162.778 

61  .0971 

122.083 

48.8831  [97.6667 

54 

215.172 

490.000 

122.590 

245.000 

81.7323 

163.333 

61.3048  122.500 

49.045)398.0000 

55 

246.003 

491  .667 

123.006 

215.833 

S2.00U3 

163.889 

61.5125 

122.917 

49.2155 

98.3333 

r^/r» 

346.833 

493.333 

123.421 

246.607 

82.2802 

164.444 

61.7203128.333 

49.3817 

98.6007 

57 

217.664 

495.000 

123.837 

247.500 

82.5632 

165.00061.9280 

128.750 

49.5480 

99.0000 

58 

218.495 

496.667 

124.252 

248.333 

82.8402 

lG5.55602.ia58 

124.167 

49  7142 

99.3333 

59  249.326 

498.333 

124.607 

249.107 

83.1171 

166.111  62.3435)124.583 

49.8804  99.6067 

54 


TABLE  XIV. — ACTUAL  TANGENTS,   ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

4° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

25  0300 

Arc. 
50.0000 

Tan. 

2272535 

Arc. 
44.4444 

Tan. 
2070332 

Arc. 

M. 

33.3615 

66.6667 

28.6002 

57.1429 

40.0000 

O 

33.5000 

66.9444 

28.7189 

57.3810 

25.1339 

50.2083 

22.3459 

44.6296 

20.1164 

40.1667 

1 

88.6386 

67.2222 

28.8377 

57.6190 

^5  2378 

M).4167 

.'2.4383 

44.8148 

20.1996 

40.3333 

2 

33.7771 

67.5000 

28.9564 

57.8571 

25.3418 

50.6250 

22.5307 

45.0000 

20.2828 

40.5000 

3 

33.9156 

67.7778 

29.0752 

58.0952 

25.4457 

50.8333 

22.6231 

45.1852 

20.3660 

40.6667 

4 

34.0542 

68.0556 

29.1940 

58.3333 

25.5496 

51.0417 

22.7155 

45.3704 

•20.4492 

40.8333 

5 

34.1927 

68.3883 

29.3127 

58.5714 

26  6536 

51.2500 

22.8079 

45.5556 

20.5324 

41.0000 

6 

34.3360 

68.6111 

29.4356 

58.8095 

25.7611 

51.4583 

22.9035 

45.7407 

20.6184 

41.1667 

7 

31.4793 

68.8889 

29.5584 

59.0476 

25.8686 

51  .  6667 

22.9991 

45.9259 

20.7045 

41.3333 

8 

34.6178 

69.1667 

29.6772 

59.2856 

25.9725 

51.8750 

23.0915 

46.1111 

20.7877 

41.5000 

9 

34.7564 

69.4444 

29.7959 

59.5238 

26.0765 

52.0833 

23.1&39 

46.2963 

20.8708 

41.6667 

10 

34.8049 

69.7222 

29.914759.7619 

26.1804 

52.2917 

23.276346.4815 

20.954041.8333 

11 

35.0334 

70.0000 

30.0335 

60.0000 

26.2843 

52.5000 

23.368746.6667 

21.037242.0000 

12 

35.1719 

70.277830.1522 

60.2381 

26.3883 

52.7083 

23.4611  46.8519 

21.120442.1667 

13 

35.3105 

70.555630.2710 

60.4762 

26.4922 

52.9167 

23.  5535!  47.  0370 

21.2036  42.3333 

14 

35.4490 

70.83:53:30.3897 

60.7143 

26.5961 

53.1250 

23.6459I47  2222 

21.2868;42.5000 

15 

35.5875 

71.1111  30.  5085|  60.  9524 

26.7000 

53.3333 

23.7383 

47.4074 

21.369942.6667 

16 

35.7261 

71.3889 

30.  6272!  61.  1905 

26.8040 

53.5417 

23.8307 

47  5926 

21.  4531  J42.  8333 

17 

35.8646 

71.6667 

30.7460 

61.4286 

26.9079 

53.7500 

23.9231 

47.7778 

21.  5363  '43.0000 

18 

30.0031 

71.9444 

30.8648 

61.6667 

27.0118 

53.9583 

24.0155 

47.9630 

21.6195 

43.1667 

19 

36.1416 

72.2222 

30.9835 

61.9048 

27.1158 

54.1667 

24.1079 

48.1482 

21.7027 

43.3333 

20 

36.2802 

72.5000 

31.1023 

62.1429 

27.2197 

54.3750 

24.2003 

48.3333 

21.7859 

43...000 

21 

86.4187 

72.7778 

31.2210 

62.3810 

27.3236 

54.5833 

24.2927 

48.5185 

21.8691 

43.6667 

22 

36.5620 

73.0556 

31.3439 

62.6190 

27  4312 

54.7917 

24.38^3 

48.7037 

21.9551 

43.8333 

23 

36.7053 

73.3333 

31.4667 

62.8571 

27.5387 

55.0000 

24.4839 

48.8889 

22.0412 

44.0000 

24 

36.8438 

73.6111 

31.5855 

63  095:. 

27.6426 

55.2083 

24.5763 

49.0741 

22.1243 

44.1667 

25 

36.982-1 

73.8889 

31.7043 

63  3333 

27.7465 

55.4167 

24.6687 

49.2593 

22.2075 

44.3333 

26 

37.1209 

74.1667 

31.8230 

63.5714 

27.8505 

55.6250 

24.7611 

49.4444 

22.2907 

44.5000 

27 

37.2594 

74  4444 

31.9418 

63.8095 

27.9544 

55.8333 

24.8535 

49.6296 

22.3739 

44.6667 

28 

37.3380 

74.7222 

32.0605 

64.0470 

28.0583 

56.0417 

24.9459 

49.8148 

22.4571 

44.8333 

29 

37.5365 

75.0000 

32.1793 

64.2R5T 

28.1623 

56.2500 

25.0383 

50.0000 

22.5403 

45  0000 

30 

37.675C 

75  2778 

32.2980 

64.5238 

28.2662 

56.4583 

25  1307 

50.1852 

22.6235 

45.1667 

31 

37  8135 

75.5556 

32.4168 

64.7619 

28.3701 

56.6667 

25.2231 

50.3704 

22.7066 

45.3333 

32 

37.9521 

75.8333 

32  5356 

65.0000 

28.4741 

56.8750 

25.3155 

50.5556 

22.7898 

45.5000 

33 

38.0906 

76.1111 

32.6543 

65.2381 

28.5780 

57.0833 

25.4079 

50.7407 

22.8730 

45.6667 

34 

38.2291 

70.3889 

32.7731 

65.4762 

28  68T9 

57.2917 

25.5004 

50.9259 

22.9562 

45.8833 

35 

3S  367? 

76  6667 

32.8918 

65.7143 

28.7859 

57.5000 

25  5928 

51.1111 

23.0394 

46.0000 

36 

38.5110 

76  9444 

33.0147 

65  9524 

28.8934 

57.7083 

25.6883 

51.2963 

23.1254 

46.1667 

37 

38.6513 

77.2222 

88.1875 

66.1905 

29.0009 

57.9167 

25.7839 

51  4815 

23.2115 

46.3333 

38 

38.7928 

77.5000 

33  2563 

66.4286 

29.1048 

58.1250 

25.8763 

51.6667 

23.2947 

46.500U 

39 

38.9313 

77.7778 

33.3751 

66.6667 

29.2088 

58.3333 

25.9687 

51.8519 

?3.3779 

46.6667 

40 

39.0699 

78.0556 

33.4938 

66.9048 

29.3127 

58  5417 

26.0612 

52.0370 

23.4610 

46.83^3 

41 

39.2084 

78.8388 

33  6126,67.1429 

29.4166 

58.7500 

26.1536 

52.2222 

23.5442 

47.0000 

42 

39.3469 

78.6111 

88.781367.8810 

29.5206 

58.9583 

26.2460152.4074 

23.6274 

47.1667 

43 

39.4854 

78.8889 

33.  8501  j  67.  61  90 

29.6245 

59.1667 

26.338452.5926 

23.7106 

47.3333 

44 

39.6240 

79.1667 

33.  9088  «7.  8571 

29.7284 

59.3750 

26.  4308!  52.  7778 

23.7938 

47.5000  45 

39  7625 

79.4444 

34.087668.0952 

29.8324 

59.5838 

26.  5232  !  52.  9630 

23.  877047.66C7   4G 

39.9010 

79.7222 

34  2064  68.8333 

29.9363 

59.7917 

26.6156J  53.  1482 

23  960247.83:i3  47 

40.0396 

80.0000 

34.3251  68.5714 

30.0402 

60.0000 

26.7080  £3.8383 

24.043348.0000 

48 

40  1781 

80  2778 

34.4439 

68.8095 

30.1442 

60.2083 

26.8004.53.5185 

24.1265 

48.1667 

49 

40.3166 

80.5556 

34.5626 

69.0476 

30.2481 

60.4167 

26.892853.7037 

24.2097 

48.3333 

5O 

40.4580 

80.833331.685569.2856 

80.3556 

60.62.M) 

26.988453.8889 

24.2958  48  5000 

51 

40  6032 

85.1111 

34.808369.5238 

30.4631 

60.8333 

27.084054  0741 

24.381848.6667 

52 

40.7418 

81.3889 

31.9271  69.7619 

30.5671 

61.0417 

27.176454.2593 

24.465048.8333 

53 

40.8803 

81.  6667!  35  045970.0000 

30  6710 

61.2500 

27.2688  54.4444 

24.548249.0000 

54 

41.0188 

81.  9444  35.  1646  70.  23S1 

30.7749 

61.4583 

27.  361  2  54.629* 

24.6314  49  1667 

55 

41.1573 

82.  2222  35.  2834  70.  47(5-. 

30.8789 

61  .66(57 

27.4536  54.8148 

24.714649.3333 

50 

41.2959 

82.500035.4021  70.  7H3 

30.9828 

61.8750 

27.546055.0000 

24.797749.5000 

57 

41.4344 

82  7778  35.5209  70.9524 

31.0867 

62  0833 

27.638455.1852 

24.880949.6667 

58 

4  1  .  5?<J$83  .  0556!35  .  6396  71  .  1  905  31  .  1  907 

62.2917 

27.7308  55.3704 

24.9641  49.8233 

59 

55 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


5° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

o 

Tau. 
2~50.157 

Arc. 

sooTooo 

Tan. 
125^083 

Arc. 

2507UOO 

Tan. 
88.3941 

Arc. 

feliTtiij? 

Tan  . 
04.5512 

Arc. 

1257000 

Tan. 
50.0466 

Arc. 

iooTooo 

1 

250.987 

501.667  125.498 

250.833 

83.6711 

1(17.222 

02.7590 

125.417150.2128 

100.333 

2 

251.818 

503.333125.914 

251.667 

83.94HO 

Hi?.  778 

62.9667 

125.83350.3790 

100.667 

3 

252.649 

505.000126.329 

252.500 

84.2250 

16H.333 

03.1745 

126.25050.5452 

101.000 

4 

258.480 

506.667 

126.745 

253.333 

84  5019 

168.889 

U3.8S22 

126  66750.7114 

101.333 

5 

254.339 

508.333 

127.174 

254.167 

84.7885 

J  69.  444 

63.5971 

127.083 

50.8834 

101.667 

6 

255.  1W 

510.000 

127.604 

255.000 

85.0750 

17U.OOO 

63.8120 

127.500 

51.0553 

102.000 

7 

256.029 

511.667J128.019 

255.833 

05.3519 

170.556 

64.0198 

127.91? 

51.2215 

102.333 

8 

256.860 

513.  333!  128.  435 

256.66? 

85.6289 

171.111 

64.2275 

128.333 

51.3877 

102.667 

9 

257.691 

515.000 

128.850 

257.500 

85.9058 

171.667 

64.4352 

128.750 

51.5539 

103.000 

10 

258.522 

516.667 

129.266 

258.333 

86.1828 

172.222 

64.6430 

129.167 

51.7202 

103  333 

11 

259.353 

518.333 

129.681 

259.167 

86.4598 

172.778 

64.8507 

129.583 

51.8864 

103.667 

12 

260  183 

520.000 

130.096 

260.000 

86  7'367 

173.333 

65.0585 

130.000 

52.0526 

104.000 

13 

261  .014 

521.667 

130.512 

260.833 

87.013? 

173.889 

65.2662 

130.417 

52.2188 

104.333 

14 

261.845 

523  333,130  927 

261.66; 

87.290? 

174.444 

65.4739 

130.833 

52.3850 

104.667 

15 

262.676 

525.000  131.343 

262.500 

87.5676 

75.000 

65.6817 

131.250 

52.5512 

105.000 

16 

263.507 

526.667 

131.758 

263.333 

87.8446 

75.556 

65.8894 

131.667 

52.7174 

105.333 

17 

26  4.  &37 

528.333 

132.174 

264.16? 

88.1215 

76.111 

66.0972 

132.083 

52.8836 

105.667 

18 

265.168 

530.000 

132.589 

265  000 

88.3985 

76.66', 

66  .  3049 

132.500 

53.0498 

106.000 

19 

266.028 

531.667 

133.019 

265.833 

88  6850 

77.222 

66.5198 

132.91? 

53.2218 

106.333 

20 

266.887 

533.333 

133.448 

266.66? 

88.9715 

177.778 

66.7347 

133.333 

53.3937 

106.667 

21 

267.718 

535.000 

133.864 

267.500 

89.2485 

78.333 

66.9421 

133.750 

53.5599 

107.000 

22 

268.549 

536.667 

131.279 

268.333 

89.5254 

178.889 

67.1502 

134.16? 

53.7261 

107.333 

23 

269.379 

538.  333 

134.695 

269.167 

89.8024 

179.444 

67.3579 

134.583 

53.8924 

107.667 

21 

270.210 

540.000 

135.110 

270.000 

90.0794 

180.000 

67.5657 

135.00054.0586 

108.000 

25 

271.041 

541  667 

135.526 

270  833 

90.3563 

180.556 

67.7734 

135.417 

54.2248 

108.333 

2G 

271.872 

543.333 

135.941 

271.667 

90.6:333 

181.111 

67.9811 

135  833 

54.3910 

108.667 

27 

272.703 

545.000 

136.356 

272.500 

90.9103 

181  .  667 

68.1889 

136  250 

54.5572 

109.000 

28 

273!  533 

546.667 

136.772 

273.333 

91.1872 

182  222 

68.3966 

136.667 

54.72-34 

109.333 

29 

274.364 

548.333 

137.18? 

274.16? 

91.4642 

182.778 

68.6044 

137.083 

54.8896 

109.667 

30 

275.195 

550.000 

137.603 

275.000 

91.7411 

183.333 

68.8121 

137.500 

55.0558 

110.000 

31 

276.055 

551.667 

138.032 

275.833 

92.0277 

183.889 

69.0270 

137.917 

55.2278 

110.333 

32 

276.914 

553.333 

138.462 

276.667 

92.3142 

184.444 

69.2419 

138.333 

55.3997 

110.667 

33 

277.745 

555.000 

138.877 

277.500 

92.5911 

185.000 

69.4496 

138.750 

55.5659 

111.000 

34 

278.576 

556.667 

139.293 

278.333 

92.8681 

185.556 

69.6574 

139.167 

55.7321 

111.333 

35 

279.406 

558.333 

139.708 

279.167 

93.1451 

186.111 

G9.8651 

139.583 

55.8983 

111.667 

36 

280.237 

560.000 

140.124 

280.000 

93.4220 

186.66? 

70.0729 

140.000 

56.0646 

112.000 

37 

281.068 

561.667 

140.539 

280.833 

93.6990 

187.222 

70.2806 

140.417 

56.2308 

112.333 

38 

281.899 

563.333 

140.955 

281.667 

93.9759 

187.778 

70.4883 

140.833 

56.3970 

112.667 

39 

282.730 

565.000 

141.370 

282.500 

94.2529 

188.333 

70.6961 

141.250 

56.5632 

113.000 

40 

283.560 

566.667 

141.785 

283.333 

94.5299 

188.889 

70.9038 

141.667 

56.7294 

113.333 

41 

284.391 

568.333 

142.201 

284.16? 

94.8068 

189.444 

71.1116 

142.083 

56.8956 

113.667 

42 

285.222 

570.000 

142.616 

285.000 

95.0838 

190.000 

71.3193 

142.500 

57.0618 

114.000 

43 

286.053 

571.667 

143.032 

285.833 

95.360? 

190.556 

71.5270 

142.917 

57.2280 

114.333 

44 

286.884 

573.333 

143.447 

286.667 

95.63?7 

191.111 

71.7348 

143.333 

57.3942 

114.667 

45 

287.743 

575.000 

143.877 

287.500 

95.9242 

191.66? 

71.9497 

143.750 

57.5662 

115.000 

46 

288.602 

576.667 

144.307 

288.333 

96.2107 

192.222 

72.1646 

144.167 

57.7381 

115.333 

47 

289.433 

578.333 

144.722 

289.167 

96.4877 

192.778 

72.3723 

144.583 

57.9043 

115.607 

48 

290.264 

580.0001  145.  137  290.  000 

96.7647 

193.333 

72.5801 

145.000 

58.0705 

116.000 

49 

291.095 

581.667 

145.553 

290.833 

97.0416 

193.889 

72.7878 

145.417 

58.2368 

116.333 

5O 

291.926 

583.333 

145.968 

291.667 

97.3186 

194.444 

72.9956 

145.833 

58.1030 

116.66? 

51 

292.756 

585.000(146.384 

292.500 

97.5955 

195.000 

73.203-3 

146.250:58.5092 

117.000 

52 

293.587 

586.667  146.799 

293.333 

97.8725 

195.556 

73.4110 

146.667  58.7354 

117.333 

53 

294.418 

588.333147.214294.167 

98.1495 

196.111 

73.  (5  188  147.0S358.9016 

117.607 

54 

295.219 

590  .  000  147  .  630  295  .  000 

98.4264 

196.667 

73.S265  147.50059.0678 

118.000 

55 

296.080 

591.667  148.045295.833 

98.7034 

197.222 

74.0343  147.  917:59.  2340 

118.333 

56 

296.910 

593.333  148.461  296.607 

98.9803 

11)7.778 

74.2420il48.H33  59.4002 

118.66? 

57 

297.770 

595  .  000  1  48  .  890  297  .  500 

99.2669;  98.333 

74.  4569  i  148.  75059.  5722 

119.000 

58 

298.629 

596.667  149.320,298.333 

99.5534  198.889 

74.  671  S'  149.  107  59.  7441 

119.333 

59 

299.460 

598.333149.736299.167 

99.  8303!  199.  444 

74.8795;  149.583  59.9103  119.067 

56 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

5° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |   Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

41.711483.3333 

!5.7584 

71.4286 

31.294662.5000 

27.8232 

55.5556 

25.047350.0000 

O 

41.850083.6111 

15  .  8?7'2 

71.6667 

1.398562.7083 

27.915655.7407 

25.  1305  ;50.  1667 

1 

41.988583.8889 

35.995971.9048 

31.502562.9167 

28.008055.9259 

25.  2137  EO.  3333 

42.127084.1667 

36.1147 

72.1429 

31.606463.1250 

28.1004 

56.1111 

25.296950.5000 

3 

42  265684  4444 

36.233472.3810 

31.710363.3333 

28.  1  928  ''  56.  2963 

25.380050.666? 

4 

42.408984.7222 

36.3563 

72.6190 

31.817963.541? 

28.288456.4815 

25.4661 

50.8333 

5 

42.552285.0000 

36.4791 

72.8571 

31.925463.7500 

28.384056.666? 

25.5521 

51.0000 

6 

42.690785.2778 

36.5979 

73.0952 

32.029363.9583 

28.476456.8519 

25.6353 

51.1667 

7 

42.8292 

85.5556 

36.716773.3333 

32.133264.166? 

28.5688 

57.0370 

25.7185 

51-.  3333 

8 

42.9678 

85.8333 

36.8354 

73.5714 

32.2372 

64.3750 

28.6612 

57.2222 

25.8017 

51.5000 

9 

43.1063 

86.1111 

36.9542 

73.8095 

32.3411 

64.5833 

28.7536 

57.4074 

25.8849 

51.6667 

1O 

43.  2448  i  86.  3889 

37.0729 

74.0476 

32.4450 

64.7917 

28.8460 

57.5926 

25.9681 

51.8333 

11 

43.  3833  1  86.  6667 

37.1917 

74.2856 

32  5490 

65.0000 

28.9384 

57.7778 

26.0513 

52.0000 

13 

43.5219 

86.9444 

37.3105 

74.5238 

32.652965.2083 

29.0308 

57.9630 

26.1344 

52  166? 

13 

43.6604 

87.22-22 

3".  4292 

74.7619 

32.7568 

65.4167 

29.1232 

58.1482 

26.2176 

52.3333 

14 

43  7989 

87.5000 

3".  5480 

75.0000 

32.8608 

65.6250 

29.2156 

58.3333 

26.3008 

o2.5000 

15 

43.D375 

87.7778 

3".  6667 

75.2381 

32.9647 

65.8333 

29.3080 

58.5185 

26.3840 

52.6667 

16 

44.0760 

88  0556 

3  -.7855 

75.4762 

33.0686 

66.041? 

29.4004 

58.7037 

26.4672 

52.8333 

17 

44.2145 

88.3333 

3~.9042 

75.7143 

33.1726 

66.2500 

29.4928 

58.8889 

26.5504 

53.0000 

18 

44.3578 

88.6111 

38.0271 

75.9524 

33.2801 

66.4583 

29.5884 

59.0741 

26.6364 

53.1667 

19 

44.5011 

88.8889 

38.1499 

76.1905 

33.3876 

66.6667 

29.6840 

59.2593 

26.7225 

53.3333 

2O 

44.639? 

89.166? 

38.2687 

76.4286 

33.4915 

66.8750 

29.7764 

59.4444 

26.8057 

53.5000 

21 

44.7782 

89.4444 

38.3875 

76.666? 

33.5955 

67.0833 

29.8688 

59.0296 

26.8888 

53.0667 

22 

44.9167 

89.7222 

38.5062 

76.9048 

33.6994 

67.291? 

29.9612 

59.8148 

26.97'20 

53.8333 

23 

45.0552 

90.0000 

38.6250 

77.1429 

33.8033 

67.5000 

30.0536 

60.0000 

27.0552 

54.0000 

24 

45.1938 

90.2778 

38.7437 

77.3810 

33.90?3i67.708b 

30.1461 

60.1852 

27.1384 

54.1667 

25 

45  3323 

90.5556 

38.  8625  !  77.  61  90 

31.0112 

67.9167 

30.2385 

60.3704 

27.2216 

54.3333 

26 

45.4708 

90.8333 

38.9813 

77.8571 

34.1151 

68.1250 

30.3309 

60.5556 

27.3048 

54.5000 

27 

45.6094 

91.1111 

39  100078.0952 

34.2191  68.3333 

30.4233 

60.7407 

27.3880 

54.666? 

28 

45.7479 

91.3889 

39.2188  78.3333 

34.3230 

68.541? 

30.515? 

60.9259 

27.4711 

54.8333 

29 

45.8864 

91.666? 

39.337578.5714 

34.4269 

68.7500 

30.6081 

61.1111 

27.5543 

55.0000 

30 

46.029? 

91.9444 

39.4604 

78.8095 

34.5345 

68.9583 

30.7037 

61.2963 

27.6404 

55.166? 

31 

46.1730 

92.2222 

39.5832 

79.0476 

34.6420 

69.1667 

30.7993 

61  .4815 

27.7264 

^5.3333 

32 

46.3116 

92.5000 

39.7020 

79.2856 

34.7459 

69.3750 

30.8917 

61.6667 

27.8096 

55.5000 

33 

46.4501 

92.7778 

39.820779.5238 

34.8498 

69.5833 

30.9841 

61.8519 

•27.8928 

55.6667 

34 

46.5886 

93.0556 

39.9395 

79.7619 

34.9538 

69.7917 

31.0765 

62.0370 

27.9760 

55.8333 

35 

46.7271 

93.3333 

40.058380.0000 

35.057? 

70.0000 

31.1689 

62.22-22 

28.0592 

56.0000 

36 

46.865? 

93.6111 

40.1770 

80.2381 

35.1616 

70.2083 

31.2613 

62.4074 

28.1424 

56.1667 

37 

47.0042 

93.8889 

40.295880.4762 

35.2656 

70.416? 

31.3537 

62.5926 

28.2255 

56.3333 

38 

47.142? 

94.166? 

40.4145 

80.7143 

35.3695 

70.6250 

31.4461 

62.7778 

28.308? 

56.5000 

39 

47.2813 

94.4444 

40.5333 

80.9524 

35.4734 

70.8333 

31.5385 

62.9630 

28.3919 

56.6667 

40 

47.4198 

94.7222 

40.6521 

81.1905 

35.5774 

71.0417 

31.6309 

63.1482 

28.4751 

56.8333 

41 

47.5583 

95.0000 

40.770881.4286 

35.6813 

71.2500 

31.7233 

63  .  333-' 

28.5583 

57.0000 

42 

47.6968 

95.2778 

40.8896 

81.666? 

35.7852 

71.4583 

31.8157 

63.5185 

28.6415 

57.166? 

43 

47.8354 

95.5556 

41.008381.9048 

35.8892 

71.6667 

31.9081 

63.703? 

28.7247 

57.3333 

44 

47.978? 

95.8333 

41.1312 

82.1429 

35.9967 

71.8750 

32.0037 

63.8889 

28.8107 

57.5000 

45 

48.1220196.1111 

41.2540 

82.3810 

36.1042 

72.0833 

32.0993 

64.0741 

28.8968 

57.6667 

46 

48.2605|  96.  3889 

41.372882.6190 

36.2081 

72.291? 

32.191764.2593 

28.9799 

57.8333 

47 

48.3990,96.666? 

41.4915 

82.8571 

36.3121 

72.5000 

32.2841  64.4444 

29.0631 

58.000( 

48 

48.5376  96.9444 

41.6103 

83.0952 

36.4160 

72.7083 

32.376564.6296 

29.1463 

58.1667 

49 

48.6761 

97.2222 

41.7291 

83.3333 

36.5199 

72.916? 

32.4689 

64.8148 

29.2295 

58.3333 

50 

48.8146:97.5000 

41.8478 

83.5714 

36.6239 

73.1250 

32.561365.0000 

29.3127 

58.5000 

51 

48.953297.7778 

41.966683.8095 

36.7278 

73.3333 

32.6537 

65.1852 

29.3959 

58.666? 

52 

49.0917^98.0556 

42.0853 

84.0476 

36.8317 

73.5417 

32.7461 

65.3704 

29.4791 

58.8333 

53 

49.230298.3333 

42.2041 

84.28H6 

36.9357 

73.7500 

32.8385 

65.5556 

29.562259.000f 

54 

49.368798.6111 

42.322984.5238 

37.0396 

73.9583 

32.930965.740" 

29.645459.1667 

55 

49.507398.8889 

42.4416 

84.7619 

37.1435 

74.166" 

33.023365.9259 

29.728659.333S 

56 

49.650699.166? 

42.504585.0000 

37.2511 

74.3750 

33.1189  66.111 

29.814759.500C 

>   57 

49.793999.4444 
49.932499.7222 

42.687385.2381 
42.8061  85.4762 

37.358674.5833 
37.4625l74.791" 

33.214566.296 
33.  3069  166.481 

29.900759.666r 
29.983959.833^ 

'   58 
\  59 

57 


TAT5LE    XIV. — ACTUAL    TANGENTS,    ETC 


6° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~O~ 

300.291 

600  .  000  1  50  .  1  5  1  300  .  000 

100.107 

200.000 

75.0873 

150.000 

00.0705 

120.000 

1 

301.122 

601.667  150.56(5  300.883 

100.3S4  200.556 

75  2950 

150.417 

60.2427 

120.3:>3 

3 

301.953 

(303.333  lf>0.  982  30  1.607 

100  661  201.111 

75.5028 

150.833 

60  4090 

120.007 

3 

302.783 

605  .  000  151  .  397  302  .  500 

100.938201.667 

75.7105 

151.250 

60.5752 

121  000 

4 

303.614 

606.  6671151.813  303.  333 

101.215 

202.222 

75.9182 

151.667 

60  7414 

121  333 

5 

304.445 

608.  333  !  152.  228  j  304.  167 

101.492 

202.778 

76.1260 

152.083 

60.9070 

121.007 

6 

305.276 

610.000  152.  643  '305.  000 

101.769 

203.333 

76.3337 

152  500 

01.0738 

122  000 

7 

306.107 

611.667 

153.059305.833 

102.046 

203.889 

76.5415 

152.917 

01.2400 

122  333 

8 

306.937 

613.333  153.  474  1306.667 

102.323 

204.444 

76.7492 

153.333 

61.4062 

122.007 

9 

307.797 

615.000 

153.904 

307.500 

102.609 

205.000 

76.9641 

153.750 

61.5782 

123.000 

10 

308.656 

616.667 

154.334 

308.333 

102.896 

205.556 

77.1790 

154.167 

61.7501 

123.333 

11 

309  487 

618.333  154.  749!309.  167 

103.173 

206.111 

77.3808 

154.583 

01.9163 

123.007 

13 

310.318 

620.000 

155.  1651310.  000 

103.450 

206.667 

77.5945 

155.000 

02.0825 

124.000 

13 

311.149 

621.667 

155.580310.833 

103.727 

207.222 

77.8022 

155.417 

02.2487 

124.333 

14 

311.979 

623.333 

155.995311.667 

104.004 

207.77878.0100 

155.833 

02.4149 

124  007 

15 

312.810 

625  000 

156.411 

312.500 

104.281 

2J8.333  78.2177 

156  250 

02  5812 

125  000 

16 

313.641 

626.667 

156.826 

313  333 

104.558 

208.889 

78.4255 

150.007 

02.7474 

125.333 

17 

314.472 

628.333 

157.242 

314.167 

104.835 

209.444 

78.6332 

157.083 

02.9136 

125.007 

18 

315.303 

630.000 

157.657 

315.000 

105.112 

210.000 

78.8409 

157.500 

63.0798 

126.000 

19 

316.162 

631.667 

158.087 

315.833 

105.398 

210.556 

79.0558 

157.917 

63.2517 

120.333 

30 

317.022 

633  333 

158.517 

316.667 

105.685 

211.111 

79.2707 

158.333 

63.4237 

126.607 

31 

317.852 

635.000 

158.932 

317.500 

105.962 

211.667 

79.4785 

15S.750 

03.5899 

127.000 

33 

318  683 

636  667 

159.347 

318  333 

106.239 

212.222 

79.0862 

159.107 

63.7501 

127.333 

33 

319.514 

638.333 

159  763 

319.167 

106.516 

212  778 

79  8940 

159  583 

03.9223 

127.667 

34 

320.345 

640.000 

160.178 

320.000 

106.793 

213.333 

80.1017 

160.000 

04.0885 

128.000 

35 

321.176 

641.667 

160.594 

320  833 

107.070 

213.889 

80  3094 

160.417 

64  2547 

128.333 

36 

322.006 

643.333 

161.009 

321.667 

107.341'. 

214.414 

80.5172 

160.833 

64.4209 

128.007 

37 

322.837 

645.000 

161.424 

322.500 

107.623 

215.000 

80.7249 

161.250 

64.5871 

129.000 

38 

323.668 

646.667 

161.840 

323.333 

107.900 

215.556 

80.9327 

161.667 

04.7534 

129.333 

39 

324.499 

648.333 

162.255 

324.167 

108.177 

216.111 

81.1401 

162.083 

64.9196 

129.607 

30 

325.330 

650.000 

162.671 

325.000 

108  454 

216.607 

81.3181 

162  500 

65.0858 

130.000 

31 

326  189651.667 

163.100 

325.833 

108.741 

217.222 

81.5630 

102.917 

05.2577 

130.333 

33 

327.048 

653.  333  163.  530 

326.667 

109.027 

217.778 

81.7779 

103.333 

65.4297 

130.607 

33 

327.879 

655.000  163.946 

327.500 

109.304 

218.333 

81.9857 

103  750 

65.5959 

131.000 

34 

328.710 

656.667164.361 

328.333 

109  581 

218.889 

82.1934 

164.167 

65.7621 

131.333 

35 

329.541 

658.333  164.776 

329.167 

109  858 

219.444 

82.4012 

164.583 

65.9283 

131.667 

36 

330.372 

660.000165.192 

330.000 

110.135 

220.000 

82.0089 

165.000 

66  0945 

132  000 

37 

331  202 

66  1  .  667  1  65  .  607  1  330  .  833 

110.412 

220.556 

82.8166 

165.417 

66.2607 

132.383 

38 
39 

332.033 
332.864 

663.333 
665.000 

166.023 
166.438 

331.667 
332.500 

110.689 
110.966 

221.111 
221.667 

83.0244 
83.2321 

105.833 
166.250 

66.4269 
66.5931 

132.607 
133.000 

40 

333.695 

666.667 

166.854 

333.333 

111.243 

222.222 

83.4399 

166.667 

66.7593 

133.333 

41 

334.554 

668.333 

167.283334.167 

111.530222  778 

83.0548 

167.083 

66.9313 

133.607 

43 

335.414 

670.000 

167.713335.000 

111.816223.333 

83.8697 

167.500 

67.1032 

134.000 

43 

336.245 

671.667 

168.128 

335.833 

112.093223.889 

84.0774 

167.917 

67.2694 

131.333 

44 

337.075 

673.333 

168.544 

336.667 

112.370 

224.444 

84.2852 

168.333 

67.4357 

134.667 

45 

337.906 

67o.OOO 

168.959 

337.500 

112.647 

225.000 

84  4929 

168.750 

67.6019 

135.000 

46 

338  737 

676.667 

169.3751338.3:53 

112.924225.556 

84.7006 

169.167 

67.7081 

135.333 

47 

339.568 

678.333 

169.7901339.167 

113.201  226.  11  1184.9084 

169.583 

07.  9343  1  135.  607 

48 

340.399 

680.000 

170.205 

340.000 

113.478 

226.667 

85.1161 

170.000 

68.1005 

130.000 

49 

341.229 

681.667 

170.621 

340.833 

113.755 

227.222 

85.3239 

170.417 

68.2667 

136.333 

50 

342.060 

683.333 

171.036 

341.667 

114.032 

227.778 

85.5316 

170.833 

08.4329 

136.607 

51 

342.891 

685.000 

171.452342.500 

114.309 

228.333 

85.7393 

171.250 

08.5991 

137.000 

53 

343.722 

686.667 

171.867J343.333 

114.586 

228.889 

85.9471 

171.667 

68.7(553 

137.383 

53 

344.581 

688.333 

172.297 

344.167 

114.872 

229.444 

86.1620 

172.083 

08.9373 

137  0(i7 

54 

345.441 

690.000 

172.727 

345.000 

115.159 

230.000 

86.3709 

172.500 

09.1092 

13H.OOO 

55 

346.271 

691.667 

173.142345.833 

115.436 

230.556 

86.5846 

172.917 

09.2754 

138.383 

56 

347.102 

693.333  173.557346.667 

115.713 

231.111 

HO.  792  4 

173.333 

09.4410 

188.007 

57  347.033I695.000I178.973J347.500 

115.990 

231.667 

87.0001 

173.750 

09.0079 

139.0'H) 

58  1  348.  704  696.667  174.388  318.333 

116.267 

232.222 

87.207'8 

174.107 

09  7741 

139  383 

59   349.595  698.333;  174.  804  349.167 

116.544 

232.778 

87.4156  174.58309.9403 

139.007 

58 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


G°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

G° 

Tan. 

Arc. 

Tan       Arc. 

Tan.  [  Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

f,0.  0709!  100  00042  924885.7143 

37.  5664!  75  0000  33.3093  66.6667 

30.0671 

60.0000 

o 

50.  2095  (100.278  43  0480  85.9524 

37.  6704  175.2083  33.4917 

66.8519 

30.1503 

60.1067 

1 

50.3480  100.556J43.HB8 

86  1905 

37.774375  4167  33.5841 

07.037( 

30.2335 

60.3333 

2 

50  4865 

100.833,43.2811 

86.42.S6 

37  8782175.6250 

33  6765 

67.2222 

30.3166 

60.5000 

3 

50.0251 

101.111 

43.3999 

86.6667 

37  9822 

75.8333 

33.7689 

67.4074 

30.399? 

60.6667 

4 

50.7636 

101.389 

43.5186 

86.9048 

38.0801 

76  0417 

33.8013 

67.5926 

30.4830 

60.8333 

5 

50.9021 

101.66743.6374 

87.1429 

38  1900 

76.2500 

33.9537 

67.7778 

30.5662 

61.000( 

6 

51.0406 

101.94443.7561 

87.3810 

38.2940 

76.4583 

34.0461 

67.9630 

30.6494 

61.1667 

7 

51.1792 

102.222 

43.8749 

87.6190 

38.3070 

70.6(167 

34.1385 

68.1482 

30.7326 

61.3333 

8 

51.8225 

102.500 

43.9977 

87.8571 

38.5054 

76.8750 

34.2341 

68.3333 

30.8186 

01.5000 

9 

51.4658 

102.778 

44.1206 

88.0952 

38.6129 

77.0833 

34.3297 

68.5185 

30.9047 

61.6667 

10 

5  1.6043  11  03.  056  44.  2394 

88.33:33 

38.710977.2917 

34.4221 

68.7037 

30.987961.8333 

11 

51.7428 

103.333 

44.3581 

88.5714 

38.820877.5000 

34.5145 

68.8889 

31.071062.0000 

12 

51  8814 

103.611 

44.4769 

88.8095 

38.924777.7083 

34.6069 

69.0741 

31.154262.1667 

13 

52.  01  991  103.  8«8 

44.5956 

89.0476 

39.028777.9167 

34.6993 

69.2593 

31.2374 

62.3333 

14 

52  15841104.167 

44-7144 

89  2856 

39  1326  78.1250 

34.7917 

69  4444 

31.3206 

62.5000 

15 

52.2009  104.444 
52.  4  355;  104.  722 

44.8331 
44.9519 

89.5238 
89.7619 

39.2365  78.3333 
39.340578.5417 

34.8842 
34.9766 

69.6296 
69.8148 

31.4038 
31  4870 

62.6667 
62.83:33 

16 

17 

52.5740  105.000 

45.0707 

90.0000 

30.4444  78.7500 

35.0690 

70.0000 

31.5702 

63.0000 

18 

52.7173 

105.278 

45.1935 

90.2381 

39.5519 

78.9583 

35.1640 

70.1852 

31.6562 

63.1667 

19 

52.8606 

105.556 

45.3164 

90.4762 

39.6594 

79.1667 

35.2601 

70.3704 

31.7423 

63.3333 

2O 

52.9991 

105.833 

45.4351 

00.7143 

39.  7634  179.3750 

35.3525 

70.5556 

31.8254 

63.5000 

21 

53.1377 

106  111 

45.5539 

90.9524 

30  8673  79.5833 

35.4450 

70.7407 

31.9080 

63.6007 

22 

53.2762 

1  06.389 

45.0726 

91.1905 

30.9712 

79.7917 

35.5374 

70.9250 

31.9918 

63.8333 

23 

53.414? 

106.667 

45  7914 

91.4286 

40.0752 

80.0000 

35.6298 

71.1111 

32.0750 

64.0000 

24 

53.5533 

106.944 

45.9102 

91.6667 

40.  1791  180.  2083 

35.7222 

71.2963 

32.1582 

64.1667 

25 

53.6918 

107.222 

46.0289 

91.9048 

40.2830180.4107 

•35.8146 

71.4815 

32.2414 

64.3333 

26 

53.8303 

107.500 

46.1477 

92.1429 

40.3870 

80.6250 

35.9070 

71.6667 

32.3246 

04.5000 

27 

53.9688 

107.778 

46.2664 

92.3810 

40.4909 

80.8333 

35.9994 

71.8519 

32.4077 

64.6667 

28 

54.1074 

108.056 

46.3852 

02.6190 

40.5948 

81.0417 

36.0918 

72.0370 

32.4909 

04.8333 

29 

54.2459 

108.333 

46.5030 

92.8571 

40.6988 

81.2500 

36.1842 

72.2222 

32.5741 

05.0000 

30 

54.3892 

108.611 

46.6268 

93.0952 

40.8063 

81  .4583 

36.2798 

72.4074 

32.6602 

05.1667 

31 

54.5325 

108.889 

46.7497 

93.3333 

40.9138 

81.6667 

36.3754 

72.5926 

32.7462 

65.3333 

'32 

54.6710 

109.16? 

46.8684 

93.5714 

41  0177 

81.8750 

36.4678 

72.7778 

32.8294 

65.5000 

33 

54.8096 

109.444 

46.9872 

93  8095 

41.1217 

82.0833 

36.5602 

72.9630 

32.9126 

65.6667 

34 

54.9481 

109.722 

47.1059 

U.0476 

41.2256 

82.2917 

36.6526 

73.1482 

32.9958 

05.8333 

35 

55.0866 

110.000 

47.2247 

94.2856 

41.3205 

82.5000 

36.7450 

73.3333 

33.0790 

66.0000 

3G 

55.2252 

110.278 

47.3434 

94.5238 

41.4335 

82.7083 

36.8374 

73.5185 

33.1621 

66.1667 

37 

55.3637 

110.55647.4622 

94.7019 

41.5374 

82.9167 

30.9298 

73.7037 

33  2453 

66.3333 

38 

55.5022 

110.  833|47.  5810 

95.0000 

41.6413 

83.1250 

37.0222 

73.8889 

33.3285 

66.5000 

39 

55.6407 

111.111147.6997 

95.2381 

41.7453 

83.3333 

37.1146 

74.0741 

33.4117 

66.6667 

4O 

55.7840 

111.3S947.8226 

95.4762 

41.8528 

83.5417 

37.2102 

74.2593 

33.4978 

66.8333 

41 

55.9274 

111.  (567  4  7.  9454 

95.7143 

41.9603 

83.7500 

37.3058 

74.4444 

33.5838 

67.0000 

42 

56.0659 

111.94448.0642 

95.9524 

42.0642 

83.9583 

37.3982 

74.6296 

33.667067.1667 

43 

56  2044 

112  222:48  1829 

96.1905 

42.1682 

84.1667 

37.490G 

74.8148 

33.7502 

67.3333 

44 

56.3429 

112.50048.3017 

96.4286 

42.2721 

84.3750 

37.5830 

75.0000 

33.8S34 

67.5000 

45 

56.4815 

112.778  48.4205 

96.6667 

42.37GO 

84.5833 

37.6754 

75.1852 

33.9165 

67.6667 

46 

56.6200 

113.05648.5392 

96.9048 

42.4800 

84.7917 

37.7678 

75.3704 

33.9997 

67.8333 

47 

56.7585 

113.333  48.6580 

97.1429 

42.583985.0000 

37.8602 

75.5556 

34.0829 

08.0000 

48 

56.8971 

113.611:48.7767 

97.3810 

42.6878 

85.2083 

37.9526 

75.7407 

34.1661 

68.1667 

49 

57.0356 

113.  880!48.  8955 

97.6190 

42.7918 

85.4167 

38.0450 

75.9259 

34.2493 

68.3333 

no 

57.1741 

114.16749.0142 

97.8571 

42.8957  85.  6250  138.  1374 

76.1111 

34.3325 

68  50CO 

61 

57.3126 

114.44449.1330 

08.0952 

42.9996 

85.8333 

38.2298 

76.2963 

34.4157 

68.6667 

52 

57.4559 

114.72249.2559 

98.3333 

43.1071 

86.0417 

38.3254 

76.4815 

34.5017 

08.8333 

53 

57.5993 

115.000:49.8787 

98.5714 

43.2147 

86.2500 

38.4210 

76.6667 

34.587869.0000 

54 

57.7378 

115.27849.4975 

98.8095 

43.  31  86  86.  4583  38.5134 

76.8519 

34.670969.1667 

55 

57.8763 

115.55649.6162 

99.0476 

48.4225  86.6667  38.6058 

77.0370 

34.7541 

09.3333 

56 

58.0148 

115.83349.7350 

99.2856 

3  .  5265  i  86  .  8750  1  38  .  6982 

77.2222 

34.8373 

69.5000 

57 

58.1534 

116.111  49.8537 

09.5238 

43.6304  87.0833  38.7906 

77.4074 

34.9205 

69.6067 

58 

58.2919 

116.38949.9725 

99.7619 

3.  7343  87.  2917  38.  8830 

77.5920 

35.003769.8333 

59 

59 


TABLE   XIV.— ACTUAL  TANGENTS,    ETC. 


7° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

3.-)0.425 

700.000 

175.219 

350.000 

1  1  6  .  820  233  .  333  87  .  6233 

175.000 

70.1065  140.000 

1 

351.25(5 

701.667 

175.635 

350.833 

117.097233.88987.8311 

175.417 

7D.2727  140.333 

3 

352.087 

703.333 

1  76.050J351  667 

1  1  7  .  374  23  4  .  444  88  .  0388  1  75  .  833 

70.4389  140.667 

3 

352.946 

705.000 

176.480352.500 

117.661  235.00088.2537 

176.250 

70.  6108:141.  000 

4 

353.806 

706  667 

176.909 

353.333 

117.947  235  .  556  88  .  4686  1  76  .  667 

70.7828  141.333 

5 

354.637 

708.333 

177.325354.167 

118  224  !  236.  111188.  6763  177.083 

70.9490141.0(57 

6 

355.467 

710.000 

177.740355  000 

118.501236.66788.8841 

177.500 

71.  1152!  142.  000 

7 

356.298 

711.667 

178.156 

355.833 

118.778237.222:89.0918 

177.917 

71.2814 

142.333 

8 

357.129 

713.333 

178  571 

356.667 

119.055237.77889.2996 

178.333 

71.4476 

142.667 

9 

357.960 

715.000 

178.987 

357.500 

119.  332  238.  333,89.  5073 

178.750 

71.6138 

143.000 

1O 

358.791 

716.667 

179.402 

358.333 

119.609 

238.889 

89.7150 

179.167 

71.7801 

143.333 

11 

359.621 

718.333 

179.  8171359.  167 

119.886  239.444  89.9228  179.583 

71.9463 

143.667 

13 

360.452 

720.000 

180.233360.000 

120.163240.00090.1305 

180.000 

72.1125 

144.000 

13 

361.312 

721.667 

180.662360.833 

120.450240.556:90.3454  180.417 

72.2844 

144.333 

14 

362.171 

723.333 

181.092361.667 

120.736241.111 

90.5603 

180.833 

72.4564 

144.667 

15 

363.002 

725.000 

181.508362.500 

121.013241.66790.7681 

181.250 

72.6226 

145.000 

16 

363.833 

726.667 

181.923,363.333 

121.290 

242.22290.9758  181.667 

72.7888 

145.333 

17 

364.664 

728.333 

182.338364.167 

121.567 

242.77891.1836 

182.083 

72.9550 

145.667 

18 

365.494 

730.000 

182.  754  ;365.000 

121.844 

243.33391.3913 

182.500 

73.1212 

146.000 

19 

366.325 

731.667 

183.169365.833 

122.121 

243.889 

91.5990 

182.917 

13.2874 

146.333 

30 

367.156 

733.333183.585366.667 

122.398 

244.444 

91.8068 

183.333 

73.4536 

146.667 

31 

367.987 

735.000184.000367.500 

122.675245.00092.0145 

183.750 

73.6198 

147.000 

33 

368.818 

736.667 

184.4163(58.333 

122.952  245.556  92.2223 

184.167 

73.7860 

147.333 

33 

369.677 

738.333184.845 

369.167 

123.238 

246.111 

92.4372 

184.583 

73.9580 

147.6(57 

34 

370.536 

740.000  185.275 

370.000 

123.525 

246.66792.6521 

185.000 

74.1299 

148.000 

35 

371.367 

741.667185.6901370.833 

123.802 

247.22292.8598185.417 

74.2961 

148.333 

3<J 

372.198 

743.333  186.  1061371.  667 

124.079 

247.77893.0675 

185.833 

T4.4623 

148.667 

37 

373  029 

745.000186.521  372.500 

124.356 

248.  333  93.  2753  186.  250 

74.62«6|149.000 

38 

373.860 

746.667  186.937 

373.333 

124.633 

24  8.  S89  93.  4830  186.667 

74.7948 

149.333 

39 

374.690 

748.833  1ST.  852 

374.167 

124.910 

249.444:93.6908 

187.083 

74.9610 

149.667 

30 

375.521 

750.000,187.768 

375.000 

125.187 

250.00093.8985 

187.500 

75.1272 

150.000 

31 

376.381 

751.667,188.197 

375.833 

125.473 

250.  556|  94.113t 

187.917 

75.2091 

150.333 

33 

377.240 

753.333  188.627 

376.667 

125.760 

251.111  94.3283 

188.333 

75.4711 

1  50.607 

33 

378.071 

755.000;  189.  042 

377.500 

126.037 

251.667 

94.5360  188.750 

75.6373 

151.000 

34 

378.902 

756.667,189.458 

378.333 

126.314 

252.222 

94.7438 

189.167 

75.8035  151.333 

35 
36 

379.733 
380.563 

758.  333;  189.  873 
760.000:190.289 

379.167 
380.000 

126.591 
126.868 

252.778 
253  333 

94.9515 
95.1593 

189.583 
190.000 

75.  9697  .151.667 
76.1359152.000 

37 

381.394 

761.6671190.704 

380.833 

127.144 

253.889 

95.3670  190.417 

76.  302l!  152.  333 

38 

382.225 

768.333101.119 

381.667 

127.421 

254.445 

95.5747 

190.833 

76.  4683  '152.667 

39 

333.056 

765.000 

191.535 

382.500 

127.698 

255.000 

95.7825 

191.250 

76.6345  153.000 

4O 

383.887 

766.667191.950 

383.333 

127.975 

255.556 

95.9902 

191.667 

76.8008 

153.333 

41 

384.746 

768.333192.380 

384.167 

128.262 

256.111 

96.2051 

192.083 

76.9727  153.667 

43 

385.605 

770.000;  192.  810 

385.000 

128.548 

256.667 

96.4200 

192.500 

77.1446  154.000 

43 

3S6.436 

771.667)193.225 

385.833 

128.825 

257.222 

96.6278  192.917 

77.3109  154.333 

44 

387.267 

773.333  193.641 

386.667 

129.102 

257.778 

96.8355 

193.333 

77.4771  154.  6G7 

45 

388.098 

775.000  194.056 

387.500 

129.379 

258.333 

97.0433 

193.750 

77.6433155.000 

46 

388.929 

776.667194.471 

388.333 

129.656 

258.889 

97.2510 

194.167 

77.8095  155.333 

47 

3S9.759 

778.333  194.887 

389.167 

129.933 

259.444 

97.4587 

194.583 

77.97'57155  667 

48 

390.590 

780,000  195.302 

390.000 

130.210 

260.000 

97.6665 

195.000 

78.1419  15(5.000 

49 

391.450 

781.667 

195.732 

390.833 

130.497 

260.556 

97.8814 

195.417 

78.3138  156.333 

50 

302.309 

783.  333  196.162 

391.667 

130.783 

261.111 

98.0963 

195.833 

78.4858  156.667 

51 

393.140 

785  000,196.577 

392.500 

131.060 

261.667 

98.3040 

19(5.250 

78.6520  157.000 

53 

393.971 

786.667^96.993 

393.333 

131.337 

262.222 

98.5118196.667 

78.8182157.333 

53 

394.802 

788.333  197.408 

394.167 

131.614 

262.778 

98.7195 

197.083 

78.9844  157.667 

54 

395.632 

790.000  197.823 

395.000 

131.891 

263.333 

98.9272197.500 

70.1506158.000 

55 

396  463 

791.607198.239 

395.833 

132.168 

263.889 

99.1350 

197.917 

79.3168158.333 

56 

397.294 

793.333  198.654 

396.667 

132.445 

264.444 

99.3427198.333 

79.4831  158.667 

57 

398.125 

795.000  199.070397  500 

132.722 

265000 

99.5505 

108.750 

70.6403  150.000 

58 

398.956 

796  .  667  1  99  .  485  1  308  333 

132  999 

265  556 

99.7582 

199.167 

79.  8155!  159.  333 

59 

399.815 

798.  3:33  199.  915i399.  167 

133.285 

266.111 

99.9731 

190.583 

79.  9874!  159.  667 

60 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6C  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

7° 

Tan. 

Arc. 
116.667 

Tan.      Arc. 

Tail. 
43.8383 

Arc. 

Tan. 

38.9754 

Arc. 

Tan. 

Arc. 

M. 
~O 

68.4304 

50.0913  100.000 

87.5000 

77.7778 

35.0869 

70.0000 

58.5(190 

116.944 

50.2100100.238 

43.9422 

87.7083 

39.0678 

77.9630 

35.1701 

70.1GG7 

I 

58.7075 

117.222 

50.3288100.476 

44.0461 

87.9167 

39.1602 

78.1482 

35.2532 

70.3333 

2 

58.8508 

117.500 

50.4516  100.714 

44.1536 

88.1250 

39.2558 

78.3333 

35.3393 

70.500( 

3 

58.  9941  1117.778 

50.5745  100.952 

44.2612 

88.3333 

39.3514 

78.5185 

35.4254 

70.6667 

4 

89.1326 

118.056 

50.6932101.190 

44.3651 

88.5417 

39.4438 

78.7037 

35.5085 

70.83S8 

5 

59.2711 

118.333 

50.8120101.429 

44.4690 

88.7500 

39.5362 

78.8889 

35.5917 

71.000( 

6 

59.4097 

118.611 

50.9308101.667 

44.5730 

88.9583 

39.6286 

79.0741 

35.6749 

71.1667 

7 

59.5482 

118.889 

51.0495101.905 

44.6769 

89.1667 

39.7210 

79.2593 

35.7581 

71.3333 

8 

59.0807 

119.16'! 

51.1683 

102.143 

44.7808 

89.3750 

39.8134 

79.4444 

35.8413 

71.5000 

9 

59.8253 

119.444 

51.2870 

102.381 

44.8848 

89.5833 

39.9058 

79.6296 

35.9245 

71.6667 

1O 

59.9638 

119.722 

51.4058102.619 

44.9887 

89.7917 

39.9982 

79.8148 

36.0076 

71.8333 

11 

00.1023 

120.000 

51.5245102.857 

45.0926 

90.0000 

40.0906 

80.0000 

36.0908 

72.0000 

12 

GO  245(5 

120.278 

51.6474 

103.095 

45.2001 

90.2083 

40.1862 

80.1852 

36.1769 

72.1667 

13 

00.3889  120.556 

51.7702 

103.333 

45.3077 

90.4167 

40  2818 

80.3704 

36.2629 

72.3333 

14 

00.5275  120.833 

51.8890 

103  571 

45.4116 

90.6250 

40.3742 

80.5556 

36.3461 

72.5000 

15 

60.6600  121.111 

52.0078 

103.810 

45.5155 

90.8333 

40.4666 

80.7407 

36.4293 

72.6667 

1G 

60.  8045  I  12  1.389 

52.1265 

104.048 

45.6195 

91.0417 

40.5590 

80.9259 

36  5125 

72.8333 

17 

60.9430 

121.66? 

52.2453 

104.286 

45.7234 

91.2500 

40.6514 

81.1111 

36.5957 

73.0000 

18 

61.  081  G 

121.944 

52.3640 

104.524 

45.8273 

91.4583 

40.7439 

81.2963 

36.6789 

73.1667 

19 

61.2201 

122.222 

52.4828 

104.762 

45.9313 

91.6667 

40.8363 

81.4815 

36.7620 

73.3333 

20 

61.3586 

122.500 

52  6016 

105.000 

46.0352 

91.8750 

40.9287 

81.6667 

36.8452 

73.5000 

21 

61.4972 

122.778 

52.7203 

105.238 

46.1391 

92.0833 

41  0211 

81.8519 

36.9284 

73.666? 

22 

61.6405 

123.056 

52.8432 

105.476 

46.2466 

92.2917 

41.1167 

82.0370 

37.0145 

73.8333 

23 

61.7838 

123.333 

52.9660 

105.714 

46.3542 

92.5000 

41.2122 

82.2222 

37.1005 

74.0000 

24 

61  .  9223 

123.611 

53.0848 

105.952 

46.4581 

92.7083 

41.3046 

82.4074 

37.1837 

74.166, 

25 

62.0608 

123.889 

53.2035 

106.190 

46.  5620  j  92  9167 

41.3971 

82.5926 

37.2669 

74.3333 

26 

62.1994 

124.167 

53.  3223  1106.429 

46.6660 

93.1250 

41.4895 

82.777'8 

37.3501 

74.5000 

27 

62.3379 

124.444 

53.4410 

106.667 

46.7699 

93  .  3333 

41.5819 

82.9630 

37.4333 

74.6667 

28 

62.4764 

121.722 

53.5598 

106.905 

46.8738 

93.5417 

41.6743 

83.1482 

37.5165 

74.8333 

29 

62.6149 

125.000 

53.6786 

107.143 

46.9778 

93.7500 

41.7667 

83.3333 

37.5996 

75.0000 

3O 

62.7582 

125.278 

53.8014 

107.381 

47.0853 

93.9583 

41.8623 

83.5185 

37.6857 

75.1667 

31 

62.9016 

125.556 

53.9243 

107.619 

47.1928 

94.1667 

41.9579 

83.7037 

37.7717 

75.3333 

32 

63.0401 

125.833 

54.0430 

107.857 

47,2967 

94.3750 

42.0503 

83.8889 

37.8549 

75.5000 

33 

63.1786 

126.111 

54.1618 

108.095 

47.4007 

94.5833 

42.1427 

84.0741 

37.9381 

75.6667 

34 

63.3171 

126.389 

54.2805 

108.333 

47.5046 

94.7917 

42.2351 

84.2593 

38.0213 

75.8333 

35 

63.4557 

126.667 

54  3993 

108.571 

47.6085 

95.0000 

42.3275 

84.4444 

38.1045 

76.0000 

36 

63.5942 

126.944 

54.5181 

108.810 

47.7125 

95.2083 

42.4199 

84.6296 

38.1877 

76.1667 

37 

63.7327 

127.222 

54.6368 

109.048 

47.8164 

95.4167 

42.5123 

84.8148 

38.2709 

76  .  3333 

38 

63.8713 

127.500 

54.7556 

109.286 

47.9203 

95.6250 

42.6047 

85.0000 

38.3540 

76.5000 

39 

64.0098 

127.778 

54.8743 

109.524 

48.0243 

95.8333 

42.6971 

85.1852 

38.4372 

76.6667 

40 

64.1531 

128.056 

54.9972 

109.762 

48.1318 

96.0417 

42.7927 

85.3704 

38.5233 

76.8333 

41 

64  2964 

128.333 

55.1200 

110.000 

48.2393 

96.2500 

42.8883 

85.5556 

38.6093 

77.0000 

42 

64.4349 

128.611 

55.2388 

110.238 

48.3432 

96.4583 

42.9807 

85.7407 

38.6925 

77.1667 

43 

64.5735 

128.889 

55.3576 

110.476 

48.4472 

96.6667 

43.0731 

85.9259 

38.7757 

77.3333 

44 

64.7120 

129.167 

55.4763 

110.714 

48.5511 

96.8750 

43.1655 

86.1111 

38.8589 

77.5000 

45 

64.8505 

129.444 

55.5951 

110.952 

48.6550 

97.0833 

43.2579 

86.2963 

38.9421 

77.6667 

4G 

64  9890 

129.722 

55.7188111.190 

48.7590 

97.2917 

43.3503 

86.4815 

39.0253 

77.8333 

47 

65.1276 

130.000 

55.8326 

111.429 

48.8629 

97.5000 

43.4427 

86.6667 

39.1084 

78.0000 

48 

65.2709 

130.278 

55.9554 

111.667 

48.9704 

97.7083 

43.5383 

86.8519 

39.1945 

78.1667 

49 

65.4142 

130.556 

56.0783 

111.905 

49.0779 

97.9167 

43  6339 

87.0370 

39.2805 

78.3333 

50 

65.5527 

130.833 

56.1971  112.143 

49.1819 

98.1250 

43.7263 

87.2222 

39.3637 

78.5000 

51 

65.6912 

131.111 

56.3158  112.381 

49.2858 

98.3333 

43.8187 

87.4074 

39.4469 

78.6667 

52 

65.  829S:  131.389 

56.4346 

112.61!) 

49.3897 

98.5417 

43.9111 

87.5926 

39.5301 

78.8333 

53 

65.  9683i  131.  667 

56.5533 

112.857 

49  4937 

98.7500 

44.0035 

87.7778 

39.6133 

79.0000 

54 

66.  1068'  131.  944 
66.  2453^1  32.  222 

56.6721 
56.790H 

113.095 
113.3*3 

49.5976 
49.7015 

OS.  0583 
99.1667 

44.0959 
44.1883 

87.9630 

88.1482 

39.6965 
39.7797 

79.1667 
79.3,333 

55 
56 

66.3839  132.500 

56.9096:113.571 

49.8055 

99.3750 

44.2807 

88.3333 

39.8628 

79.5000 

57 

66.5224  132.778 

57.0284 

113.810 

49.9094 

99.5833 

44.3731 

88.5185 

39.9460 

79.6667 

58 

66.  6657  1133.056 

57.1512 

114.048 

50.0169!  99.  791  7|  44.  4687 

88.7037 

40.0321 

79.8333 

59 

Gl 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


8° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 
~~0~ 

Tan. 

Arc. 

Tan. 

Arc. 

400.000 

Tan. 

Arc. 

266.667 

Tan. 

100.188 

Arc. 

Tan. 

Arc. 

400.674 

800.000 

200.345 

133.572 

200.000 

80.1594 

160.000 

1 

401.505 

801.667 

200.760 

400.833 

133.849 

267.222 

100.396 

200.417 

80.3256 

160.333 

2 

403.336 

803.333 

201.175 

401.667 

134.126 

267.778 

100.603 

200.833 

80.4918 

160.667 

3 

403.167 

805.000 

201.591 

402.500 

134.403 

268.333 

100.811 

201.250 

80.6580 

161.000 

4 

403.998 

806.667 

202.006 

403.333 

134.680 

268.889 

101.019 

201.667 

80.8242 

161.333 

5 

404.828 

808.333 

202.422 

404.167 

134.957 

269.444 

101.227 

202.083 

80.9904 

161.667 

6 

405.659 

810.000 

202.837 

405.000 

135.234 

270.000 

101.4:34 

202.500 

81.1566 

162.000 

7 

406.519 

811.667 

203.267 

405.833 

135.520 

270.556 

101.649 

202.917 

81.3286 

162.333 

8 

407.378 

813.333 

203.697 

406.667 

135.807 

271.111 

101.864 

203.3:33 

81.5005 

162.667 

9 

408.209 

815.000 

204.112 

407.500 

136.084 

271.667 

102.072 

203.750 

81.6667 

163.000 

10 

409.040 

816.667 

204.527 

408.333 

136.361 

272.222 

102.280 

204.167 

81.8329 

163.333 

11 

409.871 

818.333 

204.943 

409.167 

136.63S 

272.778 

102.487 

204.583 

81.9991 

163.667 

12 

410.701 

820.000 

205.358 

410.000 

136.915 

2  -'3.  333 

102.695205.000 

82.1654 

164.000 

13 

411.532 

821.667 

205.774 

410.833 

137.191 

273.889 

102.903205.417 

82.3316 

164.  333 

14 

412.363 

823.333 

206.189 

411.667 

137.468 

274.444 

103.111  205.833 

82.4978 

164.667 

15 

413.222 

8>5.000 

206.619 

412.500 

137.755 

275.000 

103.326206.250 

82.6697 

165.000 

16 

414.082 

826.667 

207.048 

413.3:33 

138.041 

275.556 

103.541  206.667 

82.8417 

165.333 

17 

414.913 

828.333 

207.464 

414.167 

138.318 

276.111 

103.748i20r.083 

83.0079 

165.667 

18 

415.743 

830.000 

207.879 

415.000 

138.595 

276.667 

103.956207.500 

83.1741 

166.000 

19 

416.574 

831.667 

208.295 

415.833 

138.872 

277.222 

104.164 

207.917 

83.3403 

166.333 

20 

417.405 

833.333 

208.710 

416.667 

139.149 

277.778 

104.371 

208.333 

83.5065 

166.667 

21 

418.236 

835.000 

209.126 

417.500 

139.426 

278.333 

104.5791208.750 

83.6727 

167.000 

22 

419.067 

836.667 

209.541 

418.333 

139.703 

278.889 

104.  787|209.  167 

83.8389 

167.333 

23 

419.926 

838.333 

209.971 

419.167 

139.990 

279.444 

105.  002!  209.  583 

84.0109 

167.667 

24 

420.785 

840.000 

210.400 

420.000 

140.276 

280.000 

105.217 

210.000 

84.1828 

168.000 

25 

421.616 

841.667 

210.816 

420.833 

140.553 

280.556 

105.424 

210.417 

84.3490 

168.333 

2(> 

422.417 

843.333 

211.231 

421.667 

140.830 

281.111 

105.632 

210.833 

84.5152 

168  667 

27 

423.278 

845.000 

211.647 

422.500 

141.107 

281.667 

105.840 

211.25084.6814 

169.000 

28 

424.109 

846.667 

212.062 

423.333 

141.384 

282.222 

106.048 

211.66784.8476 

169.333 

29 

424.939 

848.3:33 

212.478 

424.167 

141.661 

282.778 

106.255 

212.083 

85.0139 

169.667 

3O 

425.770 

850.000 

212.  8Q3 

425.000 

141.938 

283.333 

106.463 

212.500 

85.1801 

170.000 

31 

426.630 

85  1.667 

213.323 

425.833 

142.225 

283.889 

106.678  212.  9!  7185.  8520 

170.333 

32 

427.489 

853.333 

213.752 

426.667 

142.511 

284.444 

106.893 

213.33385.5240 

170.667 

33 

428.320 

855.000 

214.168 

427.500 

142.788 

285.000 

107.101 

2  13.  750  '85.  6902 

171.000 

34 

429  151  856.667 

214.583 

428.333 

143.065 

285.556 

107.308 

214.167,85.8564 

171.333 

35 

429.982858.333 

214.999 

429.167 

143.342 

286.111 

107.516 

214.58386.0226  171.667 

36 

430.  812  !  860.  000 

215.414 

430.000 

143.619 

286.667 

107.724 

215.  000|86.  1888  172.  000 

37 

431.643  861.667 

215.830 

430.833 

143.896 

287.222 

107.932 

21  5  .  41  7  i  86  .  3550  1  72  .  333 

38 

432.474863.333 

216.245 

431.667 

144.173 

287.778 

108.139 

215.  633  86.  £3121172.667 

39 

433.333 

865.000 

216.675 

432.500 

144.459 

288.833 

108.354 

216.250 

86.6932 

173.000 

4O 

434.193 

866.667 

217.104 

133.333 

144.746 

288.889 

108.569 

216.667 

86.8651 

173.333 

41 

435.024 

868.333 

217.520 

434.167 

145.023 

289.444 

108.777 

217.083  87.0313  173.667 

42 

435.854 

870.000 

217.935 

435.000 

145.300 

290.000 

108.985 

217.50087.1975  174.000 

43 

436.685 

871.667 

218.351 

43>.  833 

145.577 

290.556 

109.192 

217.91787.3637174.333 

44 

437.516 

873.333 

218.766 

136.667 

145.854 

291.111 

109.400 

218.33387.5299174.667 

45 

43  S.  3  47 

875.000 

219.181 

437.500 

146.131 

291.867 

109.608 

218.750  87.6962  175.000 

46 

439.178 

876.667 

219.597 

438.333 

146.408 

292.222 

109.816 

219.16787.8624  175.333 

47 

440.037 

878.333 

2-20.027 

439.167 

146.694 

292.778 

110.031 

219.  583  '  88  .  0343  1  75  .  667 

48 
49 

410.897 
441.727 

880.000 
881.667 

220.456 

220.872 

440.000 
440.833 

146.981 
147.258 

293.333 
293.889 

110.245 
110.453 

220.000 
220.417 

88.2062  176.000 
88.3725,176.333 

50 

412.558 

883.333 

221.287 

441.667 

147.535 

294.444 

110.661 

220.833 

88.  538?!  176.  667 

51 

443.389 

885.000 

221.703 

442.500 

147.812 

295.000 

110.869 

221  .  250  88  .  7049  1  1  77.  0(10 

52 

444.220 

886.667 

222.118 

443.333 

148.089 

295.556 

111.076 

221.  667  88.  8711  j  177.333 

53 

415.051 

888.333 

222.533 

444.167 

148.365 

296.111 

111.284 

22  .'  .  083  89  .  0373  1  77  .  667 

54 

445.881 

890.000 

222.949 

445.000 

148.642 

296.667 

111.492 

222  .  500  89  .  2035  1  1  78  .  000 

55 

116.741 

891.667 

223.379 

445.833 

148.929 

297.222 

111.707 

222  .  91  7  89  .  3755,  178  .  333 

5(1 

447.600 

893.333 

223.808 

446.667 

149.215 

297.778 

111.922 

223  .  333  89  .  5474  1  178  .  667 

57 

148.431 

895.000 

224.224 

447.500 

149.492 

298.333 

112.129 

223.75089.7136 

179.000 

58 

449.262 

896.667 

224.639 

448.333 

149.769 

298.889 

112.337 

224.16789.8798 

17'9.333 

59 

450.093 

898.333 

225.055 

449.167 

150.046 

299.444 

112.545 

224.58390.0460179.667 

TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

8° 

Tan.  |   Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

66.8090 

133.333 

57.2741 

114.286 

50.1244 

100.000 

44.5643 

88.8889 

40.1181 

80.0000 

~O 

66.9475 

133.611 

57.3928 

114.524 

50.228-1 

100.208 

44  .  6567 

89.0741 

40.2013 

80.1667 

1 

67.0861 

133.889 

57.5116 

114.762 

50.3323 

100.417 

44.7491 

89.2593 

40.2845 

80.3333 

2 

67.2246 

134.167 

57.6303 

115.000 

50.4362 

100.625 

44.8415 

89.4444 

40.367780.5000 

3 

67.3631 

134.444 

57.7491 

115.238 

50.5402 

100.833 

44.9339 

89.6296 

40.4509 

80.6667 

4 

67.5017 

134.722 

57.8679 

115.476 

50.6441 

101.042 

45.0263 

89.8148 

40.5341 

80.8333 

5 

67.6402 

135.000 

57.9866 

115.714 

50.7480 

101.250 

45.1187 

90.0000 

40.6172 

81.0000 

6 

87.7835 

ia5.278 

58.1095 

115.952 

50.8555 

101.458 

45.2143 

90.1852 

40.7033 

81.1667 

7 

67.9268 

135.556 

58.2323 

116.190 

50.9631 

101.667 

45.3099 

90.3704 

40.7894 

81.3333 

8 

68.0653 

135.8:33 

58  3511 

116.429 

51.0670 

101.875 

45.4023 

90.5556 

40.8725 

81.5000 

9 

68.2039 

136.111 

58.4698 

116.667 

51.1709 

102.083 

45.4947 

90.7407 

40.9557 

81.6667 

1O 

68.3424 

136.389 

58.5886 

116.905 

51.2749 

102.292 

45.5871 

90  9259 

41.0389 

81.8333 

11 

68.4809 

136.667 

58.7073 

117.143 

51.3788 

102.500 

45.6795 

91.1111 

41.1221 

82.0000 

13 

68.6194 

136.944 

58.8261 

117.381 

51.4827 

102.708 

45.7719 

91.2963 

41.2053 

82.1667 

13 

68.7580 

137.222 

58.9449 

117.619 

51.5867 

102.917 

45.8643 

91.4815 

41.2885 

82.3333 

14 

68.9013 

137.500 

59.0677 

117.857 

51.6942 

103.125 

45.9599 

91.6667 

41.3745 

82.5000 

15 

69.0446 

137.778 

59.1906 

118.095 

51.8017 

103.333 

46.0555 

91.8519 

41.4606 

82  6667 

16 

69.1831 

138.050 

59.3093 

118.333 

51.9056 

103.542 

46.1479 

92.0370 

41.5438 

82.8333 

17 

69.3216 

138.333 

59.4281 

118.571 

52.0096 

103.750 

46.2403 

92.2222 

41.6269 

83.0000 

18 

69.4602 

138.631 

59.5468 

118.810 

52.1135 

103.958 

46.3327 

92.4074 

41.7101 

83.1667 

19 

69.5987 

138.889 

59.6656 

119.048 

52.2174 

104.167 

46.4251 

92.5926 

41.7933 

83.3333 

20 

69.7372 

139.167 

59.7844 

119.286 

52.3214 

104.375 

46.5175 

92.7778 

41.8765 

83.5000 

21 

69.8758 

139.444 

59.9031 

119.524 

52.4253 

104.583 

46.6099 

92.9630 

41.9597 

83.6667 

22 

70.0191 

139.722 

60.0260 

119.762 

52.5328 

104.792 

46.7055 

93.1482 

42.0457 

83.8333 

23 

70.1624 

140.000 

60.1488 

120.000 

52.6403 

105.000 

46.8011 

93.3333 

42.1318 

84.0000 

24 

70.3009 

140,278 

60.2676 

120.238 

52.7443 

105.208 

46.8935 

93.5185 

42.2150 

84.1667 

25 

70.4394 

140.556 

00.3863 

120.476 

52.8482 

105.417 

46.9859 

93.7037 

42.2982 

84.3333 

26 

70.5780 

140.833 

60.5051 

120.714 

52.9521 

105.625 

47.0783 

93.8889 

42.3813 

84.5000 

27 

70.7165 

141.111 

60.6239 

120.952 

53.0560 

105.833 

47.1707 

94.0741 

42.4645 

84.6667 

28 

70.8550 

141.389 

60.7426 

121.190 

53.1600 

106.042 

47.2631 

94.2593 

42.5477 

84.8333 

29 

70.9935 

141.667 

60.8614 

121.429 

53.2639 

106.250 

47.3555 

94.4444 

42.6309 

85.0000 

30 

71.1368 

141.944 

60.9842 

121.667 

53.3714 

106.458 

47.4511 

94.6296 

42.7170 

85.1667 

31 

71.2801 

142.222 

61.1071 

121.905 

53.4790 

106.667 

47.5467 

94.8148 

42.8030 

85.3333 

32 

71.4187 

142.500 

61.2258 

122.143 

53.5829 

106.875 

47.6391 

95.0000 

42.8862 

85.5000 

33 

71.5572 

142.778 

61.3446 

122.381 

53.6868 

107.083 

47.7315 

95.ia52 

42.9694 

85.6667 

34 

71  .  6957 

143.056 

61.4634 

122.619 

53.7908 

107.292 

47.8239 

95.3704 

43.0526 

85.8333 

35 

71.8343 

143.333 

61.5821 

122.857 

53.8947 

107.500 

47.9163 

95.5556 

43.1357 

86.0000 

36 

71.9728 

143.611 

61.7009 

123.095 

53.9986 

107.708 

48.0087 

95.740? 

43.2189 

86.1667 

37 

72.1113 

143.889 

61.8196 

123.333 

54.1025 

107.917 

48.1011 

95.9259 

43.3021 

86.3333 

38 

72.2546 

144.  1G7 

61.9425 

123.571 

54.2101 

108.125 

48.1967 

96.1111 

43.3882 

86.5000 

39 

72.3979 

144.444 

62.0653 

123.810 

54.3176 

108.333 

48.2923 

96.2963 

43.4742 

86.6667 

4O 

72.5365 

144.72-' 

62.1841 

124.048 

54.4215 

108.542 

48.3847 

96.4815 

43.5574 

86.8333 

41 

72.6750 

145.000 

62.3028 

124.286 

54.5254 

108.750 

48.4771 

96.6667 

43.6406 

87.0000 

42 

72.8185 

145.278 

62.4216 

124.524 

54.6294 

108.958 

48.5695 

96.8519 

43.7238 

87.1667 

43 

72.9520 

145.55G 

62.5404124.762 

54.7333 

109.167 

48.6619 

97.0370 

43.8070 

87.3333 

44 

73.0906 

145.833 

62.a591|125.000 

54.8372 

109.375 

48.7543 

97.2222 

43.8901 

87.5000 

45 

73.2291 

146.111 

62.7779125.238 

54.9412 

109.583 

48.8467 

97.4074 

43.9733 

87.6667 

46 

73.3721 

146.389 

62.9007125.476 

55.0487 

109.792 

48.9423 

97.5926 

44.0594 

87.8333 

47 

73.5157 

146.667 

63.0236125.714 

55.1562 

110.000 

49.0379 

97.7778 

44.1454 

88.0000 

48 

73.6542 

146.944 

63.1423125.952 

55.2601 

110  208 

49.1303 

97.9630 

44.2286 

88.1667 

49 

| 

73.7928 

147.222 

63.2611  126.190 

55.3641 

110.417 

49.2227 

98.1482 

44.3118 

F8.3333 

50 

73.9313 

147.500 

63.3799 

126.429 

55.4680 

110.625 

49.3151 

98.3333 

44  .  3950 

88.5000 

51 

74.0698 

147.778 

63.4986 

126.667 

55.5719 

110.833 

49.4075 

98.5185 

44.4782 

88.6667 

52 

74.2084 

148.056 

63.6174 

126.905 

55.6759 

111.042 

49.4999 

98.7037 

44.5614 

88.8333 

53 

74.3469 

148.333 

63.7361 

127.143 

55.7798 

111.250 

49.5923 

98.8889 

44.6446 

89.0000 

54 

74.4902 

148.611 

63.a590 

127.381 

55.8873 

111.458 

49.6879 

99.0741 

44.7306 

89.1667 

55 

74.6335 

148.889 

63.9818 

127.619 

55.9948 

111.667 

49.7835 

99.2593 

44.8167 

89.  3383 

56 

74.7720 

149.167 

64.1006 

127.857 

56.0988 

111.875 

49.8759 

99.4444 

44.8998 

89.5000 

57 

74.9106 

149.444 

64.2194 

128.095 

56.2027 

112.  083 

49.9683 

99.6296 

44.9830 

89.6667 

58 

75.0491 

149.722 

64.3381 

128.333 

56.3066 

112.292 

50.0607 

99.8148 

45.0662 

89.8333 

59 

63 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


9° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
150.323 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

450.9:>3 

900.000 

225.47'0 

450.000 

300.  000 

112.753 

225.000 

90.2122 

180.000 

1 

451.754 

901.667 

225.885 

450.833 

150.600 

300.556 

112.960 

225.417 

90.3784 

180.333 

2 

452.585 

903.333 

226.301 

451.667 

150.877 

301.111 

113.168 

225.833 

90.5447 

180.667 

3 

453.445 

905.000 

226.731 

452.500 

151.164 

301.667 

113.383 

226.250 

90.7l6b 

181.000 

4 

454.304 

906.667 

227.160 

453.333 

151.450 

302.222 

113.598 

226.667 

90.8885 

181.333 

5 

455.135 

908.333 

227.576 

454.167 

151.727 

302.778 

113.806 

227.083 

91.0548 

181.667 

6 

455.966 

910.000 

227.991 

455.000 

152.004 

303.333 

114.013 

227.500 

91.2210 

182.000 

7 

456.796 

911.667 

228.407 

455.833 

152.281 

303.889 

114.221 

227.917 

91.3872 

182.333 

8 

457.627 

913.333 

228.822 

456.667 

152.558 

304.444 

114.429 

228.333 

91.5534 

182.667 

9 

458.487 

915.000 

229.252 

457.500 

152.845 

305.000 

114.644 

228.750 

91.7253 

183.000 

10 

459.340 

916.667 

229.681 

458.333 

153.131 

305.556 

114  859 

229.167 

91.8973 

183.333 

11 

460.17J 

918.333 

230.097 

459.167 

153.408 

306.111 

115.066 

229.583 

Q2.0635 

183.667 

13 

461.008 

920.000 

230.512 

460.000 

153.685 

306.667 

115.274 

230.000 

92.2297 

184.000 

13 

461.838 

921.667 

230.928 

460.833 

153.962 

307.222 

115.482 

230.417 

92.3959 

184.333 

14 

462.669 

923.333 

231.343 

461.667 

154.239 

307.778 

115.690 

230.833 

92.5621 

184.667 

15 

463.500 

925.000 

231.759 

462.500 

154.516 

308.333 

115.897 

231.250 

92.7283 

185.000 

16 

464.331 

926.667 

232.174 

463.333 

154.793 

308.889 

116.105 

231.667 

92.8945 

185.333 

17 

465.190 

928.333 

232.604 

464.167 

155.079 

309.444 

116.320 

232.083 

93.0665 

185.667 

18 

466.050 

930.000 

233.033 

465.000 

155.366 

310.000 

116.535 

232.500 

93.2384 

186.000 

19 

466.881 

931.667 

233.449 

465.833 

155.643 

310.556 

116.743 

232.917 

93.4046 

186.333 

20 

467.711 

933.333 

233.864 

466.667 

155.920 

311.111 

116.950 

233.333 

93.5708 

186.667 

21 

468.542 

935.000 

234.280 

467.500 

156.197 

311.667 

117.158 

233.750 

93.7370 

187.000 

22 

469.373 

936.667 

234.695 

468.333 

156.474 

312.222 

117.366 

234.167 

93.9033 

187.333 

23 

470.204 

938.333 

235.110 

469.167 

156.751 

312.778 

117.574 

234.583 

94.0695 

187.667 

24 

471.035 

940.000 

235.526 

470.000 

157.028 

313.333 

117.781 

235.000 

94.2357 

188.000 

25 

471.894 

941.667 

235.956 

470.833 

157.314 

313.889 

117.996 

235.417 

94.4076 

188.3:33 

26 

472.753 

943.333 

236.385 

471.667 

157.601 

314.444 

118.211 

235.833 

94.5796 

188.667 

27 

473.584 

945.000 

•236.801 

472.500 

157.878 

315.000 

118.419 

236.250 

94.7458 

189.000 

28 

474.415 

946.667 

237.216 

473.333 

158.155 

315.556 

118.627 

236.667 

94.9120 

189.333 

29 

475.246 

948.333 

237.632 

474.167 

158.432 

316.111 

118.834 

237.083 

95.0782 

189.667 

30 

476.077 

950.000 

238.047 

475.000 

158.709 

316.667 

119.042 

237.500 

95.2444 

190.000 

31 

476.936 

951.667 

£38.477 

475.833 

158.995 

317.222 

119.257 

237.917 

95.4163 

190.333 

32 

477.796 

953.333 

238.907 

476.667 

159.282 

317.778 

119.472 

238.333 

95.5883 

190.667 

33 

478.627 

955.000 

i39.322 

477.500 

159.559 

318.333 

119.680 

238.750 

95.7545 

191.000 

34 

479.457 

956.667 

239.737 

478.333 

159.835 

318.889 

119.887 

239.167 

95.9207 

191.333 

35 

480.289 

958.333 

240.153 

479.167 

160.112 

319.444 

120.095 

239.583 

96.0869 

191.667 

36 

481.119 

960,000 

240.568 

480.000 

160.389 

320.000 

120.303 

240.000 

96.2531 

192.000 

37 

481.978 

961.667 

240.998 

480.833 

160.676 

320.556 

120.518 

240.417 

96.4251 

192.333 

38 

482.838 

963.333 

241.428 

481.667 

160.962 

321.111 

120.733 

240.833 

96.5970 

192.667 

39 

483.668 

965.000 

241.843 

482.500 

161.239 

321.667 

120.941 

241.250 

96.7632 

193.000 

4O 

484.499 

966.667 

242.258 

483.333 

161.516 

322.222 

121.148 

241.667 

96.9294 

193.333 

41 

485.330 

968.333 

242.674 

484.167 

161.793 

322.778 

121.356 

242.083 

07.0956 

193.667 

42 

486.161 

970.000 

243.089 

485.000 

162.070 

323.333 

121.564 

242.500 

97.2619 

194.000 

43 

486.992 

971.667 

243.505 

485.833 

162.347 

323.889 

121.771 

242.917 

97.4281 

194.333 

44 

487.822 

973.333 

243.920 

486.667 

162.624 

324.444 

121.979 

243.3:33 

J7.5943 

194.667 

45 

488.682 

975.000 

244.350 

487.500 

162.911 

325.000 

122.194 

2-13.750 

97.7662 

195.000 

46 

189.541 

976.667 

244.780 

488.333 

163.197 

325.556 

122.409 

244.167 

97.9382 

195.333 

47 

490.372 

978.333 

245.195 

489.167 

163.474 

326.111 

122.617 

244.583 

98.1044 

195.667 

48 

491.203 

980.000 

245.610 

490.000 

163.751 

326.667 

122.825 

245.000 

98.2706 

196.000 

49 

492.034 

981.667 

246.026 

490.833 

164.028 

327.222 

123.032 

245.417 

98.4368 

196.333 

50 

492.864 

983.333 

246.441 

491.667 

164.305 

327.778 

123.240 

245.833 

98.6030 

196.667 

51 

493.724 

985.000 

246.871 

492.500 

164.592 

328.333 

123.455 

246.250 

98.7749 

97.000 

52 

494.583 

986.667 

247.301 

493.333 

164.878 

328.889 

123.670 

246.667 

98.9469 

197.333 

53 

495.414 

988.333 

247.716 

494.167 

65.155 

329.444 

123.878 

247.083 

99.1131 

197.667 

54 

496.245 

990.000 

248.132 

495.000 

165.432 

330.000 

24.085 

247.500 

99.2793 

198.000 

55 

497.076991.667 

248.547 

495.833 

65.709 

330.556 

124.293 

247.917 

99.4455 

198.333 

56 

497.907 

993.333 

248.962 

496.667 

65.986 

331.111 

124.501 

248.333 

99.6117 

198.667 

57 

498.766 

995.000 

249.392 

497.500 

66.272 

331.667 

124.716 

248.750 

99.7837 

199.000 

58 

499.625996.667 

249.822 

498.  333 

166.559 

332.222 

124.931 

249.167 

99.9556 

99.333 

59 

500.456:998.333 

250.2371499.167 

166.836 

332.778 

125.138 

249.583 

00.122 

99.667 

64 


TABLE  XIV. — ACTUAL  TANGENTS,   ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

9° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

112.500 

Tan. 
50.1531 

Arc. 

Tan. 
45.14~94 

Arc. 

90.0000 

M. 

75.1876 

150.000 

64.4569 

128.571 

56.4106 

100.000 

0 

75.3261 

150.278 

64.5756 

128.810 

56.5145 

112.70850.2455 

100.185 

45.2326 

90.1667 

1 

75.4647 

150.556 

64.6944 

129.048 

56.6184 

112.91750.3380 

100.370 

45.3158 

90.3333 

2 

75.6080 

150.833 

64.8172 

129.286 

56.7260 

113.12550.4335 

100.556 

45.4018 

90.5000 

3 

75.7513 

151.111 

64.9401 

129.524 

56.8335 

113.33350.5291 

100.741 

45.4879 

90.6667 

4 

75.8898 

151.389 

65.0588 

129.762 

56.9374 

113.542(50.6215 

100.926 

45.5711 

90.8333 

5 

76.0283 

151.667 

65  1776 

130.000 

57.0413 

113.750 

50.7139 

101.111 

45.6542 

91.0000 

6 

76.1669 

151.944 

65.2964 

130.238 

57.1453 

113.958 

50.8063 

101.296 

45.7374 

91.1667 

7 

76.3054 

152.222 

65.4151 

130.476 

57  2492 

114.167 

50.8987 

101.481 

45.8206 

91.3333 

8 

76.4487 

152.500 

65.5380 

130.714 

57.3567 

114.375 

50.9943 

101.667 

45.9067 

91.5000 

9 

76.5920 

152.778 

65.6608 

130.952 

57.4642 

114.583 

51.0899 

101.852 

45.9927 

91.6667 

10 

76.7305 

153.056 

65.7796 

131.190 

57.5682 

114.792 

51.1823 

102.037 

46.0759 

91.8333 

11 

76.8691 

153.333 

65.8983 

131.429 

57.6721 

115.000 

51.2747 

102.222 

46.1591 

92.0000 

12 

77.0076 

153.611 

66  0171 

131.667 

57.7760 

115.208 

51.3671 

102.407 

46.2423 

92.1667 

13 

77.1461 

153.889 

66.1359 

131.905 

57.8800 

115.417 

51.4595 

102.593 

46.3255 

92.3333 

14 

77.2847 

154.167 

66.2546 

132.143 

57.9839 

115.625 

51.5520 

102.778 

46.4086 

92.5000 

15 

77.4232 

154.444 

66.3734 

132.381 

58.0878 

115.833 

51.6444 

102.963 

46.  4918  192.6667 

16 

77.5665 

154.722 

66.4962 

132.619 

58.1954 

116.042 

51.7399 

103.148 

46.5779 

92.a333 

17 

77.7098 

155.000 

66.6191 

132.857 

58.3029 

116.250 

51.8355 

103.333 

46.6639 

93.0000 

18 

77.8483 

155.278 

66.7378 

133.095 

58.4068 

116.458 

51.9279 

103.519 

46.7471 

93.1667 

19 

77.9868 

155.556 

66.8566 

133.333 

58.5107 

116.667 

52.0203 

103.704 

46.8303 

93.3a33 

20 

78.1254 

155.  833 

66.9754 

133.571 

58.6147 

116.875 

52.1127 

103.889 

46.9135 

93.5000 

21 

78.2639 

156.111 

67.0941 

133.810 

58.7186 

117.083 

52.2052 

104.074 

46.9967 

93.6667 

22 

78.4024 

156.389 

67.2129 

134.048 

58.8225 

117.292 

52.2976 

104.259 

47.0799 

93.8333 

23 

78.5410 

156.667 

67.3316 

134.286 

58.9265 

117.500 

52.3900 

104.444 

47.1630 

94.0000 

24 

78.6843 

156.944 

67.4545 

134.524 

59.0340 

117.708 

52.4856 

104.630 

47.2491 

94.1667 

25 

78.8276 

157.222 

67.5773 

134.762 

59.1415 

117.917 

52.5811 

104.815 

47.3352 

94.3333 

26 

78.9661 

157.500 

f  7.  6961 

135.000 

59.2454 

118.125 

52.6735 

105.000 

47.4183 

94.5000 

27 

79.1046 

157.778 

67.8149 

135.238 

59.3494 

118.333 

52.7660 

105.185 

47.5015 

94.6667 

28 

79.2432 

158.056 

67.9336 

135.476 

59.4533 

118.542 

52.8584 

105.370 

47.5847 

94.8333 

29 

79.3817 

158.333 

68.0524 

135.714 

59.5572 

118.750 

52.9508 

105.556 

47.6679 

95.0000 

SO 

79.5250 

158.611 

68.1752 

135.952 

59.6648 

118.958 

53.0463 

105.741 

47.7540 

95.1667 

31 

79.6683 

158.889 

68.2981 

136.190 

59.7723 

119.167 

53.1419 

105.926 

47.8400 

95.3333 

32 

79.8068 

159.167 

68.4168 

136.429 

59.8762 

119.375 

53.2343 

106.111 

47.9232 

95.5000 

33 

79.9454 

159.444 

68.5356 

136.667 

59.9801 

119.583 

53.3267 

106.296 

48.0064 

95.6667 

34 

80.0839 

159.722 

68.6543 

136.905 

60.0841 

119.792 

53.4192 

106.481 

48.0896 

95.8333 

35 

80.2224 

160.000 

68.7731 

137.143 

60.1880 

120.000 

53.5116 

106.667 

48.1727 

96.0000 

36 

80.3657 

160.278 

68.8960 

137.381 

60.2955 

120.208 

53.6071 

106.852 

48.2588 

96.1667 

37 

80.5090 

160.556 

69.0188 

137.619 

60.4030 

120.417 

53.7027 

107.037 

48.3449 

96.3333 

38 

80.6476 

160.833 

69.1376 

137.857 

60.5070 

120.625 

53.7951 

107.222 

48.4280 

96.5000 

39 

80.7861 

161.111 

69.2563 

138.095 

60.6109 

120.833 

53.8875 

107.407 

48.5112 

96.6667 

40 

80.9246 

161.389 

69.3751 

138.333 

60.7148 

121.042 

53.9799 

107.593 

48.5944 

96.8333 

41 

81.0631 

161.667 

69.4938 

138.571 

60.8188 

121.250 

54.0724 

107.778 

48.6776 

97.0000 

42 

81.2017 

161.944 

69.6126 

138.810 

60.9227 

121.458 

54.1648 

107.963 

48.7608 

97.1667 

43 

81.3402 

162.222 

69.7314 

139.048 

61.0266 

121.667 

54.2572 

108.148 

48.8440 

97.3333 

44 

81.4835 

162.500 

69.8542 

139.286 

61.1342 

121.875 

54.3528 

108.333 

48.9300 

97.5000 

45 

81.6268 

162.778 

69.9771 

139.524 

61.2417 

122.083 

54.4483 

108.519 

49.0161 

97.6667 

46 

81.7053 

IGS.Oofi 

70.0958 

139.762 

61.3456 

122.292 

54.5407 

108.7'04 

49.0993 

97.8333 

47 

81.9039  103.333 

70.2146 

140.000 

61.4495 

122.500 

54.6332 

108.889 

49.1824 

98.0000 

48 

82.0424 

163.611 

70.3333 

140.238 

61.5535 

122.708 

54.7256 

109.074 

49.2656 

98.1667 

49 

82.1809 

163.889 

70.4521 

140.476 

61.6574 

122.917 

54.8180 

109.259 

49.3488 

98.3333 

50 

82.3242 

164.167 

70.5749 

140.714 

61.7649 

123.125 

54.9136 

109.444 

49.4349 

98.5000 

51 

82.4675 

164.444 

70.6978 

140.952 

61.8724 

123.333 

55.0091 

109.630 

49.5209 

98.6667 

52 

82.6061 

164.722 

70.8166  141.190 

61.9764 

123.542 

55.1015 

109.815 

49.6041 

98.8333 

53 

82.7446 

165.000 

70.9353  141.429 

62.0803 

123.750 

55.1939 

110.000 

49.6873 

99.0000 

54 

82.8831 

165.278 

71.054lil41.667 

62.1842 

123.958 

55.2864 

110.185 

49.7705 

99.1667 

55 

83.0216 

165.556 

71.  1728'  141.  905 

62.2882 

124.167 

55.3788 

110.37049.8537 

99.3333 

56 

83.1650 

165.833 

71.2957 

142.143 

62.3957 

124.37'5 

55.4743 

110.55649.9397 

99.5000 

57 

83.3083 

166.111 

71.4185 

142.381 

62.5032 

124.583 

55.5699 

110.741  50.0258 

99.6667 

58 

83.4468 

166.389 

71.5373 

142.619 

62.6071 

124.792 

55.6623 

110.92650.1089199.8333 

59 

65 


TABLE  XIV,— ACTUAL   TANGENTS,    ETC. 


10° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 
~~O 

Tan. 
501.287 

Arc. 

Tan.       Arc. 

Tan. 

Arc. 

Tan. 
125.346 

Arc. 

Tan.       Arc. 

1000.00 

250.653500.000 

167.113 

333.333 

250.000 

100.288200.000 

1 

502.118 

1001.67 

251.068500.833 

167.390 

333.889 

1  25.  554  i  250.  41  7 

100.454  200.333 

2 

50:3.949 

1003.33 

251.484501.667 

167.667 

384.444 

125.762 

250.833 

100.620200.607 

3 

503.77'.) 

1005.00 

251.899502.500 

167.944 

335.000 

125.969 

251.250 

100.787201.000 

4 

504.610 

1006.67 

252.314503.333 

168.221 

335.556 

126.177 

251.667 

100.953201.333 

5 

505.470 

1008.33 

252.744  504.167 

168.507 

336.111 

126.392 

252.083 

101.125201.607 

6 

500.329 

1010.00 

253.174  505.000 

168.794 

336.667 

126.607 

252.500 

101.297202.000 

7 

507.160 

1011.67 

253.589505.833 

169.071 

337.222 

126.815 

252.917 

101.403202.333 

8 

507.991 

1013.33 

254.005j506.  667 

169.348 

337.778 

127.022 

253.333 

101.629202.667 

9 

508.822 

1015.00 

254.420 

507.500 

169.625 

338.333 

127.230 

253.750 

101.795 

203.000 

1O 

509.652 

1016.67 

254.836 

508.333 

169.902 

338.889 

127.438 

254.167 

101.962 

203.333 

11 

5lO.5l2i10l8.33 

255.265509.167 

170.188 

339.444 

127.653 

254.583 

102.134 

203.667 

13 

511.371  1020.00 

255.695510.000 

170.475 

340.000 

127.808 

255.000 

102.305 

204.000 

13 

512.a02l021.67 

256.110510.83-3 

170.752 

340.556 

128.075 

255.417 

102.472 

204.333 

14 

513.0331023.33 

256.  526  !  51  1.667 

171.029 

341.111 

128.283 

255.833 

102.638 

204.667 

15 

513.8641025.00 

856.941512.500 

171.306 

341.667 

128.491 

256.250 

102.804 

205.000 

16 

514.  094:1026.  67 

257.357513.333 

171.582 

342.222 

128.699 

256.667 

102.970 

205.333 

17 

515.554  1028.33 

257.786!514.167 

171.869 

342.778 

128.913 

257.083 

103.142 

205.667 

18 

516.41311030.00 

258.  216  :  515.  000 

172.156 

343.333 

129.128 

257.500 

103.314 

206.000 

19 

517.244 

1031.67 

258.632 

515.833 

172.432 

343.889 

129.336 

257.917 

103.480 

206.333 

2O 

518.075 

1033.33 

259.047 

516.667 

172.709 

344.444 

129.544 

258.333 

103.647 

206.667 

21 

51  8.  906!  1035.  00 

259  462  '51  7.  500 

172.986 

345.000 

129.  752(258.750 

103.813 

207.000 

33 

519.737 

1036.67 

259.  878  1518.333 

173.263 

345  .  556 

129.959 

259.167 

103.979 

207.333 

33 

520.596 

1038.33 

260.308519.167 

173.550 

346  111 

130.174 

259.583 

104.151 

207.667 

34 

521.455 

1040.00 

260.737520.000 

173.83C. 

346.667 

130.389 

260.  OUO 

104.323 

208.000 

35 

522.286 

1041.67 

26  1.1  53  1520.  833 

174.113 

347.222 

130.597 

260.417 

104.489 

208.333 

36 

523.117 

1043.33 

261.568521.667 

174  390 

347.778 

130.805 

260.833 

104.655 

208.667 

3  7 

523.948 

1045.00 

261.9841522.500 

174.607 

348.333 

131.012 

261.250 

104.822 

209.000 

38 

524.779)1046.67 

262.399 

523.333 

174.944 

348.889 

131.220 

2(51  .  667 

104.988 

209.333 

39 

525.638 

1048.33 

262.829 

524.167 

175.231 

319:444 

131.435 

262.083 

105.160 

209.667 

30 

526.498 

1050.00 

263.258 

525  000 

75.517 

350.000 

131.650 

262.500 

105.332 

210.000 

31 

527.  328!  1051.  67 

263.674 

525.833 

75.794 

350.556 

131.858 

262.917 

105.498 

210.333 

528.159 

1053.33 

264.089 

526.667 

76.071 

351.111 

132.065 

263.333 

105.664 

210.607 

33 

528.990 

1055.00 

264.505 

527.500 

76.348 

351.607 

132.273 

263.750 

105.830 

211.000 

34 

529.821 

1056.67 

264.920 

528.333 

76.625 

352.222 

132.481 

264.167 

105.997 

211.333 

35 

530.680 

1058.33 

265.350 

529.167 

76.912 

352.778 

132.696 

264.583 

106.168 

211.667 

36 

531.540 

1060.00 

265.780 

530.000 

77.198 

353  333 

132.911 

265  .  OCO 

106.340 

212.000 

37 

532.370 

1061  67 

266.195 

530.833 

77.475 

353.889 

133.118 

205.417 

106.507 

212.333 

38 

533.201 

1063.33 

266.610 

531.667 

77.752 

354.444 

133.326 

265.833 

106.673 

212.607 

39 

534.032 

1065.00 

267.026 

532.500 

ITS.  029 

355.000 

133.534 

266.250 

106.839 

213.000 

4O 

534.863 

1066.67 

267.441 

533.333 

178.306 

355.556 

133.742 

266.667 

107.005 

213  333 

41 

535.722 

1068.33 

267.871 

534.167 

178.592 

356.111 

133.957 

267.083 

107.177 

213  667 

43 

536.582 

1070.00 

268.301 

535.000 

178.879 

356.667 

134.171 

267.500 

107  349 

214.000 

43 

537.413 

1071.67 

268.716 

535.833 

179.15(5 

357.222 

134.379 

267".  91  7 

107.515 

214.383 

44 

538.243 

1073.33 

269.132 

536.667 

179.433 

357.778 

134.587 

208.333 

107.682 

214.667 

45 

539.074 

1075.00 

269.547 

537.500 

179.710 

358.333 

134.795 

268.750 

107.848 

215.000 

46 

539.905 

1076.67 

269.962 

538.333 

179.987 

358.889 

135.002 

269.107 

108.  014  1215.333 

47 
48 

540.764 
541.624 

1078.33 
1080.00 

270.392 
270.822 

539.167 
540.000 

180.273 
180.560 

359.444 
300.000 

135.217 
135.432 

209.583 
27'0.000 

108.18fi215.007 
108.358216.0(0 

49 

542.455 

1081.67 

271.237 

540.833 

1  80.  837  j  360.  556 

135.640 

270.417 

108.524216.333 

5O 

543.285 

1083.33 

271.653 

541.667 

181.114361.111 

135.848 

270.833 

108.690 

216.067 

51 

544.116 

1085.00 

272.068 

542.500 

181.391  361.667 

136.055271.250 

108.856 

217.000 

53 

544  947 

1086.67 

272.483 

543.333 

181.668362.222 

136.263271.667 

109.023 

217.333 

53 
54 

545  806 
546.666 

1088.33 
1090.00 

272.913 
273.343 

544.167 
545.000 

181.954362.778 
182.241  363.333 

136.478  272.083 
136.693272.500 

109.195 
109.367 

217.667 
218.000 

55 

547.497 

1091.67 

273.758 

545.833 

182.518363.889 

136.901  272.917 

109.  533  1  21  8.  333 

56 

548.328 

1093.33 

274.174 

546.667 

182.795364.444 

137.10S273.333 

109  699218.667 

57 

549.187 

1095.00 

274.604 

547.500 

183.081  365.000 

137.323273.750 

109.871  219.000 

58 

550.046  1096  67 

275.033 

548.333 

183.  368;  365.  556 

137.5-J8274.107 

110  0431219.333 

59 

550.87711098  33 

275.449 

549.167 

183.645366.111 

137.  74  6  2  74.  583 

110.209219.667 

TABLE  XIV. — ACTUAL  TANGENTS,   ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

10. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

83.5853 

166.667 

71.6561!  142.  857 

62.7111 

125.000 

55.7547 

111.111 

50.1921 

100.000 

O 

83.7238 

166.944 

71.7748143.095 

(52.8150 

125.208 

55.8472 

111.29650.2753 

100.167 

1 

83.8624 

167.222 

71.8936  143.333 

62.9189 

125.417 

55.9396 

111.481 

50.3585 

100.  ass 

2 

84.0009 

167.500 

72.0123  143.571 

63.0229 

125.625 

56.0320 

111.6G7 

50.4417 

100.500 

3 

84.1394 

167.778 

72.1311  143.810 

63.1268 

125.833 

56.1244 

111.852 

50.5249 

100.667 

4 

84.2827 

168.056 

72.2539  144.048 

63.2343 

126.042 

56.2200 

112.037 

50.6109 

100.833 

5 

84.4260 

168.333 

72.3768  144.286 

63.3418 

126.250 

56.3155 

112.222 

50.6970 

101.000 

6 

84.5646 

168.611 

72.4956  144.524 

63.4458 

126.458 

56.4080 

112.407 

50.7802 

101.167 

7 

84.7031 

168.889 

72.6143  144.762 

63.5497 

126.667 

56.5004 

112.593 

50.8(534 

101.333 

8 

84.8416 

169.167 

72.7331 

145.000 

63.6536 

126.875 

56.5928 

112.778 

50.9465 

101.500 

9 

84.9802 

169.444 

72.8518 

145.238 

63.7576 

127.083 

56.6852 

112.963 

51.0297 

101.667 

10 

85.1235 

169.722 

72.  9747  1  145.  476 

63.8651 

127.292 

56.7808 

113.148 

51.1158 

101.  833 

11 

85.2668 

170.000 

73.0975  145.714 

63.9726 

127.500 

56.8763 

113.333 

51.2018 

102.000 

12 

85.4053 

170.278 

73.2163  145.952 

64.0765 

127.708 

56.9687 

113.519 

51.2850 

102.167 

13 

85.5438 

170.556 

73.3350146.190 

(54.1805 

127.917 

57.0612 

113.704 

51.3682 

102.333 

14 

85.6824 

170.833 

73.4538146.429 

64.2844 

128.125 

57.1536 

113.889 

51.4514 

102.500 

15 

85.8209 

171.111 

73.5726 

146.667 

64.3883 

128.333 

57.2460 

114.074 

51.5346 

102.667 

16 

85.9642 

171.389 

73.6954 

146.905 

64.4959 

128.542 

57.3415 

114.259 

51.6206 

102.833 

17 

86.1075 

171.667 

73.8183 

147.143 

64.  (503-1 

128.750 

57.4371 

114.444 

51.7067 

103.000 

18 

86.2460 

171.944 

73.9370 

147.381 

64.7073 

128.958 

57.5295 

114.630 

51.7899 

103.167 

19 

86.3845 

172.222 

74.0558 

147.619 

64.8112 

129.167 

57.6219 

114.815 

51.8730 

103.333 

20 

86.5231 

172.500 

74.1745 

147.857 

64.9152 

129.375 

57.7144 

115.000 

51.9562 

103.500 

21 

86.6616 

172.778 

74.2933 

148.095 

(55.0191 

129.583 

57.8068 

115.185 

52.0394 

103.667 

86.8049 

173.056 

74.4162  148.333 

65.1266 

129.792 

57.9023 

115.370 

52.1255 

103.833 

23 

86.9482 

173.333 

74.53901148.571 

65.2341 

130.000 

57.9979 

115.556 

52.2115 

104.000 

24 

87.0867 

173.611 

74.6578 

148.810 

65.3381 

130.208 

58.0903 

115.741 

52.2947 

104.167 

25 

87.2253 

173.889 

74.7765 

149.048 

65.4420 

130.417 

58.1827 

115.926 

52.3779 

104.333 

26 

87.3638 

174.167 

74.8953 

149.286 

65.5459 

130.625 

58.2751 

116.111 

52.4611 

104.500 

27 

87.5023 

174.444 

75.0140 

149.524 

65.6499 

130.833 

58.3676 

116.296 

52.5443 

104.667 

28 

87.6456 

174.722 

75.1369 

149.762 

65.7574 

131.042 

58.4631 

116.481 

52.6303 

104.833 

29 

87.7889 

175.000 

75.2597 

150.000 

65.8649 

131.250 

58.5587 

116.667 

52.7164 

105.000 

30 

87.9275 

175.278 

75.3785 

150.238 

65.9688 

131.458 

58.6511 

116.852 

52.7996 

105.167 

31 

88.0660 

175.556 

75.4973 

150.476 

66.0728 

131.667 

58.7435 

117.037 

52.8827 

105.333 

32 

88.2045 

175.833 

75.6160 

150.714 

66.1767 

131.875 

58.8359 

117.222 

52.9659 

105.500 

33 

88.3431 

176.111 

75.7348 

150.952 

66.2806. 

132.083 

58.9284 

117.407 

53.0491 

105.667 

34 

88.4864 

176.389 

75.8576 

151.190 

66.3882 

132.292 

59.0239 

117.593 

53.1352 

105.833 

35 

88.6297 

176.667 

75.9805 

151.429 

66.4957 

132.500 

59.1195 

117.778 

53.2212 

106.000 

36 

88.7682 

176.944 

76.0992 

151  .667 

66.5996 

132.708 

59.2119 

117.963 

53.3044 

106.167 

37 

88.9067 

177.222 

76.2180 

151.905 

66.7035 

132.917 

59.3043 

118.148!  53.  3876 

106.333 

38 

89.0453 

177.500 

76.3368 

152.143 

66.8075 

133.125 

59.3967 

118.333 

53.4708 

106.500 

39 

89.1838 

177.778 

76.4555 

152.381 

66.9114 

133.333 

59.4891 

118.519 

53.5540 

106.667 

4O 

89.3271 

178.056 

76.5784  152.619 

67.0189 

133.542 

59.5847 

118.704 

53.6400 

106.833 

41 

89.4704 

178.333 

76.7012!l52.a57 

67.1264 

133.750 

59.6803 

118.889 

53.7261 

107.000 

42 

89.6089 
89.7475 

178.611 

178.889 

76.8200  153.  095 
76.93871153.333 

67.2304 
67.3343 

133.958 
134.167 

59.7727 
59.8651 

119.07'4 
119.259 

53.8092 
53.8924 

107.167 
107.333 

43 
44 

89.8860 

179.167 

77.0575 

153.571 

67.4382 

134.375 

59.9575 

119.444 

53.9756 

107.500 

45 

90.0245 

179.444 

77.1762 

153.810 

67.5422 

134.583 

60.0499 

119.630 

54.0588 

107.667 

46 

90.1678 

179.722 

77.2991 

154.048 

67.6497 

134.792 

60.1455 

119.815 

54.1449 

107.833 

47 

90.3111 

180.000 

77.4220 

154.286 

67.7572 

135.  0(K 

60.2411 

120.000 

54.2309 

108.  OCX 

48 

90.4496 

180.278 

77.5407 

154.524 

67.8611 

135.208 

60.3335 

120.185 

64.3141 

108.167 

49 

90.5882 

180.556 

77.6595 

154.762 

67.9651 

135.417 

60.4259 

120.370 

54.3973 

108.333 

50 

90.7267 

180.833 

77.  7782  i  155.  000 

68.0690 

135.625 

60.5183 

120.556 

54.4805 

108.500 

51 

90.8652 

181.111 

77.8970 

155.  238 

68.1729 

135.833 

60.6107 

120,741  54.5637 

108.667 

52 

91.0085 

181.389 

78.0198 

155.476 

68.2805 

136.042 

60.7063 

120.92654.6497 

108.833 

53 

91.1518 

181.66? 

78.1427155.714 

68.3880 

136.250 

60.8019 

121.111  54.7358 

109.000 

54 

91.2904 

181.944 

78  2615;  155.  952 

68.4919 

136.458 

60.8943 

121.29654.8189 

109.167 

55 

91.4289 

182.222 

78.3802156.190 

68.5958 

136.667 

60.9867 

121.  481  154.9021 

109.333 

56 

91.5722 

182.500 

78.5031  156.429 

68.7034 

136.875 

61.0823 

121.66754.9882 

109.500 

57 

91.7155 

182.778 

7'8.  6259  156.  667 

68.8109 

137.083 

61.1779 

121  .852 

55.0742 

109.667 

58 

91.8540 

183  056 

78.7447156.905 

68.9148 

137.292 

61.2703 

122.037 

55.1574 

109.833 

59 

67 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


11° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  C  irve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

551.708 

1100.00 

275.864 

550.000 

183.922 

366.667 

137.954 

275.000 

110.375 

240.000 

1 

552.539 

1101.67 

276.280 

550.833 

184.199 

367.242 

138.161 

475.417 

110.542 

240.333 

2 

553.370 

1103.33 

276.695 

551.667 

184.476 

367.778 

138.369 

275.833 

110.708 

220.667 

3 

554.229 

1105.00 

277.125 

552.500 

184.764 

368.333 

138.584(276.250 

110.880 

241.000 

4 

555.088 

1106.67 

277.554 

553.333 

185.049 

368.889 

138.799 

276.667 

111.054 

241.333 

5 

555.919 

1108.33 

477.97'0 

554.167 

185.346 

369.444 

139.007 

477.083111.218 

441.667 

6 

556.750 

1110.00 

278.385 

555.000 

185.  60^ 

370.000 

139.214 

277.5001111.384 

244.000 

-     7 

557.581 

1111.67 

278.801 

555.833 

185.879 

370.556 

139.424 

477.917 

111.550 

222.333 

8 

558.412 

1113.33 

479.216 

556.667 

186.156 

37  1  .111 

139.630 

478.333 

111.716 

222.667 

9 

559.271 

1115.00 

279.646 

557.500 

186.443 

371.66"; 

139.845 

478.750 

111.888 

243.000 

1O 

560.131 

1116.67 

280.076 

558.333 

186.729 

372.244 

140.060 

279.167 

112.060 

223.333 

11 

560.961 

1118.33 

280.491 

559.167 

187.006 

372.778 

140.268 

279.583 

112.247 

423.667 

12 

561.792 

1120.00 

280.906 

560.000 

187.283 

373.333 

140.475 

480.000 

112.393 

224.000 

13 

562.623 

1121.67 

281.322 

560.833 

187.560 

373.889 

140.683 

480.417 

112.559 

224.333 

14 

563.454 

1123.33 

281.737 

561.667 

187.837 

374.444 

140.891 

480.833 

112.725 

224.667 

15 

564.313 

1125.00 

282.167 

562.500 

188.124 

375.000 

141.10(3 

281.250 

112.897 

425.000 

16 

565.173 

1126.67 

282.597 

563.333 

188.410 

375.556 

(41.321 

281.667 

113.069 

225.333 

17 

566.003 

1128.33 

483.014 

564.167 

188.687 

376.111 

141.548 

482.083 

113.235 

425.667 

18 

566.834 

1130.00 

283.428 

565.000 

188.964 

376.667 

141.736 

484.500 

113.401 

446.000 

19 

567.694 

1131.67 

283.857 

565.833 

189.251 

377.224 

141.951 

482.917 

113.573 

226.333 

20 

568.553 

1133.33 

284.287 

566.  667 

189.537 

377.778 

142.166 

483.333 

113.745 

226.667 

21 

569.384 

1135.00 

284.702 

567.500 

189.814 

378.333 

144.381 

483.750 

113.912 

247.000 

22 

570.215 

1136.67 

285.118 

568.333 

190.091 

378.889 

142.596 

284.167 

114.078 

247.333 

23 

571.046 

1138.33 

385.683 

569.167 

190.368 

379.444 

144.796 

284.583 

114.244 

247.667 

24 

571.876 

1140.00 

285.949 

570.000 

190.645 

380.000 

142.997 

285.000 

114.410 

448.000 

25 

572.736 

1141.67 

286.378 

570.833 

190.932 

380.556 

143.212 

285.417 

114.582 

448.333 

2G 

573.595 

1143.33 

286.808 

571.667 

191.218 

381.111 

143.447 

285.833 

114.754 

448.667 

21 

574.426 

1145.00 

287.224 

572.500 

191.495 

381.667 

143.634 

486.250 

114.920 

249.000 

28 

575.257 

1146.67 

287.639 

573.333 

191.772 

382.222 

143.842 

286.667 

115.087 

249.333 

29 

576.088 

1148.33 

288.054 

574.167 

194.049 

382.778 

144.050 

287.083 

115.253 

229.667 

30 

576.918 

1150.00 

288.470 

575.000 

192.326 

383.333 

144.258 

287.500 

115.419 

230.000 

31 

577.778 

1151.67 

288.900 

575.833 

192.612 

383.889 

144.472 

287.917 

115.591 

230.333 

32 

578.637 

1153.33 

289.329 

576.667 

192.899 

384.444 

144.687 

288.333 

115.763 

230.667 

33 

579.468 

1155.00 

289.745 

577.500 

193.  176 

385.000 

144.895 

488.750 

115.929 

231.000 

34 

580.299 

1156.67 

290.160 

578.333 

193.453 

385.556 

145.103 

289.167 

116.095 

231.333 

35 

581.158 

1158.33 

290.590 

579.167 

193.739 

386.111 

145.318 

289.583 

116.267 

231.667 

36 

582.018 

1160.00 

291.020 

580.000 

194.026 

386.667 

145.533 

490.000 

116.439 

434.000 

37 

582.849 

1161.67 

291.435 

580.833 

194.303 

387.224 

145.740 

290.417 

116.605 

232.333 

38 

583.679 

1163.33 

291.850 

581.667 

194.580 

387.778 

145.948 

290.833 

116.772 

234.667 

39 

584.510 

1165.00 

292.266 

582.500 

194.857 

388.333 

146.156 

291.250 

116.938 

233.000 

40 

585.341 

1166.67 

292.681 

583.333 

195.134 

388.889 

146.364 

291.667 

117.104 

233.333 

41 

586.200 

1168.33 

293.111 

584.167 

195.420 

389.444 

146.579 

294.083 

117.276 

233.667 

42 

587.060 

1170.00 

293.541 

585.000 

195.707 

390.000 

146.793 

294.500 

117.448 

434.000 

43 

587.891 

1171.67 

293.956 

585.833 

195.984 

390.556 

147.001 

294.917 

117.614 

234.333 

44 

588.722 

1173.33 

294.372 

586.667 

196.261 

391.111 

147.209 

293.333 

117.780 

234.667 

45 

589.581 

1175.00 

294.801 

587.500 

196.547 

391.667 

147.424 

493.750 

117.954 

235.000 

46 

590.440 

1176.67 

295.231 

588.333 

196.834 

392.222 

147.639 

494.167 

118.124 

235.333 

47 

591.271 

1178.33 

495.646 

589.167 

197.111 

392.778 

147.  846  j  494.  583 

118.290 

235.667 

48 

592.102 

1180.00 

496.062 

590.000 

197.388 

393.333 

148.054 

295.000 

118.457 

236.000 

49 

592.933 

1181.67 

296.477 

590.833 

197.665 

393.889 

148.262 

295.417 

118.623 

236.333 

50 

593.764 

1183.33 

296.893 

591.667 

197.942 

394.444 

148.470 

295.833 

118.789 

236.667 

51 

594.623 

1185.00 

297.322 

592.500 

198.228 

395.000 

148.685 

296.  2501118.  961 

437.000 

52 

595.483 

1186.67 

297.752 

593.333 

198  515 

395.556 

148  899 

296.6671119  133 

237.333 

53 

596.313 

1188.33 

298.  168  1594.167 

198.792396.111 

149.107 

297.083;  119.  299 

237.667 

54 

597.144 

1190.00 

498.583595.000 

199.  069  1396.667 

149.315 

297.500  11  9.  465  1238.  000 

55 

598.004 

1191.67 

299.013595.833 

199.355397.222 

149.530 

297.917  119.  6371238.833 

56 

598.863 

1193.33 

299.442596.667 

199.642397.778 

149.745 

298.333  119.809i238.667 

57 

599.694 

1195.00 

299.858597.500 

199.919398.333 

149.952 

498.750  119.975239.000 

58 

600.525 

1196.67 

300.273598.333 

400.195398.889 

150.160 

499.167  140.144239.333 

59 

601.355 

1198.33 

300.6891599.167 

400.472399.444 

150.368 

499.583140.308239.667 

68 


TABLE  XIV. — ACTUAL  TANGENTS,   ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve, 

1O°  Curve. 

11° 

"iST 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |    Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

91.9926 

183.333 

78.8634 

157.143 

69.0187  137.500 

61.3627122.222 

55.2406 

110.000 

~o~ 

92.1311 

183.611 

78.9822 

157.381 

69.1227137.708 

61.4551  122.407 

55.3238 

110.167 

i 

92.2696 

183.889 

79.1009 

157.619 

69.2266  137.917 

61.5475 

122.593 

55.4070 

110.333 

2 

92.4129 

184.167 

79.2238 

157.857 

69.3341  138.125 

61.6431 

122.778 

55.4930 

110.500 

3 

92.5562 

184.444 

79.3467 

158.095 

69.4416  138.333 

61.7387 

122.963 

55.5791 

1  10.607 

4 

92.6948 

184.722 

79  4654 

158.333 

69.5456  138.542 

61.8311 

123.148 

55.6623 

110  833 

5 

92.8333 

185.000 

79.5842 

158.571 

69.6405  13P..750 

61.9235 

123.333 

55.7455 

111.000 

6 

92.9718 

185.278 

79.7029 

158.810 

69.7534138.958 

62.0159  123.519 

55.8286 

111.1(57 

7 

93.1104 

185.556 

79.8217 

159.048 

69.8574  139.167 

62.10831123.704 

55.9118 

111.333 

8 

93.2537 

185.833 

79.9445 

159.286 

69.9649 

139.375 

62.2039 

123.889 

55.9979 

111.500 

9 

93.3970 

186.111 

80.0674 

159.524 

70.0724 

139.583 

62.2995 

124.074 

56.0839 

111  667 

1O 

93.5355 

186.389 

80.1861 

159.762 

70.1763 

139  792 

62.3919 

124.259 

56.1671 

111.833 

11 

93.6740 

186.667 

80.3049 

160.000 

70.2803 

140000 

62.4843 

124.444 

56.2503 

112.000 

12 

93.8126 

186.944 

80.4237 

160.238 

70.3842 

140.208 

62.5767 

124.630 

56.3335 

112.167 

13 

93.9511 

187.222 

80.5424 

160.476 

70.4881 

140.417 

62.6691 

124.815 

56.4167 

112.333 

14 

94.0944 

187.500 

80.6653 

160.714 

70.5957 

140.625 

62.7647 

125.000 

56.5027 

112.500 

15 

94.2377 

187.778 

80.7881 

160.952 

70.7032 

140.833 

62.8603 

125.185 

56.5888 

112.667 

16 

94.3762 

188.056 

80.9069 

161.190 

70.8071 

141.042 

62.9527 

125.370 

56.6720 

112.833 

17 

94.5147 

188.333 

81.0256 

161.429 

70.9110 

141.250 

63.0451 

125.556 

56.7551 

113.000 

18 

94.6581 

188.611 

81  .  1485 

161.667 

71.0186 

141.458 

63.1407 

125.741 

56.8412 

113.167 

19 

94.8014 

188.889 

81.2713 

161.905 

71.1261 

141.667 

63.2363 

125.926 

56.9273 

113.333 

20 

94.9399 

189.167 

81.3901 

162.143 

71.2300 

141.875 

63.3287 

126.111 

57.0104 

113.500 

21 

95.0784 

189.444 

81.5089 

162.381 

71.3339 

142.083 

63.4211 

126.296 

57.0936 

113.667 

22 

95.2169 

189.722 

81.6276 

162.619 

71.4879 

142.292 

63.5135 

126.481 

57.1768 

113.833 

23 

95.3555 

190.000 

81.7464 

162.857 

71.5418 

142.500 

63.6059 

126.667 

57.2600 

114.000 

24 

95:4988 

190.278 

81.8692 

163.09? 

71.6493 

142.708 

63.7015 

126.852 

57.3460 

114.167 

25 

95.6421 

190.556 

81.9921 

163.333 

71.7568 

142.917 

63.7971 

127.037 

57.4321 

114.333 

26 

95.7806 

190.833 

82.1108 

163.571 

71.8608 

143.125 

63.8895 

127.222 

57.5153 

114.500 

27 

95.9191 

191.111 

82.2296 

163.810 

71.9647 

143.333 

63.9819 

127.407 

57.5985 

114.667 

28 

96.0577 

191.389 

82.3484 

164.048 

72.0686 

143.542 

64.0743 

127.593 

57.6817 

114.833 

29 

96.1962 

191.667 

82.4671 

164.286 

72.1726 

143.750 

64.1667 

127.778 

57.7648 

115.000 

30 

96.3395 

191.944 

82.5900 

164.524 

72.2801 

143.958 

64.2623 

127.963 

57.8509 

115.167 

31 

96.4828 

192.222 

82.7128 

164.762 

72.3876 

144.167 

64.3579 

128.148 

57.9369 

115.333 

32 

96.6213 

192.500 

82.8316 

165.000 

72.4915 

144.375 

64.4503 

128.333 

58.0201 

115.500 

33 

96.7599 

192.778 

82.9503 

165.238 

72.5955 

144.583 

64.5427 

128.519 

58.1033 

115.667 

34 

96.9032 

193.056 

83.0732 

165.476 

72.7030 

144.792 

64.6383 

128.704 

58.1894 

115.833 

35 

97.0465 

193.333 

83.1960 

165.714 

72.8105 

145.000 

64.7339 

128.889 

58.2754 

116.000 

36 

97.1850 

193.611 

83.3148 

165.952 

72.9144 

145.208 

64.8263 

129.074 

58.3586 

116.167 

37 

97.3235 

193.889 

83.4336 

166.190 

73.0184 

145.417 

64.9187 

129.259 

58.4418 

116.333 

38 

97.4621 

194.167 

83.5523 

1-66.429 

73.1223 

145.625 

65.0111 

129.444 

58.5250 

116.500 

39 

97.6006 

194.444 

83.6711 

166.667 

73.2262 

145.833 

65.1035 

129.630 

58.6082 

116.66V 

40 

97.7439 

194.722 

83.7939 

166.905 

73.3338 

146.042 

65.1991 

129.815 

58.6942 

116.833 

41 

97.8872 

195.000 

83.9168 

167.143 

73.4413 

146.250 

65.2947 

130.000 

58.7803 

117.000 

43 

98.0257 

195.278 

84.0355 

167.381 

73.5452 

146.458 

65.3871 

130.185 

58.8635 

117.167 

43 

98.1643 

195.556 

84.1543 

167.619 

73.6491 

146.667 

65.4795 

130.370 

58.9466 

117.333 

44 

98.3076 

195.833 

84.2772 

167.857 

73.7567 

146.875 

65.5751 

130.556 

59.0327 

117.500 

45 

98.4509 

196.111 

84  .  4000 

168.095 

73.8642 

147.083 

65.6707 

130.741 

59.1187 

117.667 

46 

98.5894 

196.389 

84.5188 

168.333 

73.9681 

147.292 

65.7631 

130.926 

59.2019 

117.833 

47 

98.7279 

196.667 

84.6375 

168.571 

74.0720 

147.500 

65.8555 

131.111 

59.2851 

118.000 

48 

98.8665 

196.944 

84.7563 

168.810 

74.1760 

147.708 

65.9479 

131.296 

59.3683 

118.167 

49 

99.0050 

197.222 

84.8750 

169.048 

74.2799 

147.917 

66.0403 

131.481 

59.4515 

118.333 

50 

99.1483 

197.500 

84.9979 

169.286 

74.3874 

148.125 

66.1359 

131.667 

59.5375 

118.500 

51 

99.2916 

197.778 

85.1207 

169  524 

74.4949 

148.333 

66.2315 

131.852 

59.6236 

118.667 

52 

99.4301 

198.056 

S5.2395 

169.762 

74.5989 

148.542 

66.3239 

132.037 

59.7068 

118.833 

53 

99.5687 

198.333 

85.3583 

170.000 

74,7028 

148.750 

66.4163 

132.222 

59.79*00 

119.000 

54 

99.7120 

198.611 

85.4811 

170.238 

74.8103 

148.958 

66.5119 

132.407 

59.8760 

119.167 

55 

99.8553 

198.889 

85.6040 

170  476 

74.9178 

149.167 

66.6075 

132.593 

59.9621 

119.333 

56 

99.9938 

199.167 

85.7227 

170.714 

75.0218 

149.375 

66.6999 

132.778 

60.0453 

119.500 

57 

100.132 

199.444 

85.8415 

170.952 

75.1257 

149.583 

66.7923 

132.963 

60.1284 

119.667 

58 

100.271 

199.722 

85.9602 

171.190 

75.2296 

149.792 

66.8847 

133.148 

60.2116 

119.833 

59 

69 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


12° 
liiT 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  C 
Tan. 

urve. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

o 

eoOre 

1200.oO 

301.104 

600.000 

200  749 

400  .  001 

150.576 

300.000 

120.474 

240.000 

i 

603.046 

1201  .67 

301,531 

600.833 

201.030 

400.556 

150.791 

300.417 

120.646 

240.333 

2 

603.90o 

1203.33 

301,964 

601.667 

201  322 

401.111 

151.006 

300.833 

120.818 

240.667 

3 

604.788 

1205.00 

302.379 

602.500 

201.599 

401  .  667 

151.213 

301.250 

120.984 

241.000 

4 

505.567 

1206.67 

302  79  J 

603.333 

201.876 

402.222 

151.421 

301.667 

121.150 

241.333 

5  600.4-26 

1208.33 

303.224 

604.167 

202.163 

402.778 

151.636 

302.083 

121.322 

241  667 

G 

607  286 

1210.00 

3)3  654 

o05.000 

202.449 

403.333 

151.851 

302.500 

121.494 

242.000 

7 

60S.  116 

1211.67 

3  J  4.  069 

•505.833 

202.  72( 

403.889 

152.059 

302.917 

121.660 

242.333 

8 

608.917 

1213.33 

304.485 

606  .  667 

203.003 

404.444 

152.266 

303.333 

121.827 

242.667 

9 

60  J.  778 

1215.00 

304.900 

607.500 

203.230 

405.000 

152.474 

303.750 

121.993 

243.000 

10 

610.609 

1216.67 

305.316 

603.333 

203  .  557 

405.556 

152.682 

304.167 

122.159 

243.333 

11 

611.468 

1218.33 

3)5.745 

509.167 

203  .  844 

406.111 

152.897 

304.583 

122.331 

243.667 

13 

612.328 

1220.00 

306.175 

510.000 

201.13) 

4015.667 

153.112 

305.000 

122.503 

244.000 

13 

613.158 

1221.67 

306.590 

610  833 

204.407 

407.222 

153.319 

305.417 

122.669 

244.333 

14 

513.989 

1223.33 

30r.006611.66r 

201.684 

407.778 

153.527  305.833 

122.835 

244.667 

15 

614.849 

1225.00 

307  436612.500 

204.971 

408.333 

153.  742  1306.  250 

1-23.007 

245.000 

16 

615.708 

1226.67 

30  7.  865 

613.333 

2  35  .  257 

408.889 

153.  957  1306.667 

123.179 

245.333 

17 

616.539 

1228.33 

303.281 

611.167 

205.534 

409.444 

154.165  307.083 

123.345 

245.667 

18 

617.370 

1230.00 

503.696  615.000 

3*5.811 

410.000 

54.372307.500 

1-23.512 

246.000 

19 

618.229 

1231.67 

309.126 

615.833 

208.  09  > 

410.556 

154.587 

307.917 

123.684 

246.333 

30 

619.089 

1233.33 

309.556 

616.667 

206.381 

411.111 

54.802 

308.333 

123.856 

246.667 

21 

619.919 

1235.00 

309.971 

617.500 

206.661 

411.667 

55.010 

308.750 

124.022 

247.000 

22 

620.750 

1236.67 

310.33? 

618.333 

206.938 

412.222 

55.218 

309.167 

124.188 

217.333 

23 

621.581 

1238.35 

310.802 

619.167 

207.215 

112.778 

55.4ft 

309.583 

124.354 

247.667 

34 

622.412 

1240.00 

311.217 

620.000 

207.492 

413.333 

55.633 

310.000 

124.520 

248.000 

35 

625.271 

1241.67 

311.647 

620.833 

207.779 

413.889 

55.848 

310.417 

121.692 

248.333 

36 

624.131 

1243.33 

312.077 

621.667 

203.065 

414.444 

56.003 

310.833 

24.864 

248.607 

37 

521.962 

1245.00 

312.492 

622.500 

208.342 

415.000 

56.271 

311.250 

125.030 

219.000 

28 

625.792 

1246.67 

312  908 

623.333 

208.619 

415.556 

56.478 

311.667 

125.197 

249.333 

39 

626.652 

1248.33 

313.337 

624.167 

208.905 

416.111 

56.693 

312.083 

125.369 

249.667 

30 

627.511 

1250.00 

313.767 

625.000 

209.192 

416.667 

58.908 

312.500 

25.541 

250.000 

31 

628.342 

1251.67 

314.183 

625.833 

209.469 

417.222 

57.116 

312.917 

25  .  7i  i7 

250.333 

33 

629.173 

1253.33 

314.598 

626.667 

209.746 

417.778 

57.324 

313.333 

145.878 

250.667 

33 

630.032 

1255.00 

315.028 

627.500 

210.032 

418.333 

57.539 

313.750 

126.045 

251.000 

34 

630.892 

1256.67 

315.457 

623.333 

210.319 

418.889 

57.753 

314.167 

126.217 

251.333 

35 

6H.723 

125S.33 

315.873 

629.167 

210.596 

419.444 

57.961 

314.583 

126.3S3 

251.667 

36 

632.553 

1260.00 

316.288 

630.000 

210.873 

420  000 

58.169 

315.000 

126.549 

252.000 

37 

633.413 

1261.67 

316.718 

630.833 

211.159 

420.556 

58.384 

315.417 

126.721 

252.333 

38 

634.272 

1263.33 

317.148 

631.667 

211.446 

421.111 

58.59'.) 

315.833 

126.893 

252.607 

39 

635.103 

1265.00 

317.563 

632.500 

211.723 

421.667 

158.807 

316.250 

127.059 

253.000 

4O 

635.931 

1266.67 

317.979 

633.333 

212.000 

422.222 

159.014 

316.667 

127.226 

253.333 

41 

636.765 

1268.33 

318  394 

634.167 

212.2771422.778 

159.222 

317.083 

127.392 

253.607 

43 

137.595 

1270.0D 

318.809635.000 

212.554423.333 

159.430 

317.500 

127.558 

254.000 

43 

638.455 

1271.67 

319.239615.833 

212.840423.889 

159.645 

317.917 

127.730 

254.333 

44 

639.31411273.33 

319.669 

636.667 

213.127424.444 

159.860 

318.333 

127.902 

254.667 

45 

610.145 

1275.00 

320.08} 

637.500 

213.404425.000 

160.067 

318.750 

128.068 

•255.000 

46 

610.976 

1276.67 

320.500638.333 

213.681425.556 

160.275 

319.167 

128.231 

255.333 

47 

541.835 

1278.33 

320.929639.167 

213.967426.111 

160.490 

319.583 

128.40(5 

255.667 

48 

612.695 

1280.00 

32  1.359  6  to.  000 

214.251426.667 

160.705 

320.000 

128.578 

256.000 

49 

643.526 

1281.67 

321.775 

610.833 

214.531427.222 

160.913 

320.417 

12H.744 

256.333 

1 

5O 

644.356 

1283.33 

322.190 

641.667 

214.808427.778 

161.120 

320.833 

128.911 

256.607 

51 

645.216 

1285.00 

322.620642.500 

215.094428.333 

161.335 

321.250 

129.033 

257.000 

53 

646.075 

1286.67 

323.050:643.333 

215.381  428.889 

161.550 

321.667 

129.255 

257.333 

53 

616  906 

12,88.33 

323.  465;  644.  167 

215.658429.444 

161.758 

322.083 

129.421 

257.667 

54 

647.737 

1290.00 

323.880645.000 

215.935430.000 

161.966 

322.500 

129.587 

258.000 

55 

648.596 

1291.67 

32  1.  310645.  833 

216.221  430.556 

162.181 

322.917 

129.759 

258.333 

56 

649.456 

1293.33 

324.740646.607 

216.508431.111 

162.395 

323.333 

129.931 

•258.667 

57 

650.287 

1295.00 

325.155647.500 

216.785431.667 

162.603 

323.750 

130.  097  1259.000 

58 

651.117 

1296.67 

895.871648.888 

217.061  432.222 

162.811 

324.167 

130.  263  1  259.  333 

59  651.977 

1298.33 

326.  000  1649.1  67 

217.348432.778 

163  026 

324  583 

130.  435  1  259.  667 

70 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

12° 
M. 

Tan. 

Arc. 

Tan. 

Arc.   1  Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

100.409 

200.000 

86.0790 

17  1.429  175.3336 

150.000 

66.9771 

133.333 

60.2948 

120.  000 

~o" 

100.553 
100.696 

200.278 
200.556 

86.2019 
86.3247 

171.  667)75.  4411  150.208 
171.90575.5486  150.417 

67.0727 
67.1683 

133.519 
133.704 

60.3809 
60.4669 

120.167 
120.333 

1 
2 

100.834 

200.833 

86.4435 

172.143 

75.6525 

150.625 

67.2607 

133.889 

60.5501 

120.500 

3 

100.973 

201.111 

86.5622 

172.381 

75.7565 

150.833 

67.3531 

134.074 

60.6333 

120.667 

4 

101.116 

201.389 

86.6851 

172.619 

75.8640 

151.042 

67.4487 

134.259 

60.7193 

120.833 

5 

101.260 

201.667 

86.8079 

172.857 

75.9715 

151.250 

67.5442 

134.444 

60.8054 

121.000 

G 

101.398 

201.944 

86.9267 

173.095 

76.0754 

151.458 

67.6366 

134.630 

60.8886 

121.167 

7 

101.537 

202.222 

87.0454 

173.333 

76.1794 

151.667 

67.7291 

134.815 

60.9718 

121.333 

8 

101.675 

202.500 

87.1642 

173.571 

76.2833 

151.875 

67.8215 

135.000 

61.0550 

121.500 

9 

101.814 

202.778 

87.2830 

173.810 

76.3872 

152.083 

67.9139 

135.185 

61.1381 

121.667 

1O 

101.957 

203.056 

87.4058 

174.048 

76.4948 

152.292 

68.0094 

135.370 

61.2242 

121.833 

11 

105.100 

203.333 

87.5287 

174.286 

76.6023 

152.500 

68.1050135.556 

61.3102 

122.000 

1  2 

102.239 

203.611 

87.6474 

174.524 

76.7062 

152.708 

68.1974135.741 

61.3934 

122.167 

13 

102.377 

203.889 

87.7662 

174.762 

76.8101 

152.917 

68.2898135.926 

61.4766 

122.333 

14 

102.521 

204.167 

87.8890 

175.000 

76.9177 

153.125 

68.3854136.111 

61.5627 

122.500 

15 

102.664 

204.444 

88.0119 

175.238 

77.0252 

153.333 

68.4810  136.296 

61.6487 

122.667 

16 

102.803 

204.722 

88.1306 

17'5.476 

77.1291 

153.542 

68.  5734  1136.481 

61.7319 

122.833 

17 

102.941 

205.000 

88.2494 

175.714 

77.2330153.750 

68.6658136.667 

61.8151 

123.000 

18 

103.084 

205.278 

88.3723 

175.952 

77.3406 

153.958 

68.7614 

136.852 

61.9011 

123.167 

19 

103.228 

205.556 

88.4951 

176.190 

77.4481 

154.167 

68.8570 

137.037 

61.9872 

123.333 

20 

103.366 

205.833 

88.6139 

176.429 

77.5520  154.375 

68.9494 

137.222 

62.0704 

123.500 

21 

103.505 

206.111 

88.7326 

176.667 

77.6559154.583 

69.0418 

137.407 

62.1536 

123.667 

22 

103.643 

206.384 

88.8514 

176.905 

77.7599  154.792 

69.1342 

137.593 

62.2368 

123.833  23 

103.782 

206.667 

88.9701 

177.143 

77.  8638  1155.  000 

69.2266 

137.778 

62.3199 

124.000 

24 

103.  925  1206.944 

89.0930 

177.381 

77.9713J155.208 

69.3222 

137.963 

62.4060 

124.167 

25 

104.  068!  207.  222 

89.2158 

177.619 

78.07881155.417 

69.4178 

138.148 

62.4920 

124.333 

26 

104.207 

207.500 

89.3346 

177.857 

78.1828 

155.625 

69.5102 

138.333 

62.5752 

124.500 

27 

104.345 

207.778 

89.4534 

178.095 

78.2867 

155.833 

69.6026 

138.519 

62.6584 

124.667 

28 

104.489 

208.056 

89.5762 

178.333 

78.3942 

156.042 

69.6982 

138.704 

62.7445 

124.833 

29 

104.632 

208.333 

89.6991 

178.571 

78.5017 

156.250 

69.7938 

138.889 

62.8305 

125.000 

30 

104.771 

208.611 

89.8178 

178.810 

78.6057 

156.458 

69.8862 

139.074 

62.9137 

125.167 

31 

104.909 

208.889 

89.9366 

179.048 

78.7096 

156.667 

69.9786 

139.259 

62.9969 

125.333 

32 

105.  052  1209.167 

90.0594 

179.286 

78.8171 

156.875 

70.0742 

139.444 

63.0829 

125.500 

33 

105.196:209.444 

90.1823 

179.524 

78.9246 

157.083 

70.1698 

139.630 

63.1690 

125.667 

34 

105.  334  1209.  722 

90.3010 

179.762 

79.0286 

157.292 

70.2622 

139.815 

63.2522 

125.833 

35 

105.473  210.000 

90.4198 

180.000 

79.1325 

157.500 

70'.  3546 

140.000 

63.3354 

126.000 

36 

105.616J210.278 

90.5427 

180.238 

79.2400 

157.708 

70.4502 

140.185 

63.4214 

126.167 

37 

105.759i210.556 

90.6655 

180.476 

79.3475 

157.917 

70.5458 

140.370 

63.5075 

126.333 

38 

105.898 

210.833 

90.7843 

180.714 

79.4515 

158.125 

70.6382 

140.556 

63.5907 

126.500 

39 

106.036 

211:111 

90.9030 

180.952 

79.5554 

158.333 

70.7306 

140.741 

63.6738 

126.667 

40 

106.175 

211.389 

91.0218 

181.190 

79.6593 

158.542 

70.8230 

140.926 

63.7570 

126.833 

41 

106.314211.667 

91.1405 

181.429 

79.  7633  '158.  750 

70.9154 

141.111 

63.8402 

127.000 

42 

106.459211.944 

91.2634 

181.667 

79.8708  158.958 

71.0110 

141.296 

63.9263127.167 

43 

106.600212.222 

91.3862 

181.905 

79.9783159.167 

71.1066 

141.481 

64.0123  127.333 

44 

106.739212.500 

91.5050 

182.143 

80.0822  159.375 

71.1990 

141.667 

64.  0955  ;  127.  500 

45 

106.877 

212.778 

91.6238 

182.381 

80.1862 

159.583 

71.2914 

141.852 

64.1787127.607 

46 

107.020 

213.056 

91.7466 

182.619 

80.2937 

159.792 

71.3870 

142.037 

64.2647127.833  47 

107.164 

213.333 

91.8695 

182.857 

80.4012 

160.000 

71.4826 

142.222 

64.3508  128.000  48 

107-302 

213.611 

91.9882 

183.095 

80.5051 

160.208 

71.5750 

142.407 

64.4340 

128.167,49 

107.441 

213.889 

92.1070 

183.333 

80.6091 

160.417 

71.6674 

142.593 

64.5172 

1  28.333  50 

107.584 

214.167 

92.209H 

183.571 

80.7166 

160.625 

71.7630 

142.778 

64.6032128.500  51 

107.727 

214.444 

92.3527 

183.810 

80.8241 

160.833 

71.8586 

142.96?, 

64.6893  128.667:  52 

107.  866 

214  722 

92.4714 

184.048 

80.9280 

161.042 

71.9510 

143.148 

64.  7725!  128.  833  53 

108.005 

21  o!  000 

92.5902 

184.286 

81.0320 

161.250 

72.0434  143.333 

64.8556  129.000  54 

108.148 

215.278 

92.7131 

184.524 

SI.  1395 

161.458 

72.1390143.519 

64.9417:129.167  55 

108-291 

215.556 

92.8359 

184.762 

SI.  2470 

161.667 

72.2345143.704 

65.0278  129.333  56 

108.430 

215.833 

92.9547 

185.000 

81.3509 

161.875 

'2.3270143.889 

65.1109  129.500 

57 

108.568 

216.111  93.0734 

185.238 

81.4549 

162.083 

"2.4194  144.074 

65.1941  129.667 

58 

108.712 

21  6.  389  193.1  963 

185.  476181.  5624 

162.292 

"-2.5149  144.259 

65.  28021  129.  833 

59 

71 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC- 


13° 

1°  Curve. 

2°  Carve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tau. 

Are. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

652.8:3(3  1300.00 

326.430 

650.000217.632 

433.333 

163.241  325.000 

130.60? 

260.000 

1 

653.667 

1301.67 

326.846 

650.833217.911 

433.  889  163.  448  325.  4  r 

130.77:3  260.8:3:3 

2 

654.498 

1303.3 

327.261 

651.667.218.188 

434.444  163.656325.83: 

130.940260.607 

3 

655.329 

1305.00 

327.676 

652.500218.465 

435.000  163.864326.250 

131.106261.000 

4 

656.164 

1308.6? 

328.092 

653.  333  '218.  7452 

435.556 

164.  072  326.  66~ 

181.  27S 

261.333 

5 

657.011 

1308.33 

328.522 

654.167219.029 

436.111 

164.287327.08: 

131.444 

261.667 

6 

657.878 

1310.00 

328.951 

655.000219.315 

436.667 

164.501 

327.500 

131.616 

262.000 

7 

658.  70J 

1311.67 

329.367 

655.833219.592 

437.222 

164.709 

327.917 

131.782 

262.333 

8 

659.510 

1313.33 

329.782 

656.6671219.869 

437.778 

164.917 

328.  33? 

131.948 

262.667 

9 

660.399 

1315.00 

330.212 

657.500 

220.156 

438.333 

165.132 

328.750 

132.120 

263.000 

10 

661.259 

1316.67 

330.642 

658.333 

220.442 

438.889 

165.347 

329.167 

132.292 

263.333 

11 

662.090 

1318.33 

331.057 

659.167220.719 

439.444 

165.554 

329.583 

132.458 

263.667 

13 

662.921 

1320.00 

331.472 

660.000220.996 

440.000 

165.762 

330.000 

132.625 

264.00) 

13 

663.780 

1321.67 

331.902 

660.833221.283 

440.556 

165.977 

330.417 

132.797 

264.333 

14 

664.639 

1323.33 

332.332 

661.667221.569 

441.111 

166.192 

330.833 

132.968 

264.667 

15 

665.470 

1325.00 

332.747 

662.500i221.846 

441.66? 

166.400 

331.250 

133.135 

265.000 

16 

666.301 

1326.67 

533.163 

663.333222.123 

442.222 

166.608 

331.667 

133.301 

265.333 

17 

667.160 

1328.  ,33 

333.592 

664.167222.410 

442.778 

166.822 

332.08:3 

133.473 

265.667 

18 

668.020 

1330.00 

334.022 

665.OOiV222.696 

443.333 

167.037 

332.500 

133.645 

266.000 

19 

668.851 

1331.67 

334.438 

665.833 

222.973 

443.889 

167.245 

332.917 

133.811 

266.333 

30 

669.681 

1333.33 

194.858 

666.667 

223.250 

444.444 

167.453 

333.333 

133.977 

266.667 

21 

670.541 

1335.00 

335.283 

667.500 

223  537 

445.000 

167.668 

333.750 

134.149 

267.000 

22 

671.400 

1336.67 

335.712 

668.333 

223.823 

445.556 

167.883 

334.167 

134.  32  1(267.  333 

23 

672.231 

1338.33 

336.128 

669.167 

224.100 

446.111 

168.090 

334.583 

134.487 

267.667 

34 

673.062 

1340.00 

336.543 

670.000 

224.377 

446.667 

1  68.  298 

335.000 

34.654 

268.000 

35 

673.921 

1341.67 

336.973 

670.833 

224.664 

447.222 

168.513 

335.417 

34.825 

268.303 

36 

674.781 

1343.33 

3:37.403 

671.667 

224.950 

447.778 

168.728 

335.833 

34.997 

268.667 

37 

675.612 

1345.00 

337.818 

672.500 

225.227 

448.333 

168.936 

336.250 

35.164 

269.000 

38 

676.442 

1346.67 

338.234 

673.333 

225.504 

448.889 

169.143 

336  667 

35.330 

269.333 

39 

677.302 

1348.33 

338.663 

674.167 

225.791 

449.444 

169.358 

337.083 

135.502 

269.667 

30 

678.161 

1350.00 

339.093 

675.000 

226.077 

450.000 

169.573 

337.500 

35.674 

270.000 

31 

678.992 

1351.67 

339.509 

675.833 

226.354 

450.556 

169.781 

337.917 

35.840 

270.333 

33 

679.823 

1353.33 

339.924 

676.667 

226.631 

451.111 

169.989 

338.3:33 

36.006 

270.667 

33 

680.682 

1355.00 

340.354 

677.500 

226.918 

451.667 

170.204 

338.750 

36.178 

271.000 

34 

681.542 

1356.67 

340.783 

678.333 

227.204 

452.222 

170.418 

339.167 

36.350 

271.333 

35 

682.373 

1358.33 

341.199 

679.167 

227.481 

452.778 

70.626 

339.583 

36.516 

271.667 

36 

683.203 

1360.00 

341.614 

680.000 

227.758 

453.333 

70.834 

340.000 

36.682 

272.000 

37 

684.063 

1361.67 

342.044 

680.833 

228.044 

453.889 

171.049 

340.417 

36.854 

272.333 

38 

684.922 

1363.33 

542.474 

681.667 

228.331 

454.444 

71  .264 

340.833 

37.026 

272.667 

39 

685.753 

1365.00 

342.889 

682.500 

228.608 

455.000 

71.472 

341.250 

37.193 

273.000 

4O 

686.584 

1366.67 

343.305 

683.333 

228.885 

455.556 

71.679 

341.667 

37,359 

273.333 

41 

687.443 

1368.33 

343.734 

684.167 

229.171 

456  111 

171.894 

342  083 

37.531 

273.667 

43 

688.303 

1370.00 

344.164 

685.000 

229.453 

456  .  667 

172.109 

342.500 

37.703 

274.000 

43 

689  134 

1371  67 

344.579 

685.833 

229.735 

457.222 

172.317 

342.917 

37.869274.333 

44 

689.964 

1373.33 

344.995 

686.667 

230.012 

457.778172.525 

343.333 

38.035 

274  .  667 

45 

690.824 

1375.00 

345.425 

687.500 

230  29S 

458.333  172.739 

343  750 

38.207 

275.000 

46 

691.683 

1376.67 

345.854 

688.333 

230.585 

458.889  172.954 

344.167 

38.379 

275.333 

47 

692.514 

1378.33 

346.270 

689.167 

330.862 

459.444  173.102 

344.583 

38.545 

275.667 

48 
49 

693.345 
694.204 

1380.00 
1381.67 

346.685 
347.115 

690.000 
690.833 

231.139 
231.425 

460.000 
460.556 

173.370 
173.585 

345.000 
345.417 

38.711 
38.883 

276.000 
276.333 

5O 

695.064 

1383.33 

347.545 

691.667 

231.712 

461.111 

173.800 

345.833 

39.055 

276.667 

51 

695.895 

1385  00 

347.960 

692.500231.989 

461.  667  1174.007 

346.250 

39.221 

277.000 

53 

696.725 

1386.67 

348.375 

693.333232.266 

462.222  174.215 

346.667 

39.388 

277.333 

53 

697.585 

1388.33 

348.805 

604.167:232.552 

462.778:174.430 

347.083 

39.560 

277.667 

54 

698.444 

390.00 

349.235 

695.000232.839 

463.333  174.  645  i  347.  500 

39.732 

278.000 

55 

599.275 

1391.67 

349.650 

695.833233.116 

463.889  174.853347.917 

39.898 

278.333 

56 

700.106 

1393.33 

350.066 

696.667233.393 

464.444  175.060348.333 

40.064 

278.607 

57 

700.965 

395.00 

350.496 

697.500233.679 

465.000  175.275|348.750 

40.236 

279.000 

.58 

701.895 

1396.67 

50.925 

698.333233.966 

465.556  175.490:349.167 

40.408 

279.333 

59 

702.656 

1398.33 

51.341 

699.167,234.243 

466.  Ill  1175.698:349.  583 

40.574 

279.667 

TABLE  XIV. — ACTUAL  TANGENTS,  ETC 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

13° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan 

Arc. 

M. 

103.855:216.607 

93.3191 

185.714 

81.0699162.500 

72.6105 

144.444 

65.3662 

130.000 

() 

106.  993  216.  944 

93.4379 

185.952 

81.7738162.708 

72.7029 

144.630 

65.4494 

130.167 

1 

109.  132  217.  22£ 

93.5566 

186.190 

81.8778162.917 

72  7  953 

144.815 

65.5326 

130.333 

2 

109.2701217.500 

93.6754 

186.429 

81.9817  163.125 

72.8878 

145.000 

65.6158 

130.500 

3 

109.409 

217.778 

93.7942186.667 

82.0856  163.333 

72.9802 

145.  185 

65.6990 

130.667 

4 

109.552 

218.056 

93.9170 

186.905 

82.1932163.542 

73.0757 

145.370 

65.7850 

130.833 

5 

109.696 

218.333 

94.  0399  187.  143 

82.  3007)163.  750 

73.1713 

145.556 

65.8711 

131.000 

6 

109.834 

218.611 

94.1586 

187.381 

82.4046:163.958 

73.2637 

145.741 

65.9543 

131.167 

7 

109.973 

218.889 

94.2774 

187.619 

82.  5085  1164.167 

73.3561 

145.926 

66.0374 

131.333 

8 

110.116 

219.167 

94.4002 

187.857 

82.6161 

164.375 

73.4517 

146.111 

66.1235 

131.500 

9 

110.259 

219.444 

94.5231 

188.095 

82.7236 

164.583 

73.5473 

146.296 

66.2096 

131.667 

1O 

110.398 

219.722 

94.6419  188.333 

82.8275 

164.792 

73.6397 

146.481 

66.2927 

131.833 

11 

110.53(3 

220.000 

94.7606 

188.571 

82.9314 

165.000 

73.7321 

146.667 

66.3759 

132.000 

12 

110.680 

220.278 

94.8835  188.810 

83.0390 

165.208 

73.8277 

146.852 

66.4620 

132.167 

13 

110.823 

220.556 

95.0063 

189.048 

83.1465 

165.417 

73  9233 

147.037 

66.5480 

132.333 

14 

110.961 

220.833 

95.1251 

189.286 

83.2504 

165.625 

74.0157 

147.222 

66.6312 

132.500 

15 

111.100 

221.111 

95.2438 

189.524 

83.3543 

165.8:33 

74.1081 

147.407 

66.7144 

132.667 

16 

111.243 

221.389 

95.3667 

189.762 

83.4619 

166.042 

74.2037 

147.593 

66.8005 

132.833 

17 

111.387 

221.667 

95.  4895  1190.000 

83.5694 

166.250 

74.2993 

147.778 

66.8865 

133.000 

18 

111.525 

221.944 

95.6083 

190.238 

83.6733 

166.458 

74.3917 

147.963 

66.9697 

133.167 

19 

111.664 

222.222 

95.7271 

190.476 

83.7772 

166.667 

74.4841 

148.148 

67.0529 

133  333 

20 

111.807 

222.500 

95.8499 

190.714 

83.8848 

166.875 

74.5797 

148.333 

67.1389 

133.500 

21 

111.950 

222.778 

95.9728 

190.952 

as.  99243 

167.083 

74.6753 

148.519 

67.2250 

133.667 

22 

112.089 

223.056 

96.  0915'  191.  190 

84.0962 

167.292 

74.7677 

148.704 

67.3082 

133.833 

23 

112.227 

223.338 

96.2103ll91.429 

84.200! 

167.500 

74.8601 

148.889 

67.3914 

134.000 

24 

112.371 

223.611 

96.3331 

191.667 

84.3077 

167.708 

74.9557 

149.074 

67.4774 

134.167 

25 

112.514 

223.889 

96.4560 

191.905 

84.4152 

167.917 

75.0513 

149.259 

67.5635 

1:34.333 

26 

112.652 

224.167 

96.5747 

192.143 

84.5191 

168.125 

75.1437 

149.444 

67.6467 

134.500 

27 

112.791 

224.444 

96.6935 

192.381 

84.623U 

168.333 

75.2361 

149.630 

67.7298 

134.667 

28 

112.934 

224.722 

96.8163 

192.619 

84.7306 

168.542 

75.3317 

149.815 

67.8159 

134.833 

29 

113.078 

225.000 

96.9392 

192.857 

84  8381 

168.750 

75.4273 

150.000 

67.9019 

135.000 

3O 

113.216 

225.278 

97.0580 

193.095 

84.9450 

168.958 

75.5197 

150.185 

G7.9851 

135.167 

31 

113.356 

225.556 

97.1767 

193.333 

85.0459 

169.167 

75.6121 

150.370 

68.0683 

135.3:33 

32 

113.498 

225.833 

97.2996 

193.571 

85.1535 

169.375 

75.7077 

150.556 

68.1544 

135.500 

33 

113.641 

226.111 

97.4224 

193.810 

85.2610 

169.583 

75.8033 

150.741 

68.2404 

135.667 

34 

113.780 

226.389 

97.5412 

194.048 

85  3649 

169.792 

75.8957 

150.926 

68.3236 

135  833 

35 

113.918 

226.667 

97.6599 

194.2<86 

85.4688 

170.000 

75.  -9881 

151.111 

68.4068 

136.000 

36 

114.062 

226.944 

97.7828 

194.524 

85.5764 

170.208 

76.0837 

151.296 

68.4928 

136.167 

37 

114.205 

227.222 

97.9056 

194.762 

R5.6839 

170.417 

76.1793 

151.481 

68.5789 

136.333 

38 

114.343 

227.500 

08.0244 

195.000 

85.7878 

170.625 

76.2717 

151.667 

68.6621 

136.500 

39 

114.482 

227.778 

98.1432 

195.238 

85.8917 

170.833 

76.3641 

151.852 

68.7453 

136.667 

40 

114.625 

228.056 

98.2660 

195.476 

85.9993 

171.042 

76.4596 

152.037 

68.8313 

136.833 

41 

114.769 

228.333 

98.3889  195.714 

86.1068 

171.250 

76.5552 

152.222 

68.9174 

137.000 

42 

114.907 

228.611 

98.5076 

195.952 

86.2107 

171  .458 

76.6476 

152.407 

69.0006 

137.167 

43 

115.046 

228.889 

98.6264 

196.190 

86.3146 

171.667 

76.7400 

152.593 

69.0837 

137.333 

44 

115.189 

229.167 

98.  7492  i  196.  429 

86.4222 

171.875 

76.8356 

152.778 

69.1698 

137.500 

45 

115.332 

229.444 

98.8721 

196  667 

86.5297 

172.083 

76.9312 

152.963 

69.2559 

137.607 

46 

115.471 

229.722 

98.9908196.905 

86.6336 

172.292 

77.0236 

153.148 

69.3390 

137.833 

47 

115.609 

230.  (00 

99.1096 

197.143 

86.7375 

172.500 

77.1160 

153.333 

69.4222 

138.000 

48 

115.7'53 

230.278 

99.2325  197.381 

86.8451 

172.708 

77.2116 

153.519 

69.5083 

138.167 

49 

115.896 

230  556 

09.3553  197.619 

86.9526 

172.917 

77.3072 

153.704 

69.5943 

138.3:33 

5O 

116.034 

230.833 

99.4741 

197.857 

87.0565 

173.125 

77.3996 

153.889 

69.6775 

138.500 

51 

116.173231.111 

99.5928198.095 

87.1604 

173  333 

77.4920 

154.074 

69.7607 

138.667 

52 

116.316 

231.389 

99.7157 

198.333 

87.2680 

173.542 

77.5876 

154.25969.8468 

1:38.833 

53 

116.460 

231.667 

99  8385 

198.571 

87.3755 

173.750 

77.6832 

154  44469.9328139000 

54 

116  5981281.944 

99  9573  198.810 

87.4794 

173.958 

77.7756 

154.630170  0160 

139.167 

55 

116.737232  222 

100.07'6 

199  048 

87.5833 

174  167 

77  8680 

154.  81  5  ;  70.  0992 

139.333 

56 

116.880232.500 

100.199  199.286 

87.6909 

174.375 

77.9636 

155.00070.1852 

139.500 

57 

117.023232.778 

100.322 

199  524 

87.7984 

174.583 

78.0592 

155.1&5J70.2713 

139.667 

58 

117.162233.056 

100.440  199.762 

87.9023 

174.792 

78.1516 

155.370170.3545 

139.833 

59 

73 


TABLE  XIV. — ACTUAL,  TANGENTS,    ETC. 


140 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

IviT 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
2347520 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

o 

703.480 

1400.00 

851.756 

7UO.OOO 

406.667 

175.906 

350.000 

140.  740  280.  000 

i 

04  346  1401.67 

S53.186 

700.833 

J34.806 

467.222 

176.121 

350.417 

140.912 

280.3*3 

2 

705.  205    403.33 

352.616 

701.667 

235.093 

467.778 

176.335 

350.833 

141.084 

V80.007 

3 

"06.065 

405.00 

353.045 

702.500 

235.379 

468.333 

176.550 

'351.250 

141.2561281.000 

4 

"06.924 

406.67 

353.475 

703.333 

.>35.606 

408.889 

176.765 

•351.607 

141.428 

281.333 

5 

"07.755 

408.133 

353.890 

704.107 

235.943 

469.444 

176.973 

352.083 

141.594 

281  607 

0 

708.586 

410.00 

354.306 

705.000 

236.220 

470.000 

177.181 

352.500 

141.760 

282.000 

7 

"09.445 

411.67 

354.736 

705.833 

236.506 

470.556 

177.396 

352.917 

141.932 

282.333 

8 

"10  305 

1413.33 

355.165 

706.667 

236.793 

471.111 

177.611 

353.3:33 

142.104 

282.607 

9 

"11.136 

1415.00 

355.581 

707.500 

237.070 

471.667 

177.818 

353.750 

142.271 

283.000 

10 

"11.966 

1416.67 

355.996 

708.333 

237.347 

472.222 

178.026 

354.167 

142.437 

283.  a33 

11 

"12.826 

1418.33 

356.426709.167 

237.633 

472  7i'8 

178.241  354.583 

142.609 

283.667 

12 

713.685 

1420.00 

356.856 

710.000 

237.920 

473  '.333 

178.456355.000 

142.781 

284.000 

13 

714.516 

1421.67 

357.271 

710.833 

238.197 

473.889 

178.  664  a55.  41  7 

142.947 

284.333 

14 

715.347 

1423.33 

357.687711.667 

238.473 

474.444 

178.871 

355.833 

143.113 

284.667 

15 

716.206 

1425.00 

358.116 

712.500 

238.760 

475.000 

179.086,356.250 

143.285 

285.000 

10 

717.066 

1426.67 

358.546 

713.333 

239.047 

475.556 

179.301 

356.667 

143.457 

285.333 

17 

717.896 

1428.33 

358.961 

714.167 

239.323 

476.111 

179.509 

357.083 

143.623 

285.667 

18 

718.727 

1430.00 

359.377 

715.000 

239.600 

476.667 

179.717 

357.500 

143.789 

286.000 

19 

719.587 

1431.67 

359.807 

715.833 

239.887 

477  .  222 

179.932 

357.917 

143.961 

286.333 

2O 

720.446 

1433.33 

360.236 

716.667 

240.173 

477.778 

180.146 

358.333 

144.133 

286.667 

21 

721.277 

14&5.00 

360.652 

717.500 

240.45: 

478.333 

180.354 

358.750 

144.299 

287.000 

22 

722.108 

1436.67 

361.067 

718.333 

240.727 

478.889 

180.502 

359.167 

144.466 

287.333 

23 

722.967 

1438.33 

301.497 

719.167 

241.014 

479.444 

180.777 

359.583 

144.638 

287.007 

24 

723.827 

1440.00 

361.927 

720.000 

241.  300 

480.000 

180.992 

300.000 

144.  810  1288.000 

25 

724.657 

1441.67 

362.342 

720.833 

241.577 

480.556 

181.199 

360.417 

144.976 

288.333 

26 

725.488 

1443.33 

362.757 

721.667 

241.854 

481.111 

181.407 

360.8313 

145.142288.607 

27 

726.348 

1445.00 

363.187 

722.500 

242.141 

481.667 

181.622 

361.250 

145.314 

289.000 

28 

727.207 

1446.67 

363.617 

723,333 

242.427 

4S2.222 

181.837 

361.607 

145.486289.333 

29 

728.067 

1448.33 

364.047 

724,167 

242.714 

482.778 

182.052 

362.083 

145.658289  607 

SO 

728.926 

1450.00 

364.476 

725.000 

243.000 

483.333 

182.267 

362.500 

145.8:30290.000 

31 

729.757 

1451.67 

364.892 

725.833 

243.277 

483.889 

182.475 

362.917 

145.996290.333 

32 

730.588 

1453.33 

365.307 

726.667 

243.554 

484.444 

182.682 

363.333 

146.162 

290.607 

33 

731  .447 

1455.00 

365.737 

727.500 

243.841 

485.000 

182.897 

303.750 

146.  334  291.  000 

34 

732.307 

1456.67 

366.167 

728.333 

244.127 

485.556 

183.112 

304.167 

146.506 

291.333 

35 

733.137 

1458.33 

366.582 

729.167 

244.404 

486.111 

183.320 

364.583 

146.672 

201.607 

36 

733.968 

1460.00 

366.998 

730.000 

244.681 

486.667 

183.528 

365.000 

146.  838  :  292.  000 

37 

734.828 

1461.67 

367.427 

7:30.833 

244.968 

487.222 

183.742 

365.417 

147.010 

292.333 

38 

735.687 

1463.33 

367.857 

731.667 

245.254 

487.778 

183.957 

305.83: 

147.  182  292.  Of  7 

39 

736.518 

1465.00 

368.272 

732.500 

245.531 

488.333 

i  84.  165 

306.250 

147.349 

293.000 

4O 

737.349 

1466.67 

368.688 

7:33.333 

245.808 

488.889 

184.373 

366.66" 

147.515 

293.333 

41 

738.208 

1468.33 

369,118 

734.167 

216.095 

489.444 

184.588 

307.083 

147.687 

293.667 

42 

739.068 

1470.00 

369.547 

735.  000 

246.381 

490.000 

184.803 

307.500 

147.859 

294.000 

43 

739.927 

1471.67 

369.977 

735.833 

246.668 

490.556 

185.018 

307.91" 

148.031'294.333 

44 

740.786 

1473.33 

370.407 

736.667 

246.954 

491.111 

185.232 

308.  ass 

148.203 

294.007 

45 

741.617 

1475.00 

370.822 

737.500 

247.231 

491.66" 

185.440 

368.750 

148.369295.000 

46 

742.448 

1476.67 

371.233 

738.333 

247.508 

492.22'. 

185.648 

369.16" 

148.535 

295.333 

47 

743.307 

1478.33 

371.667 

739.167 

247.795 

492.778 

185.803 

369.583 

148.7W 

205.007 

48 

744.167 

1480.00 

372.097 

740.  (XX 

248.081 

403.33: 

186.078 

370.000 

148.879 

296.000 

49 

744.998 

1481.67 

372.513 

740.833 

248.358 

493.889 

186.286 

370.417 

149.045,296.333 

1 

50 

745.829 

1483.  a 

372.928 

741.667 

248.635494.444 

186.493 

370  83: 

149.211 

206.667 

51 

7'46.688 

1485.00 

373.358 

742.500 

248.922495.000 

186.708 

371.250 

149.383297.000 

52 

747.547 

1486  67 

373.787 

743.333 

249.208495  5U 

186.923 

371.60" 

149.555 

297.333 

53 

748.378 

1488.33 

374.203 

744.167 

249  4&5406.111 

187.131 

372.08: 

149.721 

2»7.f>07 

54 

749.209 

1490.00 

374.618 

745.000 

249.762496.66" 

187.339 

372.500 

149.  888  298.  Of  0 

55 

750.068 

1491.6" 

375.048 

745.833 

250.  049  497.  22x 

187.553372.91" 

150.060 

208.333 

56 

750.928 

1493.3: 

375.478 

746.66" 

250.335497.778 

187.768373.33: 

150.231 

208.007 

57 

751.787 

1495.00 

375.907 

747.500 

250.622498.333 

187.983373.750 

150.403 

209.000 

58 

752.  647  1496.6" 

376.337 

748.33: 

250.908498.881) 

188.198374.16* 

150.575 

200.333 

59 

753.47811498.3: 

376.753 

749.16" 

251.185499.444 

188.406 

374.58: 

1  50.  742  299.  Of,  7 

74 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

14° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

117.300 

233.333 

100.559 

200.000 

88.0062 

175.000 

78.2440 

155.556 

70.4377 

140.000 

0 

117.444 

233.611 

100.682 

200.238 

88.1138 

175.208 

78.3396 

155.741 

70.5237 

140.167 

1 

117.587 

233.889 

100.805 

200.476 

88.2213 

175.417 

78.4352 

155.926 

70.6098 

140.333 

2 

117.730 

234.167 

100.928 

200.714 

88.3288 

175.625 

78.5308 

156.111 

70.6958 

140.500 

3 

117.874 

234.444 

101.051 

200.952 

88.4363 

175.833 

78.6264 

156.296 

70.7819 

140.667 

4 

118.012 

234  722 

101.169201.190 

88.5402 

176.042 

78.7188 

156.481 

70.8651 

140.833 

5 

118.151 

235.000 

101.288201.429 

88.6442 

176.250 

78.8112 

156  667 

70.9482 

141.000 

6 

118.294 
118.437 

235.278 
'35.556 

101.411  201.667 
101.  534  1201.  905 

88.7517 
88.8592 

176.458 
176.667 

78.9068 
79.0024 

156.852 
157.037 

71.0343 
71.1203 

141.167 
141.333 

7 
8 

118.576 

235.833 

101.653 

202.143 

88.9631 

176.875 

79.0948 

157.222 

71.2035 

141.500 

9 

118.714 

236.111 

101.771  202.381 

89.0671 

177.083 

79.1872 

157.407 

71.2867 

141.667 

10 

118.858 

236.389 

101.894  202.619 

89.1746 

177.292 

79.2828 

157  593 

71.3728 

141.833 

11 

119.001 

•,»36  667 

102.017202.857 

89.2821 

177.500 

79.3783  157.778 

71.4588 

142.000 

12 

119.139J236.944 

102.130203.095 

89.3860 

177.708 

79.4708 

157.963 

71.5420 

142.167 

13 

119.278237.222 

102.255203.333 

89.4900 

177.917 

79.5632158.148 

71.6252 

142.333 

14 

119.421i237.500 

102.377203.571 

89.5975 

178.125 

79.6587 

158.333 

71.7112 

142.500 

15 

119  565237.778 

102.500203.810 

89.7050 

178.333 

79.7543158.519 

71.7973  142.667 

16 

119.703238.056 

102.619204.048 

89.8089 

178.542 

79.8467 

158.704 

71.8805142.833 

17 

H9.  842  238.383 

102.738204.286 

89.9129 

178.750 

79  9391 

158.889 

71  9637  143.000 

18 

119.985 

238.611 

102.861 

204.524 

90.0204 

178  958 

80.0347 

159.074 

72.0497 

143.167 

19 

120.128 

238.889 

102.984 

204.762 

90.1279 

179.167 

80.1303 

159.259 

72.1358 

143.333 

20 

120.267 

239.167 

103.102 

205.000 

90.2318 

179  375 

80.2227 

159.444 

72.2190 

143.500 

21 

120.405 

239.444 

103.221 

205.238 

90.3358 

179.583 

80.3151 

159  630 

72.3021 

143.667 

22 

12.).  549 

239.722 

103.344 

205.476 

90.4433 

179.792 

80.4107  159.815 

72.3882 

143.833 

23 

120.692 

240.000 

103.467 

205.714 

90.5508 

180.000 

80.5063 

160.000 

72.4743 

144.000 

24: 

120.830 

240.278 

103.585 

205.952 

90.6547 

180.208 

80.5987 

160.185 

72.5574 

144.167 

2r> 

120.969 

240.556 

103.704 

206  190 

90.7587 

180.417 

80.69llil(.;0.370 

72.6106 

144.333 

26 

121.112 

240.833 

103.827 

206.429 

90  8662 

180.625 

80.7867 

160.550 

72  .  7267 

144.500 

27 

121.256 

241.111 

103.950 

206.667 

90.9737 

180.833 

80.8823 

160.741 

72.8127 

144.667 

28 

121.399 

241.3-9 

104.073 

206.905 

91.0812 

181.042 

80.9779 

160.  92€ 

72.8988 

144.833 

29 

121.542 

241.667 

104.196 

207.143 

91.1887 

181.250 

81.0735 

161.111 

72.9848 

145.000 

30 

121.681 

241.944 

104.314 

207.381 

91.2927 

181.458 

8l.1659il61.296 

73.0680 

145.167 

31 

121.819 

242.222 

104.433 

207.619 

91.3966 

181.667 

81.2583 

161.481 

73.1512 

145.333 

32 

121.962 

242.500 

104.556 

207.857 

91.  5041  '181.  875 

81.3539161.667 

73.2373 

145.500 

33 

122.106 

242.778 

104.679 

208.095 

91.61161182  083 

81.4486 

161.852 

73.3233 

145.667 

34 

122.244 

243.056 

104.798 

208.333 

91.7156 

182.292 

81.5419 

162.037 

73.4065 

145.838 

35 

122.383 

243  333 

104.916 

208.571 

91.8195 

182.500 

81.6343 

162.222 

73.4897 

146.000 

36 

122.526 

243.611 

105.039 

208.810 

91.9270 

182.708 

81.7299162.407 

73  .  5757 

146.167 

37 

122.669 

243.889 

105.162 

209.048 

92.0345 

182.917 

81.8255 

162.593 

7'3.  66  18 

146.333 

38 

122.808 

244.167 

105.281 

209.286 

92.1385 

183.125 

81.9179 

162.778 

73.7450il46.50u 

39 

122.947 

244.444 

105.400 

209.524 

92.2424 

183.333 

82.0103 

162.963 

73.8282 

146.  6G7 

40 

123.090 

244.722 

105.522 

209.762 

92.3499 

183.542 

82.1059  163.148 

73  9142 

146.833 

41 

123.233 

245.000 

105.645 

210.000 

92.4574 

183.750 

82.2015 

163.333 

74.0003 

147.000 

42 

123.376 

245.278 

105.768 

210.23S 

92.5650 

183.958 

82.2970 

163.519 

74.0863 

147.167 

43 

123.520 

245.556 

105.891 

210.476 

92.6725 

184.167 

82  3926  163.704 

74.1724 

147.333 

44 

123.658 

245.833 

106.010 

210.714 

92.7764  184.375 

82.4850 

163.889 

74.2556 

147.500 

45 

123.797 

246.111 

106.129 

210.952 

92.8S03  184.583 

82  5774 

164.074 

74.3387 

147.667 

46 

123.940 

246.389 

106.251  211.190 

92.  9879  1  184.  792 

82.6730  164.259 

74.4248 

147.833 

47 

124.083 

246.667 

106.  374  1211.  429 

93.0954 

185.000 

82.7686164.444 

74.5109 

148.000 

48 

124.222 

246.944 

106.493 

211.667 

93.1993 

185.208 

82.8610 

164.630 

74.5940 

148.167 

49 

124.360 

247.22? 

106.612211.905 

93.3032 

185.417 

82.9534 

164.815 

74.6772 

148.333 

5O 

124.504 

247.500 

106.735212.143 

93.4108 

185.625 

83.0490165.000 

74.7633148.500 

51 

124.647 

247.778 

106.857212.381 

93.5183 

185.833 

83.1446 

1  («5.185 

74.  84  93  1148.  667 

52 

124.786 

848.036 

106.976212.619 

93.6222 

186.  042  83.  23701  65.  37'0 

74.9325148.833 

53 

124.924 

248.333 

107.095212.857 

93.721.1 

186.  250  I  83.  3294 

165.556 

75.0157  149.000 

54 

125.067 

248.611 

107.218213.095 

93.8337 

1  86  .  4  58  1  S3  .  4250  1  65  .  741 

75.1018 

149.167 

55 

125.211 

248.889 

107.341  213.333 

93.9412 

186.  667  183.5206 

165.926 

75.1878  149.333 

5fi 

125.354 

249.167  107.464  213.571 

94.0487 

186.  875;  83.  61  62  166.111 

75.2739  149  500 

57 

125.497 

249.444  107.586  213.810 

94.1562 

187.083 

83.7118 

166.296 

75.3599  149.667 

58 

125.  6361249.  7221107.  705  214.048 

94.2601 

187.292 

83.8042  166.481 

75.4431  149.833 

59 

75 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


15° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

377.168 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

150.908 

Arc. 

0 

754.3081500.00 

750.000 

251.402 

500.000 

188.614 

375.000 

300.000 

1 

755.1681501.07 

377.598 

750.833 

251  .  740 

500.550 

188.828 

375.417 

151.080300.333 

2 

756.027  1503.33 

378.028 

751.607 

252.035 

501.111 

180.043 

375.833 

151.252300.007 

3 

756.8581505.00 

378.443 

752.500 

252.312 

501.007 

180.251 

376.250 

151.418301.000 

4 

757.689  1506.67 

378.858 

753.333252.589 

502.222 

189.459 

370.607 

151.584,301.333 

5 

758.5481508.33 

379.288 

754.167i252.875 

502.778 

189.674 

377  .  083 

151.756301.607 

6 

759.408  1510.00 

379.718 

755.000253.162 

503.333 

189.889 

377.500 

151.  928  1302.  000 

7 

700.2671511.67 

380.148 

755.833253.449 

503.880 

190.104377.917 

152.100302.333 

8 

761.  1271513.  33 

380.577 

756.667 

253.735 

504.444 

100.319378.333 

152.272 

302.607 

9 

761.9581515.00 

380.993 

757.500 

254.012 

505.000 

190.  526]  378.  750 

152.438 

303.000 

1 

10 

762  788  1516.67 

381.408 

758.333 

254.289 

505.556 

190.734379.167 

152.604 

303.333 

11 

703.648  1518.33 

381.838 

759.167 

254.575 

506.111 

190.949379.583 

152.776 

303.007 

12 

764.5071520.00 

382.268 

760.000 

254.862 

506.607 

101.1041380.000 

152.948 

304.000 

13 

765.338  1521.67 

382.683 

760.833 

255.139 

507.222 

191.372380.417 

153.114 

304.333 

14 

706.169  1523.33 

383.098 

761.667 

255.416 

507.778 

191.579380.833 

153.281 

304.607 

15 

767.0281525.00 

383.528 

762.500 

255.702 

508.333 

191.794 

381.250 

153.453 

305.000 

16 

767.888  1526.67 

383.958 

763.333 

255.989 

508.889 

192.009 

381.667 

153.624 

305.333 

17 

768.7471528.33 

384.388 

764.167 

256.275 

509.444 

192.224 

382.083 

153.  796!  305.  607 

18 

769.6071530.00 

384.817 

705.000 

256.562 

510.000 

192.439 

382.500 

153.968306.000 

19 

770.437 

1531.67 

385.233 

765.833 

256.839 

510.556 

192.647 

382.917 

154.135300.333 

20 

771.268 

1533.33 

385.648 

766.667 

257.116 

511.111 

192.854 

383.333 

154.301 

306.667 

21 

772.1281535.00 

380.078 

767.500 

257.402 

511.607 

193.009 

383.750 

154.473307.000 

22 

772.  987  i  1536.  67 

386.508 

768.333 

257.680 

512.222 

193.284 

384.107 

154.645307.333 

23 

773.8471538.33 

386.937 

769.167 

257  .  975 

512  778 

193.499 

384.583 

154.817 

307.007 

24 

774.706  1540.00 

387.367 

770.000 

258.202 

513.333 

103.714 

385.000 

154.089:308.000 

25 

775.5371541.67 

387.783 

770.833 

258.539 

513.880 

103.922 

385.417 

155.155 

308.333 

26 

776.368  1543.33 

3<88.198 

771.607 

258.810 

514.444 

104.120 

385.833 

155.321 

308.607 

27 

777.227J  1545.  00 

388.628 

772.  500  259.1  02 

515.000 

194.344 

380.250 

155.403300.000 

28 

778.086  1546.07 

389.057 

773.333259.389 

515.550 

194.550 

386.067 

155.605 

309.333 

29 

778.917 

1548.33 

389.473 

774.167 

059.666 

516.111 

104.767 

387.083 

155.831 

300.007 

30 

779.748 

1550.00 

389.888 

775.000 

259.943 

516.667 

194.975 

387.500 

155.997 

310.000 

31 

780.6081551.67 

390.318 

775.833 

260.229 

517.222 

195.100 

387.917 

156.169,810.383 

32 

781.  467  i  1553.  33 

300.748 

776.667 

260.510 

517.778 

195.405 

388.333 

156.  341  1310.667 

33 

782.326  1555  00 

301.178 

777.500 

200.802 

518.333 

195.619 

388.750 

156.513311.000 

34 

783.186 

1556.07 

301.607 

778.333 

261.080 

518.889 

195.834 

389.167 

156.685  311.333 

35 

784.017  1558.33 

392.023 

779.167 

261.366 

519.444 

196.042 

389.583 

156.851  311.667 

36 

784.  84711560.  00 

392.438 

780.000 

261.643 

520.000 

196.250 

300.000 

157.017 

312.000 

37 

38 

785.707 
786.566 

1561.67 
1563.33 

302.868 
303.298 

780.833 
781.667 

261.929520.556 
202.216521.111 

196.465 
196.680 

300.417 
390.833 

157.189  312.333 
157  3611312.667 

39 

787.426 

1565.00 

393.727 

782.500 

262.502521.667 

196.895 

301.250 

157.533313.000 

40 

788.285 

1566.67 

394.157 

783.333 

262.789 

522.222 

197.109 

391.667 

157.705 

313.333 

41 

789.116 

1568.33 

394.572 

784.167 

203.066 

522.778 

157.317 

302.083 

157.871  313.667 

42 

789.947 

1570.00 

394.988 

785.000 

203.343 

523.333 

197.525 

302.500 

158.038  314.000 

43 

790.806 

1571.67 

395.418 

785.833 

263.029 

523.889 

107.740 

392.917 

158.  210;  31  4.  333 

44 

791.666 

1573.33 

395.847 

786.007 

263.910 

524.444 

107.055303.333 

158.382314.667 

45 

792.497 

1575.00 

396.263 

787.500 

264.193 

525.000 

198.  103  1  303.  750 

158.  548!  315.  000 

46 

793.327  1576.67 

396.078 

188.333264.470 

525.556 

198.370304.107 

158.714315.333 

47 

794.187 

1578.33 

397.108 

789.167 

204.750 

526.111 

198,585894.583 

158.886  315.667 

48 

795.046 

1580.00 

397.538 

700.000205.043 

526.607 

108.800!305.000 

159  058316.000 

49 

795.906 

1581.67 

397.967 

790.833  205.329 

527.222 

199.015 

395.417 

159.230316.333 

50 

796.765 

1583.33 

308.397 

791.667 

205.610 

527.778 

199.230 

305.833 

159.  402  '310  007 

51 

797.596 

1585.00 

308.813  792.500  205.893  528.333 

100.438306.250 

159.568317.000 

52 

798.427 

1586.67 

399  .  228  703  .  333  '  206  .  1  70  1  528  .  880 

109.645306.667 

159.734317.333 

53 

799.286 

1588.33 

399  .  658  794  .  1  07  j  266  .  450  520  .  444  1  99  .  860  307  .  083 

150.006 

317.607 

54 

800.146 

1590.00 

400.087 

705.000  200.743  530.000  200.075  307.500 

100.078 

318.000 

55 

801.005 

1591.67 

400.517  705.833  207.020  53  >.556  200.200  307.017 

100.250 

318.333 

56 

801.865 

1593.33 

400  .  947  706  .  007  207  .  31(5  j  53  1  .  1  1  1  '  200  .  505  308  .  333 

160.42-2 

318.667 

57 

802.605 

1595.00 

401  .  302  707  .  500  i  207  .  503  53  1  .  607  200  .713  308  .  750 

100.588 

310.000 

58 

803.526 

1596.67 

401  .  778  i  708  .  333  207  .  870  53-2  .  22:2  200  .  920  300  .  1  67 

100.754 

310.333 

59 

804.386  1598.33 

402.208  799.167  208.156  532.77.8  1201  .135  399,583  160.926 

319.607 

TABLE  XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve.       1O°  Curve. 

15° 

Tail. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc.   i     Tan. 

Arc. 

M. 

1*5.774 

250.000 

107.824 

214.286 

94.3641 

187.50083.8966 

166.06775.5*63 

150.000 

0 

125.918 

250.278 

107.947 

214.524 

94.4716 

187.708  83.9922 

166.85275.6123 

150.167 

1 

126.061 

250.556 

108.070 

214.762 

94.5791 

187.91784.0878 

167.03775.6984 

150.333 

2 

126.200 

250.833 

108.188 

215.000 

94.6830 

188.12584.180^ 

1U7.  222  75.  7816 

150.500 

3 

126.338 

251.111 

108.307 

215.238 

94.7870 

188.33384.2726 

167.40775.8648 

150.667 

4 

126.481 

251.389 

108.430 

215.476 

94.8945 

188.54284.3682 

167.59375.9508 

150.833 

5 

126.625 

251.667 

108.553 

215.714 

95.U02U 

188.75084.4638 

167.  778  7'6.  0369 

151.000 

6 

126.768 

251.944 

108.67'6 

215.952 

95.1095 

188.95884.5594 

167.  9C3  76.1229 

151.167 

7 

126.911 

252.222 

108.799 

216.190 

95.2171 

189.167:84.6549 

108.  148  '76.  2090 

151.333 

8 

127.050 

252.500 

108.917 

216.429 

95.3210 

189.  37584.  747  3 

168.33376.2922 

151.500 

9 

127.188 

252.778 

109.036 

216.667 

95.4249 

189.58384.8398 

168.51976.3753 

151.667 

1O 

127.332 

253.056  109.159 

216.905 

95.5324 

189.79284.9353 

168.70476.46i4 

151.833 

11 

127.475 

253.333 

109.282 

217.143 

95.6400 

190.000  85.0309 

168.8897'(i.5i75 

152.000 

12 

127.613 

253.611 

109.401 

217.381 

95.7439 

190.20885.12:33 

169.07470.6300 

152.167 

13 

127.752 

253.889 

109.519 

217.619 

95.8478 

190.41785.2157 

169.25976.7138 

152.333 

14 

127.895 

254.  1G7 

109.642 

217.857 

95.9553 

190.62585.3113 

169.44476.7999 

152.500 

15 

128.039 

254.444 

109.765 

218.095 

96.0629 

190.88885.4069 

169.63076.8859 

152.667 

16 

128.182 

254.722 

109.888 

218.333 

96.1104 

191.  042  '85.  5025 

169.815  76.9720 

152.833 

17 

128.325 

255.000 

110.011 

218.571 

96  2779 

191.  250185.5981 

170.00077.0580 

153.000 

18 

128.464 

255.278 

110.129 

218.810 

96.3818 

191  ,458'85.  6905 

170.18577.1412 

153.167 

19 

128.602 

255.556 

110.248 

219.048 

96.4858 

191.667 

85.7829 

170.37077.2244 

153.333 

2O 

128.746 

255.833 

110.371 

219.286 

96.5933 

191.  875  185.  87  85 

170.556  77.3105 

153.500 

21 

128.889 

256.111 

110.494 

219.524 

96.7008 

192.083  85.9741 

17  0.741;  77.  3965 

153.667 

22 

129.032 

256.389 

110.617 

219.762 

96.8063 

192.  292  '86.  0697 

17'0.92677.4826 

153.833 

23 

129.176 

256.667 

110.740 

220.000 

96.9158 

192.  500  '86.1653 

171.111  77.5686 

154.000 

24 

129.314 

256.944 

110.856 

220.238 

97.0198 

192.70886.2577 

171.29677.6518 

154.167 

25 

129.453 

257.222 

110.977 

220.  47  (J 

97.1237 

192.917 

86.3501 

171.481  77.7'350 

154.333 

26 

129.596 

257.500 

111.100 

220.714 

97.2312 

I  U3.  125  86.  4457 

171.  667I77.  8210 

154.500 

27 

129.739 

257.778 

111.223 

220.952 

97.3387 

193.333  #  i.  5413 

171.85277.9071 

154.667 

28 

129.878 

258.  C56 

111.342 

.'21.190 

97.4427 

1  93.  542  :  86.  6337 

172.  037  i  7  7.  9903 

154.833 

29 

130.016 

258.333 

111.460 

221.429 

97'.  5466 

193.750 

86.7261 

172.222  78.07'35 

155.000 

3O 

130.160 

258.611 

111.583 

221.667 

97.6541 

193.95886.8217 

172.4077'8.1595 

155.167 

31 

130.303 

258.889 

111.706 

221.905 

97.7616 

194.167 

86.9173 

172.59378.2456 

155.333 

32 

130.446 

259.167 

111.829 

222.143 

97.8691 

194.375 

87.0128 

172.  77'8:7'8.  3316 

155.500 

33 

130.589 

259.444 

111.952 

222.381 

97.9767 

194.58387.1084 

172.96378.4177 

155.667 

34 

130.728 

259.722 

112.071 

222.619 

98.0806 

194.79287.2008 

173.14878.5009 

155.833 

35 

130.867 

260.000 

112.189 

222.857 

98.1845 

195.000!  87.  2932 

173.33378.5841 

156.000 

36 

131.010 

260.278 

112.312 

223.095 

98.2920 

195.20887.3888 

173.51978.6701 

156.167 

37 

131.153 

260.556 

112.435 

223.333 

98.3996 

195.41787.4844 

173.704  7'8.75<32 

156.333 

38 

131.296 

260.833 

112.558 

2^3.571 

98.5071 

195.625 

87.5800 

173.  889  7'8.  8422 

156.500 

39 

131.440 

261.111 

112.681 

223.810 

98.6146 

195.833 

87.6756 

17'4.07478.9283 

156.667 

4O 

131.578261.389 

112.799 

224.048 

98.7185 

196.042 

87.7680 

174.25979.0115 

156.833 

41 

131.717261.667 

112.918 

224.286 

98.8225 

196.250 

87.8604 

174.44479.0946 

157.000 

42 

131.  860J261.944 

113.041 

224.524 

98.9300 

196.458 

87.9560 

174.63079.1807 

157.107 

43 

132.003262.222 

113.164 

224.762 

99.0375 

196.667  88.0516 

174.81579.2667 

157.3S3 

44 

132.  142  1262.500 

113.283 

225.000 

99.1414 

196.87588.1440 

175.00079.3499 

157.500 

45 

132.280J262.778 

113.401 

225.238 

99.2454 

197.083  88.2364 

175.18579.4331 

157.667 

46 

132.424263.056 

113.524 

225.476 

99.3529 

197.  292  188.3320 

175.37079.5192 

157.833 

47 

132.567263.333 

113.647 

225.714 

99.4604 

197.500 

88.4276 

175.55679.6052 

158.000 

48 

132.710 

263.611 

113.770 

225.952 

99.5679 

197.708 

88.5232 

175.741  79.6913 

158.  167' 

49 

132.854 

263.889 

113.893 

226.190 

99.6754 

197.917 

88.6188 

175.92679.7773 

158.3-33 

50 

132.992264.167 

114.012 

226.429 

99.7794 

198.125 

88.7112 

176.111  79.8605 

158.500 

51 

133.131  264.444 

114.130 

226.667 

99.8833 

198.333 

88.8036 

176.29679.9437 

158.607 

52 

133.274264.722 

114.253 

226  905 

99.9908 

198.542 

88.8992 

176.481  80.0298 

158.833 

53 

133.417265.000 

114.376 

227.143 

100.098 

198.750 

88.9948 

176.66780.1158 

159.000 

54 

133.561  265.278 

114.499 

227.381 

100.206 

198.958 

89.0903 

176.85280.2019 

159.167 

55 

133.704  Of  -5.  550 

114.622 

227.619 

100.313 

199.167 

89.1859 

177.03780.2879 

159.333 

56 

133.H43-2fi5.83:-! 

114  741  227.857 

100.417 

199.375 

89.2783 

177.22280.3711 

159.500 

57 

133.981  266.111 

114.859228.095 

100.521 

199.583 

89.3707 

177.40780.4543 

159.667 

58 

134.124  266.389 

1  t4.882J228.333jlOO.629 

199.792 

89.4663 

177.59380.5403 

159.833 

59 

77 


TABLE  XIV. — ACTUAL   TAKGENTS,    ETC. 


16° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

A  re. 

~~O~ 

805.245 

1600.00 

402.1537 

800.000 

268.443 

533.333ia01.350 

400.000 

161.098 

320.000 

1 

806.104 

1601.67 

403.067 

800.833 

268.729 

533.  889i201.565 

400.417 

101.270 

320.333 

3 

806.964 

1603.33 

403.497 

80  1.607'!  269.  01  6 

534.444201.780 

400.833 

161.442 

320.667 

3 

807.795 

1605.00 

403.912 

802.  500)269.  293 

535  .000!  201.  988 

401.250 

161.608 

321.000 

4 

808.626 

1606.6? 

404.328 

803.  33-1209.  570 

535.556 

202.190 

401.667 

161.774 

321.333 

5 

809.485 

1608.33 

404.757 

bO  4.  107  269  856 

536.111 

202.410 

402.083 

161.946 

321  .  667 

6 

810.344 

1610.00 

405.187 

805.000270.143 

536.667 

202.625 

402.500 

162.  118  322.  000 

7 

811.204 

1611.67 

405.617 

805  833270.429 

537.222 

202.840 

402.917 

162.290322  333 

8 

812.063 

1613.  33 

406.047 

306.  667|270.  716 

537.778 

203.  055  403.  333 

162.462322.007 

9 

812.894 

1615.00 

406.462 

807.500 

270.993 

538.333 

203.263 

403.750 

162.628323.000 

10 

813.725 

1616.67 

406  877 

808.333 

271.270 

538.889 

203.471 

404.167 

162.795323.333 

11 

814.584 

1618.  as 

407.307 

809.167 

271  .556 

539.444 

203.686404.583 

162.967|323.067 

12 

815.444 

1620.00 

407.737 

810.000 

271.843 

540.000 

203.900405.000 

163.  131)  '324  000 

13 

816.303 

1621.67 

408.167 

810.833 

272.129 

540.556 

204.115405.417 

163.311  o24.3:%3 

14 

817.163 

1623.  33 

408.596 

811.667 

272.416 

541.111 

d04.SJ040o.833 

163.482324.667 

15 

817  993 

1625.00 

409.012 

812.500 

272.693 

541.667 

204.  538!  406.  250 

103.649,325  000 

16 

818.824 

1626.67 

409.4-37 

813.333 

272.970 

542.222 

204  746 

406.667 

103.8151325.333 

17 

819.684 

1628.33 

409.857 

814.16. 

273.256 

542.778 

204.961 

407.083 

163.987325.667 

18 

820.543 

1630.00 

410.287 

815.000 

273.543 

543.333 

205.176 

407.500 

164.159326.000 

19 

821.403 

1631.67 

410.716 

815.833 

273.829 

543.889 

205.390 

407.917 

104.331  320.333 

2O 

822.262 

1633  33 

411.  14G 

816.667 

274.116 

544.414 

205  605 

408.333 

164.503  326  667 

31 

823.122 

1035  00 

411.576 

817.500 

274.402 

545.000 

205.820 

40S.750 

164.  675|  327  000 

23 

823.981 

1636  67 

412.00(5 

818333 

274.639 

545.556 

206.035 

409.16; 

164  847 

327  333 

23 

824.812 

1638.33 

412.421 

819.167 

274.966 

546.111 

206.243 

40!)  583 

165.013 

327  667 

24 

825.643 

1640.00 

412.836 

820.000 

275.243 

516.667' 

206.451 

410.000 

105.179 

328.000 

25 

826.502 

1641.67 

413.260 

820.8-33 

275.529 

547.222 

-.'06.606 

410  417 

165.351 

328.333 

26 

827.361 

1643.33 

413.696 

821.667 

275.816 

547.778 

206.880 

410.833 

165.523 

328.607 

27 

828.221 

1645.00 

414.126 

822.500 

276.102 

548.333 

207.095 

411.250 

165.695 

329.000 

28 

829.080 

1616.67 

414.555 

823.333 

278.898 

548.889 

207.310 

411.667 

165.867 

329.333 

29 

829.911 

1648.  33 

414.971 

824.167 

276.666 

549.444 

207.518 

412.063 

166.033 

329.667 

30 

830.742 

1650.00 

415.386 

825.000 

276.912 

550.000 

207.726 

412  500 

166.199 

330.000 

31 

831.601 

1651  .  67 

415  816 

825.833 

277.229 

550.556 

207.941 

412.917 

166.371 

330,333 

32 

832  461 

1653  33 

416.246 

826.667 

277  516 

551.111 

208.156 

413.333 

166.543 

330.667 

33 

833.320 

1655.00 

410.675 

827.500 

277.802 

5M.667 

208.370 

413.750 

166  715 

331.000 

34 

834.180 

1656.67 

417.105 

828.333 

278.089 

552.222 

208.  5S5 

414.167 

166.887 

331.333 

35 

835.011 

1658.33 

417.521 

829.167 

278.366 

5?>2  778 

208.793 

414.583 

107.053 

331.667 

36 

835.841 

1660.00 

417.936 

830.000 

278.642 

553.333 

309.001 

415.000 

167.219 

332  000 

37 

836.701 

1661.67 

418.366 

830.833 

278.929 

553.889 

209.216 

415.417 

167.391 

332.833 

38 

837.560 

1663.33 

418.795 

831.667 

279.215 

554.444 

209.421 

415.833 

167.563 

332.667 

39 

838.420 

1665.00 

419.225 

832.500 

279.502 

555.000 

209.646 

416.250 

167.735 

333.000 

40 

839.279 

1666.67 

419.655 

833.333 

279.789 

555.556 

209.860 

416.667 

167.907 

333.333 

41 

840.139 

1668.33 

420.085 

834.167 

280.075 

556.111 

210.075 

417.083 

168  079 

333.667 

42 

840.998 

1670.00 

420.514 

835  000 

280.362 

556.667 

210.290 

417.500 

168.251 

334.000 

43 

841.829 

1671.67 

420.930 

835.833 

280.639 

557.222 

210.498 

417.917 

168.417 

334.333 

44 

842.660 

1673.33 

421.345 

836  667 

280.915 

557.778 

310.706 

418.333 

168.  583!  334.  667 

45 

843.519 

1675.00 

421.775 

837.500 

281.202 

5.58.333 

210  921 

418.750 

168  755335.000 

46 

844.379 

1676.67 

422.205 

838.333 

281.  48S 

558.889 

211.136 

416.167 

168.927  335.  ,333 

47 

845.238 

1678.33 

422.634 

839.167 

281.775 

V>9.444 

211.350 

419.583 

169.099335.667 

48 

846.097 

1680.00 

423.  06  4 

840.000 

282  062 

560.000 

211.565 

420.000 

169.271  336.000 

49 

846.928 

1681.67 

423  480 

840.833 

282.338 

500.556 

211.773,  420.  417 

169.437  336.333 

50 

847.759 

1683.33 

423.895 

841.667 

282.615 

561.  111 

211.981  420.833 

169.604  336.667 

51 

848.618 

1685.00 

424.325 

842.500 

2S2.902 

•)(•>].  607 

21  2.  19(5;  42  1.250 

169.776337.000 

53 

849.478 

1686.67 

424.755 

843.333 

283.188 

562.222 

212.411  421.667 

169.947  337.333 

53 

850.337 

1688.33 

125.184 

844.167 

2S3  .  475  "62  .  778  i  2  1  2  .  626  4  22  .  083 

170.119:337.007 

54 

851.197 

1690.00 

425.614  845.000 

283  .  7  u  i  5<  J:J  .  330  !  21  2  .  840  422  .  500  1  1  70  .  291  i  338  .  000 

55 

852.056 

1691.67 

426.044  845.  83:5 

28LOJ8  5(i:]  SS^  •.'!:-.  055  422.0171170.463  338.3*3' 

56 

852.916 

1693  33 

426.473  846.667  284.335  ;754  444  213.270  423.  333'  170.  635  .348.  667 

57 

853.746 

1695.00 

426.889  847.500  284.011  <5  5.0:M>  213.478  423.  750,170.8111  339.000 

58 

854.577 

1696.67 

427  .  304  818.  333  ,  284  .  888  !  5<  15  f,r,6  2  !  3  .  686  424  .  1  (57  1  70  .  968  389  .  333 

59 

855.437 

1698.33 

427.734  849.167  285.175i566.lHhJ13.90I  424.  583  J  7  1.1  40  3:39.067 

TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  C 

Tan. 

iirve. 

Arc. 

9°  Curve. 

1O°  Curve. 

16° 
M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

1  34.208 

266.667 

115.105 

228.571  100.736 

200.00089.5619 

177.778 

80.6264 

160.000 

o 

134.411 

266.944 

115.228 

228.810100.844 

200.20889.6575 

177.963 

80.7124 

160.167 

1 

134.554 

267.222 

115  351 

229.048100.951 

200.41789.7531 

17B.148 

80.7985 

160.333 

2 

134.693 

267.500 

115.469 

229.286101.055 

200.62589.8455 

178.333 

80.8817 

160.500 

3 

134.831 

267.778 

115.588 

229.524  101.159 

200.83389.9379 

178.519 

80.9649 

160.667 

4 

184.975 

268.056 

115.711 

229.762101.267 

201.04290.0335 

178.704 

81.0509 

160.833 

5 

135.118 

268  333 

115.834 

230.000!  101.  374 

201.250:90.1291 

178.889 

81.1370 

161.000 

6 

135.261 

268.611 

115.957 

230.238  101  482 

201.  458!90.  2247 

179.074 

81.2230 

161.167 

7 

1,35.405 

268.889 

116.080 

230.476  101.589 

201.667 

90.3203 

179  259 

81.3091 

161.333 

8 

135.543 

269.167 

116.198 

230.714 

101.693 

201.875 

90.4127 

179.444 

81.3923 

161.500 

9 

135.682 

269.444 

116.317 

230.952 

101  .  7  97 

202.083 

90.5051 

179.630 

81.4754 

161.667 

10 

135.825 

269.722 

116  4401231.190 

101.905 

202.  292  190.6007 

179.815 

81.5615 

161.833 

11 

135.968!  270.  000 

11  6.  563^  231.  429 

102.012 

202.500 

90.6903 

180.000 

81.6476 

162.000 

12 

136.112 

270.278 

116.686J231.667 

102.120 

202.708 

90.7919 

180.185 

81.7336 

162.167 

13 

136.255 

270.556 

116  809231.905 

102.227 

202.917 

90.8874 

180.370 

81.8197 

162.333 

14 

136.393 

270.833 

116.927 

232.143 

102.331 

203.125 

90  9798 

180.556 

81.9028 

162.500 

15 

136.532 

271.111 

117.046 

232  381 

102.435 

203  333 

91.07'*3 

180.741 

81.9860 

162.667 

16 

136.675 

271.389 

117.169 

232.619 

102.542 

203.542 

91.1078 

180.936 

82.0721 

162.833 

17 

136.818 

271.667 

117.292 

232.857 

102.650 

203.750 

91.2634 

181.11] 

82.1581 

163.000 

18 

136.902 

271.944 

117.415 

233.095 

102.758 

203.958 

91.3590 

181.290 

82.2442 

163.167 

19 

137.105 

272.222 

117.538 

233.333 

102  865 

204.167 

91  .4546 

181.481 

82.3302 

163.333 

2O 

137.248 

272.500 

117.600 

233.571 

102.973 

204.375 

91.5502 

181.667 

82.4163 

163.500 

21 

137.302 

272.778 

117.783 

233.810 

103.080 

204.583 

91.64.-8 

181.852 

82.50^4 

163.667 

22 

137.530 

273.056 

117.902 

234.048 

103.184 

204.792 

91.7382 

182.037 

82.  sans 

163.833 

23 

137.669 

273.333 

118.021 

234.286 

103  288 

205.000 

91.8300 

182.222 

82.6087 

164.00U 

24 

137.812 

273.011 

118.144 

234.524 

103.395 

205.208 

91.9262 

182.407 

82.7548 

104.167 

25 

137.955 

273.889 

118.266 

234.762 

103.503 

205.417 

92.0218 

182.593 

82.8408 

164.333 

26 

138.099 

274.167 

118.389 

235.000 

103.610 

205.625 

92.1174 

182.778 

82.9269 

1(54.500 

27 

138.242 

274.444 

118.512 

235.238 

103.718 

205.833 

92.2130 

182.963 

83.0120 

164.667 

28 

138.381 

274.722 

118.631 

235.476 

103.822 

206.042 

92.3054 

183.148 

83.0961 

164.833 

29 

138  519 

275-.  000 

118.750 

235.714 

103.926 

206.250 

92.3978 

183.333 

S3  1793 

165.000 

30 

138.662 

275.278 

118.873 

235.952 

104.033 

206.458 

92.4934 

183.519 

b3  2(554 

105.167 

31 

188.800 

275.556 

118.995 

236.190 

104.141 

206.667 

92.5890 

183.704 

83.3514 

165.333 

32 

183.949 

275.833 

119.118 

236.429 

104.248 

206  875 

92.6845 

183.889 

83.4375 

105.500 

33 

139.092 

276.111 

119.241 

236.667 

104.356 

207.083 

92.7801 

184.074 

83.5285 

165.607 

34 

139.231 

276.389 

119.360 

236.905 

104.460 

207  292 

92.(S725 

184.259 

83.6007 

105.833 

35 

139.309 

276.667 

119.479 

237.143 

104.564 

207.500 

92.9649 

184.444 

83.0809 

106.000 

36 

139  513 

276.944 

119.601 

237.381 

104.671 

207.708 

93.0605 

184.630 

83.7750 

166.107 

37 

139  656 

277  222 

119.724 

237.619 

104.779 

207.917 

D3.1561 

184.815 

83.8620 

106.333 

38 

139.799 

277!  500 

119  847 

237.857 

104.886 

208.125 

93.2517 

185.000 

83.9481 

166.500 

39 

139.943 

277.778 

119.970 

238  095 

104.994 

208.333 

93.3473 

185.185 

84.0341 

166.C67 

4O 

140.086 

278.050 

120.093 

238.  S33 

105.101 

208.542 

93.4429 

185.370 

84.1202 

166.833 

41 

140.229 

278.333 

120.216 

238.571 

105  209 

208.750 

93.5385 

185.556 

84.2062 

167.000 

42 

140.308 

278.611 

120.334 

238.810 

105.313 

208.958 

93.6309 

185.741 

84.2804 

167.107 

43 

140.500 

278.889 

120.453 

239.048 

105.417 

209.167 

93.7233 

185.926 

84.3726 

167.334 

44 

140.050 

279  107 

120.576 

239.286 

105.524 

209.375 

93.H189 

186.111 

84.4586 

167.500 

45 

140.793 

2T9.444 

120.699 

239.524 

105.632 

209.583 

03.9145 

186.296 

84.5447 

167.667 

46 

140.930 

279.722 

120.822 

239.762 

105.739 

209.792 

94.0101 

186.481 

84.6307 

167  833 

47 

141.079 

280.000 

120.945 

240.000 

105.847 

210.  OM  194.  1057 

186.667 

84.7168 

168.000 

48 

141.218 

280.278 

121.063 

240  238 

105.951 

210.208 

94.1981 

18G.852 

84.8000 

168.167 

49 

141.356 

280.550 

121.182 

240.476 

10fi.0'.5 

210.417 

04.2905 

187.C37 

84.8832 

168.333 

50 

141.500280  833 

121.305240.714  106.162 

210.625 

94.3861 

187.222 

84.9692 

168.500 

51 

141.  6431281.  111 

121.  4281240.  952  106  270 

210.833 

94.4810 

187.407 

85.05*8 

168.667 

52 

141  .  786  281  .  38!)  j  1  21  .  55  1  1  241  .  1  90i  1  00  .  3T7 

211.042 

94.5772 

187.503 

85.1413 

168.833 

53 

141.930!  281.  667 

121.074 

241.429  100.485 

211.25094.6728 

187.778 

85.2274 

169.000 

54 

142.073:281.944 

121.796 

241.067(106.592 

211.458  94.7684 

1S7.903 

85.3134 

169.167 

55 

142.216 

282.222 

121.919!241.905100.700 

211.167  94.  80401  18-'.  148 

85.3905 

169.333 

56 

142.355 

282.500 

1  22  .  038  242  .  1  43  1  06  .  804 

211.87594  9504:  188.3:  ;H 

85.4827 

169.500 

57 

142.493  282.778 

122.157242.381  106.908 

212.  C83  95.0488J188.519 

85.5050 

109  007 

58 

142  6371283.056 

122.280  242.619  107.015  212.292  96.  1444}  188.  704 

85.6519 

109.833 

59 

79 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


17° 

1S7 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~o" 

850.296 

1700.00 

428.164 

85').  000 

285.461 

5H6.667 

214.116 

425.000 

171.312 

340.000 

1 

857.156 

1701.67 

428.594 

850.833 

285.748 

567.222 

214.330 

425.417 

171.483 

340.333 

2 

858.015 

1703.33 

429.023 

851.667 

286.034 

567.778 

214.545 

425.833 

171.655 

340.667 

3 

858.875 

1705.00 

429.453 

852.500 

286.321 

568.333 

214.760 

426.250 

171.827 

341.00(3 

4 

859.734 

1706  67- 

429.883 

853.333 

286.608 

568.889 

214.975 

426.667 

171.999 

341.333 

5 

860.565 

1708.33 

430.298 

854.167 

286.884 

569.444 

215.183 

427.083 

172.166 

341.667 

6 

861.396 

1710.00 

430.714 

855.000 

5287.161 

570.000 

215.391 

427.500 

172.332 

342.000 

7 

86-2.255 

1711.67 

431.143 

855.833 

287.448 

570.556 

215.606 

427.917 

172.504 

342.3:53 

8 

863.114 

1713.33 

431.573 

856.667 

287.734 

571.111 

215.820 

428.333 

172.676 

342.667 

9 

863.974 

1715.00 

432.003 

857.500 

288.021 

571.667 

216.035 

428.750 

172.848 

343.000 

10 

864  833 

1716.67 

432.433 

858.333 

288.307 

572.222 

216.250 

429.167 

173.020 

343.333 

11 

865.693 

1718.33 

432.862 

859.167 

288.594 

572.778 

216.465 

429.583 

178.191 

343.667 

12 

866.552 

1720.00 

433.292 

860.000 

288.880 

573.888 

216.680 

430.000 

173.363 

344.000 

13 

867.383 

1721.67 

433.707 

860.833 

289.157 

573.889 

210.888 

430.417 

173.530 

344.333 

14 

868.214 

1723.33 

434  123 

861.667 

289.434 

574.444 

217.096 

430.833 

173.696 

344.667 

15 

869.073 

1725.00 

434.553 

862.  5rO 

289  721 

575.000 

217.310 

431.250 

173.868 

345.000 

16 

869.933 

1726.67 

434.982 

863.333 

290.007 

575.556 

•217.5-tf 

431.667 

174.040 

345.333 

17 

870.792 

1728.33 

435.412 

864.167 

290.294 

576.111 

217.740 

432.083 

174.212 

345.667 

18 

871.652 

1730.00 

435.842 

865.000 

290.580 

576.607 

217.955 

432.500 

174.384 

346.000 

19 

872.511 

1731.67 

436.272 

865.833 

290.867 

577.222 

218  170 

432.917 

174.556 

346.333 

20 

873.371 

1733.33 

436.701 

866.667 

291.153 

577.778 

218  385 

433.333 

174.727 

346.667 

21 

874.201 

1735.00 

437.117 

867.500 

291.430 

578.333 

218  593 

433.750 

174.894 

347.000 

22 

875.032 

1736.67 

437.532 

868.333 

291.707 

578.  S89 

218.800 

434.167 

175.060 

347.333 

23 

875.892 

1738.33 

437.962 

869.167 

291.994 

579.444 

219.015 

434.583 

175.232 

347.667 

24= 

876.751 

1740.00 

438.392 

870.000 

292.280 

580.000 

219.230 

435.000 

175.404 

348.000 

25 

877.610 

1741.67 

438.821 

870.833 

292.567 

580.556 

219  445 

435.417 

175.576 

348.333 

26 

878.470 

1743.33 

439.251 

871.667 

202.853 

581.111 

219.660 

43'».833 

175.748 

348.667 

27 

879.329 

1745.00 

439.681 

872.500 

293.140 

581.667 

219.875 

436.250 

175.920 

349.000 

28 

880.189 

1746.67 

440.111 

873.333 

293.426 

582.222 

220.090 

436.667 

176.092 

349.333 

29 

881.020 

1748.33 

440.526 

874.167 

293.703 

582.778 

220.298 

437.083 

176.258 

349.667 

30 

881.850 

1750.00 

440.941 

875.000 

-?93.980 

583  333 

220.505 

437.  5HO 

176.424 

350.000 

31 

882.710 

1751.67 

441.371 

875.833 

294.267 

583.889 

220.720 

437.917 

176.596 

350.333 

32 

883.569 

1753.33 

441.801 

876.667 

294.553 

584.445 

220.935 

438.333 

176.768 

350.667 

33 

884.429 

1755.00 

442.231 

877.500 

294.840 

585.000 

221.150 

438.750 

176.940 

351.000 

34 

885.288 

1756.67 

442.660 

878.333 

295.126 

585.556 

221.365 

439.167 

177.112 

351.333 

35 

886.148 

1758.33 

443.090 

879.167 

295.413 

586.111 

221.580 

439.583 

177.284 

351.667 

36 

887.007 

1760.00 

443.520 

880.000 

295.699 

586.667 

221.795 

440.000 

177.450 

352.000 

37 

887.867 

1761.67 

443.950 

880.833 

295.986 

587.222 

222.010 

440.417 

177.628 

352.333 

38 

888.726 

1763.33 

444.379 

881.667 

296.273 

587.778 

222.225 

440.833 

177.799 

352.607 

39 

889.557 

1765.00 

444.795 

882.500 

296.549 

588.333 

222.432 

441.250 

177.966 

353.000 

40 

890.388 

1766.67 

445.210 

883.333 

296  826 

588.889 

222.640 

441.667 

178.132 

353.333 

41 

891.247 

1768.33 

445.640 

884.167 

297.113 

589.444 

222.855 

442.083 

178  304 

353.667 

42 

892.107 

1770.00 

446.070 

885.000 

297.399 

590.000 

223.070 

442.500 

178.476 

354.000 

43 

892.966 

1771.67 

446.499 

885.833 

297  686 

590.556 

223.  2S5 

442.917 

178.648 

354.333 

44 

893.825 

1773.33 

446.929 

886.667 

297.972 

591.111 

223.500 

443.333 

178.820 

354.667 

45 

894.685 

1775.00 

447.359 

887.500 

298.259 

591.667 

223.715 

443.750 

178.992 

355.000 

46 

895.544 

1776.67 

447.789 

888.333 

298.546 

592.222 

223.929444.167 

179.164 

355.333 

47 

896.404 

1778.33 

448.218 

889.167 

298.832 

592.778 

224.144444.583 

179.336 

355.667 

48 

897.263 

1780.00 

448.648 

890.000 

299.119 

593.333 

224.  359  !  4  45.  000 

179.507 

356.000 

49 

898.094 

1781.67 

449.063 

890.833 

299.395 

593.889 

224.567 

445.417 

179.674 

356.333 

50 

898.925 

1783.33 

449.479 

891.667 

299.672 

594.444 

-.'24.775 

445.833 

179.840 

356.067 

51 

899.784 

1785.00 

449.909 

892.500 

299.959 

595  000 

224.W044ti.250 

180.012357.000 

53 

900.644 

1786.67 

450  338 

893.333 

300.245 

595  556 

225  .  2(  )5  416  .  f  U57  !  1  80  1  84  357  .  333 

53 

901.503 

1788.33 

450.7(58 

894.167 

300.532 

596  1  1  1  1  225  .  4  1  9  4  4  7  .  083  1  80  .  3M5  357  .  667 

54 

902.363 

1790.00 

451.198 

895.000 

300.818 

596.  667  J225.63  4  4-17.500  180.528  358.  000 

55 

903  222 

1791.67 

451  628 

895.833 

301.105 

597  .  222  225  849  447  .  9  1  7  1  80  .  700  358  .  333 

56 

904.081 

1793.33 

452.057 

896.667 

301.302 

597  .  778  i  226  .  064  448  .  333  1  1  80  872  35S  .  6H7 

57 

904.941 

1795.00 

452.487 

897.500 

301.67S 

598.333  226.279  448.750  1  SI  .043  359.000 

58 

905.800 

1796.67 

452.917 

898.333 

301.965 

598.  889  1  226.  494  449.167  181  .215  359.333 

59 

906.631 

1798  ..33 

453.332 

899.1671302  242 

599.  444  1226.702  449.  583  11  81.  382  359.007 

TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

17° 

Tan. 

Arc. 
2837333 

Tan. 

122.402 

Arc. 

Tan. 

Arc. 

212.500 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

142.780 

242.857 

107.123 

95.2400 

188.889 

85.7380 

170.000 

0 

142.923 

283.611 

122.525 

243.095 

107.230 

212.708 

%  3356 

1  89.  074  j  85.  8240 

170.107 

1 

143.007 

283.889 

122.648 

243.333 

107.338 

212.917 

95.4312 

189.259 

85.9101 

170.333 

2 

143.210 

284.167 

122.771 

243.571 

107.445 

213.125 

95.5268 

189.444 

85.9961 

170.500 

3 

143.353 

284.444 

122.894 

243.810 

107.553 

213.333 

95.6224 

189.630 

86.0822 

170.667 

4 

143.492 

284.722 

123.013 

244.048 

107.657 

213.542 

95.7148 

189.815 

86.1654 

170.833 

5 

143.630 

285.000 

123.131 

244.286 

107.761 

213.750 

95.8072 

190.000 

86.2486 

171.000 

6 

143.774 

285.278 

123.254 

244.524 

107.868 

213.958 

95.9028 

190.185 

86.3346 

171.167 

7 

143.917 

285.556 

123.377 

244.762 

107.976 

214.167 

95  9983 

190.370 

86.4207 

171.333 

8 

144.060 

285.833 

123.500 

245.000 

108.083 

214.375 

96.0939 

190.556 

86.5067 

171.500 

9 

144.203 

286.111 

123.623 

245.238 

108.191 

214.583 

96.1895 

190.741 

86.5928 

171.667 

10 

144.347 

286.389 

123.746245.476 

108.298 

214.792 

96.2851!  190.  926 

86.6788 

171.833 

11 

144.490 

286.667 

123.869i245.7l4 

108.406 

215  000 

96.  3807J191.111 

86.7649 

172.000 

13 

144.629 

286.944 

123.987245.952 

108  510 

215.208 

96.4731 

191.296 

86.8481 

172.167 

13 

144.767 

287.222 

124.  106!  246.  190 

108.614 

215.417 

96.5655 

191.481 

86.9312 

172.333 

14 

144.910 

287.500 

124.  229  1246.  429 

108.721 

215  625 

96.6611 

191.667 

87.0173 

172.500 

15 

145.054 

287.778 

124.352246.667 

108.829 

215.833 

96.7567 

191.852 

87.1033 

172.667 

16 

145.197 

288.056 

124.4751246.905 

108.936 

216  042 

96.8523 

192.037 

87.1894 

172.833 

17 

145.340 

288.333 

124.5971247.143 

109.044 

216.250 

96.9479 

192.222 

87.2755 

173.000 

18 

145.484 

288.611 

124.720 

247.381 

109.151 

216.458 

97.0435 

192.407 

87.3615 

173.167 

19 

145.627 

288.889 

124.843 

247.619 

109.259 

216.667 

97.1391 

192.593 

87.4476 

173.333 

3O 

145.766 

289.167 

124.9621247.857 

109.363 

216.875 

97.2315 

192.778 

87.5307 

173.500 

31 

145.904 
146.047 

289.444 

289.722 

125.081 
125  204 

248.095 
248.333 

109.467 
109.574 

217.083 
217.292 

97.3239 
97.4195 

192.963 

193.148 

87.6139 
87.7000 

173.667 
173.833 

33 

146.191 

290.000 

125.326 

248.571 

109.682 

217.500 

97.5151 

193.333 

87.7860 

174.000 

34 

146.334 

290.278 

125.449 

248.810 

109.789 

217.708 

97.6106 

193.519 

87.8721 

174.167 

35 

146.477 

290.556 

125.572 

249.048 

109.897 

217.917 

97.7062 

193.704 

87.9581 

174.333 

36 

146.621 

290.833 

125.695 

249.286 

110.004 

218.125 

97.8018 

193.889 

88.0442 

174.500 

37 

146.764 

291.111 

125  818 

249.524 

110.112 

218.333 

97.8974 

194.074 

88.1303 

174.667 

38 

146.902 

291.389 

125.937 

249.762 

110.216 

218.542 

97.9898 

194.259 

88.2134 

174.833 

39 

147.041 

291.667 

126.055 

250.000 

110.320 

218.750 

98.0822 

194.444 

88.2966 

175.000 

30 

147.184 

291.944 

126.178 

250.238 

110.427 

218.958 

98.1778 

194.630 

88.3827 

175.167 

31 

147.328 

292.222 

126.301 

250.476 

110.535 

219.167 

98.2734 

194.815 

88.4687 

175.333 

33 

147.471 

292.500 

126.424 

250.714 

110.642 

219.375 

98.3690 

195.000 

88.5548 

175.500 

33 

147.614 

292.778 

126.547 

250.952 

110.750 

219.583 

98.4646 

1P5.185 

88.6408 

175.667 

34 

147.757 

293.056 

126.670 

251.190 

110.857 

219.792 

98.5602 

195.370 

88.7269 

175.833 

35 

147.901 

293.333 

126.792 

251.429 

110.965 

220.000 

98.6558 

195.556 

88.8129 

176.000 

36 

148.044 

293.611 

126.915 

251.667 

111.072 

220.208 

98.7514 

195.741 

88.8990 

176.167 

37 

148.187 

293.889 

127.038 

251.905 

111.180 

220.417 

98.8469 

195.926 

88.9850 

176.333 

38 

148.326 

294.167 

127.157 

252.143 

111.284 

220.625 

98.9393 

196.111 

89.0682 

176.500 

39 

148.464 

294.444 

127.276 

252.381 

111.388 

220.833 

99.0318 

196.296 

89.1514 

176.667 

4O 

148.608 

294  722 

127.399 

252.619 

111.495 

221.042 

99.1273 

196.481 

89.2375 

176.833 

41 

148.751 

295.000 

127.521 

252.857 

111.603 

221.250 

99.2229 

196.667 

89.3235 

177.000 

43 

148.894 

295.278 

127.644 

253.095 

111.710 

221.458 

99.3185 

196.852 

89.4096 

177.167 

43 

149.038 

295.556 

127.767 

253.333 

111.818 

221.667 

99.4141 

197.037 

89.4956 

177.333 

44 

149.181 

295.833 

127.890 

253.571 

111.925 

221.875 

99.5097 

197.222 

89.5817 

177.500 

45 

149.324 

296.111 

128.013 

253.810 

112.033 

222.083 

99.6053 

197.407 

89.6677 

177.667 

46 

149.468 

296.389 

128.136254.048 

112.140 

222.292 

99.7009 

197.593 

89.7538 

177.833 

47 

149.611 

296.667 

128.258 

254.286 

112.248 

222.500 

99.7965 

197.778 

89.8398 

178.000 

48 

149.749 

296.944 

128.377 

254.524 

112.352 

222.708 

99.8889 

197.963 

89.9230 

178.167 

49 

149.888 

297.222 

128.496 

254.762 

112.456 

222.917 

99.9813 

198.148 

90.0062 

178.333 

5O 

150.031 

297  500 

128.619  255.000 

112.563223.125 

100.077 

198.333 

90.0923 

178.500 

51 

150.175 

297.778 

128.742 

255.238 

112.671  223.333 

100.172 

198.519 

90.1783 

178.607 

53 

150.  31  81298.056 

128.865 

255.476 

112.778223.542 

100.208 

198.704 

90.2644 

178.833 

53 

150.  461  J298.333 

128.  9871255.  714 

112.886223.750 

100.364 

198.889 

90.3504 

179.000 

54 

150.604  298.611 

129.110:255.952 

112.993223.958 

100.  459:199.  074 

90.4365 

179.107 

55 

150.  748i  298.  889 

129.233256.190 

113.101  224.167 

100.555199.259 

90.5225 

179.33:' 

56 

150.891  299.167 

129.356256.429 

113.208224.375 

100.650199.444 

90.6086 

179.500 

57 

1  5  1.  03  4  '  299.  444 

129.479256.667 

113.316224.583 

100.746  199.630 

90.6946 

179.007 

58 

151.  173  1299.722 

1  29  .  598  ;  256  .  905  1  1  13  .  420  224  .  792 

100.838^99^ 

aO.TTTb 

179.833 

59 

81 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


18° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.   1    Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

907^462 

1800.00 

453  748 

900.000 

302  51S  600.  000 

226.909 

450.000 

181.548 

360.000 

1 

908.  321 

1801.67 

454.177 

900.K33 

302.805600.556 

227.124 

450.417 

181.720 

360.333 

2 

909.181 

1803.33 

454.60? 

901.6157 

303.  091  '601.  Ill 

227.339 

450.833 

181.892 

360.007 

3 

910.040 

1805.00 

455.037 

902.500 

303.378601.667 

227  554 

451.250 

188.064 

361.000 

4 

910.900 

1806.67 

455.467 

903.333 

303.  665  1  602.  222 

227.709 

451  .  667 

182.236 

361.333 

5 

911.759 

1808.33 

455.896 

904.167 

303.  951  1602.778 

227.984 

452.083 

182.408 

361  .  007 

6 

912.619 

1810.00 

456.326 

905.000 

304.  238  1603.333 

228.199 

452.500 

182.579 

302.000 

7 

913.478 

1811.67 

456.756 

905.833 

304.524 

603.889 

228.414 

452.917 

182.751 

362.333 

8 

914.338 

1813.33 

457.186 

906.667 

304.811 

604.444 

228.629 

453.333 

182.923 

362.007 

9 

915.197 

1815.00 

157.615 

907.500 

305.097 

605.000 

228.844 

453.750 

183.095 

363.000 

10 

916.056 

1816.67 

15S.045 

908.333 

305.384 

605.556 

229.058 

454.167 

183.267 

363  333 

11 

91(5.887 

1818.35 

458.4HO 

<)<  19.167 

305.661 

606.111 

229.206 

454.583 

183.433 

303  007 

13 

917.718 

1820.00 

458.876 

910.000 

305.938 

606.667 

229.474 

455.000 

183.600 

304.000 

13 

918.577 

1821.67 

459.806 

910.833 

306.224 

607.222 

229.689 

455.417 

183.772 

304.333 

14 

919.437 

1823  33 

459.73o 

911.667 

306.511 

607.778 

229.904 

455.833 

183.944 

364.667 

15 

920.296 

1825.00 

460.165 

912.500 

306.797 

(508.333 

230.119 

456.250 

184.115 

305.000 

16 

921.156 

1826.67 

460.595 

013.333 

307.084 

608.889 

230  334 

456.607 

184.287 

365.333 

17 

922.015 

1828.33 

461.025 

914.167 

307.370 

609.444 

230.548 

457.083 

184.459 

365.667 

18 

922.875 

1830.00 

461.454 

915  000 

307.657 

610.000 

230.763 

457.500 

184.631 

366.000 

19 

923.734 

1831.67 

461.884 

915.833 

307.943 

610.550 

230.978 

457.917 

184.803 

366.333 

20 

924.594 

1833.33 

462.314 

916.667 

308.230 

611.111 

231.193 

458.333 

184.975 

366.667 

21 

925.453 

1835.00 

462.743 

917.500 

308.516 

611.067 

231.408 

458.750 

185.147 

367.000 

22 

926.313 

1836.67 

463.173 

918.333 

308  803 

612  222 

231  .  623 

459.167 

185.319 

367.333 

23 

927.143 

1838.33 

463.589 

919.167 

309.080 

612  778 

231.831 

459.583 

185.485 

367.607 

34 

927.974 

1840.00 

464.004 

920.000 

309.357 

613.333 

232.038 

460.000 

185.652 

368.000 

25 

928.834 

1841  67 

464.434 

920  833 

309.643 

613.889 

232.253 

460.417 

185.823 

368.333 

26 

929.693 

1843  33 

464.864 

921.667 

309.930 

614.444 

232.408 

460  833 

185.995 

368.067 

21 

930.552 

1845.00 

465.293 

922.500 

310.216 

615.000 

232.683 

461  250 

186.167 

369.000 

28 

931.412 

1846.67 

465.723 

923.333 

310.503 

015.  550 

232.898 

461.067 

186.339 

369.333 

29 

932.271 

1848.33 

460.153 

924.167 

310.789 

616.111 

233.113 

462.083 

186.511 

369.  G67 

3O 

933.131 

1850.00 

466.582 

925.000 

311.076 

616.667 

233.328 

462.500 

186.683 

370.000 

31 

933.990 

1851.67 

467.012 

925.833 

311.362 

6!  7.  222 

233.543 

462.917 

186.855 

370.333 

33 

934.850 

1853.33 

4157.442 

926.667 

311.049 

617.778 

233.758 

463.3-33 

187.027 

370.  G67 

33 

935.709 

1855.00 

467.872 

927.500 

311.93o 

018.333 

233.973 

463.750 

187.199 

371.000 

34 

936.569 

1856.67 

468  301 

928.333 

312.222 

618.889 

234.  1S8 

464.167 

187.371 

371.333 

35 

937.428 

1858.33 

468.731 

929.167 

312.508 

619.444 

234.402 

464.583 

187.543 

171.607 

36 

938.287 

1860.00 

469.161 

930.000 

312.795 

620.000 

234.617 

465.000 

187.715 

372.000 

37 

939.118 

1861.67 

469.576 

930.833 

313.072 

020.550 

234.825 

465.417 

187.881 

372.333 

38 

939.949 

1863.33 

469.992 

981.667 

313.319 

621.111 

235.033 

465.833 

188.047 

372.667 

39 

940.809 

1865.00 

470.422 

932.500 

313.635 

621.667 

235.248 

466.250 

188.219 

373.000 

4O 

941.668 

1866.67 

470.851 

933.333 

313.922 

622.222 

235.463 

466.667 

188.391 

373.333 

41 

942.527 

1868.33 

471.281 

934.167 

314.208 

622.778 

235.678 

167.083 

188.563 

373.667 

43 

943.387 

1870.00 

471.711 

935.000 

314.495 

023.333 

235.892 

467.500 

188.735 

374.000 

43 

944.246 

1871.67 

472.140 

935.833 

314.781 

623.889 

236.107 

467.917 

188.907 

374.333 

44 

945.106 

1873.33 

472.570 

936.667 

315.008 

624.444 

236.322 

468.333 

189.079 

374.067 

45 

945.965 

1875.00 

473.000937.500 

315.354 

625.000 

236.537 

468.750 

189.251 

375.000 

46 

946.825 

1876.67 

473.430938.333 

31^.641 

625.556 

236.752469.167 

189.423 

375.383 

47 

947.684 

1878.33 

473.859939.167 

315.927 

626.111 

236.  967  1  469.  583 

189.595 

375.607 

48 

948.544 

1880.00 

474.289940.000 

316.214 

626.667 

237.182:470.000 

189.767 

376.000 

49 

949.403 

1881.67 

474.719 

940.833 

316.500 

627.222 

237.397 

470.417 

189.939 

376.333 

50 

950.262 

1883.33 

475.149 

941.667 

316.787627.778 

237.612 

470.833 

190.111 

376.607 

51 

951.122 

1885.00 

475.578:942.500 

317.073628.333 

237.827 

471.250 

190.282 

377.000 

53 

951.981 

1886.67 

476.008:943.333 

317.360628.889 

238.041 

471.667 

190.454 

377.333 

53 

952.841 

1888.33 

476.  438  1  944.  167 

317.646629.444 

238.256 

472.083 

190.626 

377.667 

54 

953.700 

1890.00 

476.868945.000 

317.933630.000 

238.471 

472.500 

190.798 

378.000 

55 

954.531 

1891.67 

477.283945.833 

318.210  6:30.556 

238.679 

472.917 

190.965 

378.333 

56 

955.362 

1893.33 

477.698946.607 

318.487631.111  238.887 

473.333 

191.131 

378.667 

57 

956.321 

1895.00 

478.128947.500 

31  8.  773  631.  667 

239.102 

478.750 

191.303379.000 

58 

957.081 

1896.67 

478.558948.333 

319.060632.222239.317 

474.167 

191.475379.333 

59 

957.940 

1898.33 

478.988949.167 

319.346632.778:239.531 

474.583  1  91.6471379.  667 

TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9C  Curve. 

1O°  Curve, 

18° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc, 

Tan. 

Arc. 

Tan. 

Arc.  " 

M. 

151.311 

300  000 

129.716257.143  113.524 

225.000 

100.931 

200.000 

90.8610 

180.000 

o 

151.455 
151.598 

300.278 
300.556 

129.839257.381H13.631 
129.962257.619  113  739 

225  208 
225.417 

101.026 
101.122 

200.185 
200.370 

90.9471 
91.0331 

180.167 
180.333 

1 
2 

151.741 

300.833 

130.085j257.857 

113.846 

2-,'5.625 

101.218 

200.556 

91.1192 

180.500 

3 

151.885 

301.111 

130.208258.095 

113.954 

225.833 

101.313 

•J00.741 

91.2052 

180.667 

4 

158.088 

301.389 

130.331  258.333 

114.061 

226.042 

101.409 

200.926 

91.2913 

180.833 

5 

152.171 

301.667 

130.4531258.571 

114.169 

226.250 

101.504 

201.111 

91.3773 

181.000 

6 

15*.  315 

301.944 

130.576 

258.810 

114.276 

226.458 

101.600 

201.296 

91  .4634 

181.167 

7 

152.458 

30  .5.  222 

130.699 

259.048 

114.384 

226.667 

101.695 

201.481 

91.5494 

181.333 

8 

152.601 

302.500 

130.822 

259.286 

114.491 

226.875 

101.791 

201.667 

91.6355 

181.500 

9 

152.745 

302.778 

130.945 

259.524 

114.599 

227.083 

101.887 

201.852 

91.7216 

181  667 

1O 

158.888 

303.056 

131.064 

259.762 

114.703 

227.292 

101.979 

202.037 

91  8047 

181.833 

11 

153.022 

303.333 

131.182 

260.000 

114.807 

227.500 

102.071 

202.222 

91.8879 

182.000 

13 

153.165 

303.611 

131.305 

260.238 

114.914 

227.708 

102.167 

202.407 

91.9740 

182.167 

13 

153.308 

303.889 

131.428 

260.476 

115.022 

227.917 

102.263 

202.593 

92.0600 

182.333 

14 

153.451 

304.167 

131.551 

260.714 

115.129 

228.125 

102.358 

202.778 

92.1461 

182.500 

15 

153.595 

304.444 

131.674 

260.952 

115.237 

228.333 

102.454 

202.963 

92.2321 

182  667 

16 

153.738 

304.722 

131.797 

261.190 

115.344 

228.542 

102.549 

203.148 

92.3182 

182.833 

17 

153.881 

305.000 

131.920 

261.429 

115.452 

228.750 

102.645 

203.333 

92.4042 

183.000 

18 

154.025 

305.27'8 

132.042 

261.667 

115.559 

228.958 

102.741 

203.519 

92.4903 

183.167 

19 

154.168 

305.556 

132.165 

261.905 

115  667 

229.167 

102.836 

203.704 

92.5764 

183.333 

20 

154.311 

305.833 

132  288 

262.143 

115.774 

229.375 

102.932 

203.889 

92.6624 

183.500 

21 

154.455 

306.111 

132.411 

262.381 

115.882 

229.583 

103.027 

204.074 

92.7485 

183.667 

22 

154.593 

306.389 

132.530 

262.619 

115.986 

229.792 

103.120 

204.259 

92.8316 

183.833 

23 

154.732 

306.667 

132.648 

268.857 

116.090 

230.000 

103.212 

204.444 

92.9148 

184.000 

34 

154.875 

306.944 

132.771 

263.095 

116.197 

230.208 

103.308 

204.630 

93.0009 

184.167 

25 

155.018 

307.222 

132.894 

263  333 

116  305 

230.417 

103.403 

204.815 

93.0869 

184.333 

26 

155.162 

307.500 

133.017 

263.571 

116.412 

230.625 

103.499 

205.000 

93.1730 

184.500 

21 

155.30n 

307.778 

133.140 

263.810 

116.520 

230.833 

103.595 

205.185 

93.2590 

184.667 

28 

155.448 

308.056 

133.263 

264.048 

116.627 

231.042 

103.690 

205.370 

93.3451 

184.833 

29 

155.592 

308.333 

1  as.  386 

264.286 

116.735 

231.250 

103.786 

205.556 

93.4311 

185.000 

3O 

155.735 

308.611 

133.508 

264.524 

116.842 

231  458 

103.881 

205.741 

93.5172 

185.167 

31 

155.878 

308.889 

133.631 

264.762 

116.950 

231.667 

103.977 

205.926 

93.6033 

185.333 

32 

156.021 

309.167 

133.754 

265.000 

117.057 

231.875 

104.073 

«06.111 

93.6893 

185.500 

33 

156.165 

309.444 

133.877 

265.238 

117.165 

232.083 

104.168 

206.296 

93.7754 

185.667 

34 

156.308 

309.722 

134.000 

265.476 

117.272 

232.292 

104.264 

206.481 

93.8614 

185.833 

35 

156.451 

310.000 

134.123 

*'65.714 

117.380 

232.500 

104.359 

206.667 

93.9475 

186.000 

36 

156.590 

310.278 

134.241 

265.952 

117.484 

232.708 

104.452 

206.852 

94.0307 

186.167 

37 

156.728 

310.556 

134.360 

266.190 

117.588 

232.917 

104.544 

207.037 

94.1138 

186.333 

38 

156.872 

310.833 

134.483 

206.429 

117.695 

233.125 

104.640 

207.222 

94.1999 

186.500 

39 

157.015 

311.111 

134.606 

266.667 

117.803 

233.333 

104.735 

207.407 

94.2859 

186.667 

40 

157.158 

311.389 

134.729 

266.905 

117.910 

233.542 

104.831 

207.593 

94.3720 

186.833 

41 

157.302 

311.677 

134.852 

267.143 

118.018 

233.750 

104.926 

207.778 

94.4581 

187.000 

43 

157.445 

311.944 

134.974 

267.381 

118.125 

233  958 

105.022 

207.963 

94.5441 

187.167 

43 

157.588 

312.222 

135.097 

267.619 

118.233 

234.167 

105.118 

208.148 

94.6302 

187.333 

44 

157.732 

312.500 

135.220 

267.857 

118.340 

234.375 

105.213 

208.333 

94.7162 

187.500 

45 

157.875 

312.778 

135.343 

268.095 

118.448 

234.583 

105.309 

208.519 

94.8023 

187.667 

46 

158.018 

313.056 

135.466 

268.333 

118.555 

234  792 

105.404 

208.704 

94.8883 

187.833 

47 

158.1(51 

313.333 

135.589 

268.571 

118.663 

235.000 

105.500 

208.889 

94.9744 

188.000 

48 

158.305 

313.611 

135.712 

268.810 

118.770 

235.208 

105.596 

209.074 

95.0604 

188.167 

49 

158.448 

313.889 

135.834 

269.048 

118.878 

235.417 

105.691 

209.259 

95.1465 

188.333 

5O 

158.591 

314.167 

135.957 

269.286'll8.985 

235.625 

105  787 

209.444 

95.2325 

188.500 

51 

158.735 

314.444 

136  080  1  269.  524  119.093 

235.833 

105.882 

209.630 

95.3186 

188.667 

53 

158.878 

314.722 

136.203269.762  119.200 

236.042 

105.978 

209.815 

95.4046 

188.833 

53 

159.021 

315.000 

136.326 

270.000119.308 

236.250 

106.074 

210.000 

95.4907 

189  000 

54 

159.160 

315.278 

136.445 

270.238119.412 

236.458 

106.166 

210.185 

95.5739 

189.167 

55 

159.298 

315.556 

136.563 

270.476119.516 

236.667 

106.258 

210.370 

95.6571 

189.333 

5<> 

159.442 

315.833 

136.686 

270.714  119.623 

236.875 

106.354 

210.556 

95.7431 

189.500 

57 

159.585 

316.111 

136.809 

270.952  119.731 

237.083 

106.450 

210.741 

95.8292 

189.667 

58 

159.728316.389 

136.932 

271.190119.838 

237.292 

106.  5451210.  926 

95.9152 

189.833 

59 

83 


TABLE   XTV.— ACTUAL   TANGENTS,    ETC. 


10= 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O  958.800 

1900.00 

479.417 

950.000 

319.633  (533.333 

239.746,475.000 

191.818 

380.000 

1  959.659 

1901.67 

479.847 

950.833 

319.9196:33.889 

239.961  475.417 

191.990 

380.333 

2  960.  £19 

1903.33 

480.277 

951.667 

320.206  634.444 

240.176 

475.833 

192.162 

380.607 

3  961.378 

1905.00 

480.707 

952.500 

320.49-2.635.000 

240.391 

476.250 

192.334 

381.000 

4 

962.237 

1906.67 

481.136 

953.3-33 

320.779  035.  556 

240.606 

476.667 

192.506 

381.333 

r> 

968.097 

1908.  as 

481.566 

954.167 

321.065636.111 

240.821 

477.083 

192.678 

381.667 

G 

903.956 

1910.00 

481.996 

955.000 

321.352 

636.667 

241.036 

477.500 

192.850 

382.000 

7 

964.816 

1911.67 

482.426 

955.833 

321.638 

637.222 

241.251 

477.917 

193.022 

382.333 

8 

905.675 

1913.33 

482.855 

956.667 

321.925 

637.778 

241.466 

478.333 

193.194 

382.667 

9 

966.535 

1915.00 

483.285 

957.500 

322.211 

638.333 

241.680 

478.750 

193.366 

383.000 

1O 

967.394 

1916.67 

483.715 

958.333 

322.498 

638.889 

241.895 

479.167 

193.538 

383.333 

11 

968.254 

1918.33 

484.145 

959.167 

322.784 

639.444 

242.110 

479.583 

193.710 

383.667 

12 

969.113 

1920.00 

484.574 

960.000 

323.071 

640.000 

242.325  480.000 

193.882 

384.000 

13 

969.972 

1921.67 

485.004 

960.833 

323.357 

640.556 

242.540480.417 

194.054 

384.333 

14 

970.832 

1923.33 

485.434 

961.667 

323.644 

641.111 

242.755;480.833 

194.228 

384.667 

15 

971.691 

1925.00 

485.863 

962.500 

323.930 

641.667 

242.  970  '481.  250 

194.398 

385.000 

16 

972.551 

1926.67 

486.293 

963.333 

324.217 

642.222 

243.1851481.667 

194.570 

385.333 

17 

973.410 

1928.33 

486.723 

964.167 

324.503 

642.778 

243.400 

482.083 

194.742 

385.667 

18 

974.270 

1930.00 

487.153 

965.  Ottii 

324.790 

643.333 

243.615 

482.500 

194.913 

386.000 

19 

975,100 

1931.67 

487.568 

965.833 

325.067 

643.889 

243.822 

482.917 

195.080 

386.333 

20 

975.931 

1933.33 

487.984 

966.667 

325.344 

644.444 

244.030 

483.333 

195.246 

386.667 

21 

976.791 

1935.00 

488.413 

967.500 

325.630 

645.000 

244.245 

483.750 

195.418 

387.000 

22 

977.650 

1936.67 

488.843 

968.333 

325.917 

645.556 

244.460 

484.167 

195.590 

387.333 

23 

978.510 

19:38.33 

489.273 

969.167 

326.203 

646.111 

244.675 

484.583 

195.762 

387.667 

24 

979.369 

1940.00 

489.702 

970.000 

326.490 

646.667 

244.890 

485.000 

195.934 

388.000 

25 

980.229 

1941.67 

490.132 

970.833 

326.776 

647.222 

245.105 

485.417 

196.106 

388.333 

26 

981.088 

1943.33 

490.562 

971.667 

327.063 

647.778 

245.320 

485.833 

196.278 

388.667 

27 

981.947 

1945.00 

490.992 

972.500 

327.350 

648.  3m 

245.534 

486.250 

196.449 

389.000 

28 

982.807 

1946.67 

491.421 

973.333 

327.636 

648.889 

245.749 

486.007 

196.621 

389.333 

29 

983.666 

1948.33 

491.851 

974.167 

327.923 

649.444 

245.964 

487.083 

196.793 

389.667 

30 

984.526 

1950.00 

492.281 

975.000 

328.209 

650.000 

246.119 

487.500 

196.965 

390.000 

31 

985.385 

1951.67 

492.711 

975.833 

328.496 

050.556 

246.394 

487.917 

197.137 

390.333 

32 

986.245 

1953.33 

493.140 

976.667 

328.782 

651.111 

246.609 

488.333 

197.309 

390.667 

33 

987.104 

1955.00 

493.570 

977.500 

329.069 

651.667 

246.824 

488.750 

197.481 

391.000 

34 

987.964 

1956.67 

494.000 

978.333 

329.355 

652.222 

247.039 

489.167 

197.653 

391.333 

35 

988.823 

1958.33 

494.430 

979.167 

329.642 

652.778 

247.254 

489.583 

197.825 

391.667 

36 

989.682 

1960.00 

494.859 

980.000 

329.928 

653.3:33 

247.469 

490.000 

197.997 

392.000 

37 

990.542 

1961.67 

495.289 

980.833 

330.215 

653.889 

247.683 

490.417 

198.169 

392.3133 

38 

991.401 

1963.33 

495.719 

981.607 

330.501 

654.444 

247.898 

490.833 

198.341 

392.667 

39 

992.261 

1965.00 

496.149 

982.500 

330.788 

655.000 

248.113 

491.250 

198.513 

393.000 

40 

993.120 

1966.67 

496.578 

983.333 

331.074 

655.556 

248.328 

491.667 

198.685 

393.333 

41 

993.980 

1968.33 

497.008 

984.167 

331.361 

656.111 

248.543 

492.083 

198.857393.667 

42 

994.839 

1970.00 

497.438 

985.000 

331.647 

656.667 

248.758 

492.500 

199.029  394.000 

43 

995.699 

1971.6? 

497.868 

985.833 

331.934 

657.222 

248.973 

492.917 

199.201  394.333 

44 

996.558 

1973.33 

498.297 

986.667 

332.220 

657.778 

249..  188 

493.333 

199.372394.667 

45 

997.417 

1975.00 

498.727 

987.500 

332.507 

658.333 

249.403 

493.750 

199.544395.000 

46 

998.277 

1976.67 

499.157 

988.333 

£32.793 

658.889 

249.618 

494.167 

199.716395.333 

47 

999.136 

1978.33 

499.586 

989.167 

333.080 

659.444 

249.832 

494.583 

199.888395.067 

48 

999.996 

1980.00 

500.016 

990.000 

333.366 

660.000 

250.047 

495.000 

200.060:396.000 

49 

1000.86 

1981.67 

500.446 

990.833 

333.653 

600.556 

250.262 

495.417 

200.232 

396.333 

50 

1001.71 

1983.33 

500.876 

991.667 

333.939 

661.111 

250.477 

495.8:33 

200.404 

396.667 

51 

1002.57 

1985.00 

501.305 

992.500 

334.226 

661.667 

250.692 

496.250 

200.  576  !  397.  000 

52 

1003.43 

1986.67 

501.735 

993.333 

334.512 

662.222 

250.907 

496.667 

200.748397.333 

53 

1004.29 

1988.33 

502.165 

994.167 

334.799 

66  2.  778  1251.  122 

497.083 

200.920397.667 

54 

1005.15 

1990.00 

502.595 

995.000 

335.085 

663  .  333  251  .  337  497  .  500 

201.092398.000 

55 

1006.01 

1991.67 

503.024 

995.833 

335.372 

003.  889  251.  552  '497.  91  7 

2dl.264398.333 

56 

1006.87 

1993.33 

503.454 

996.667 

335.658 

664.444251.767498.333 

201.436398.667 

57 

1007.73 

1995.00 

503.884 

997.500 

335.945 

665.000,251.982498.750 

201.608399.000 

58 

1008.59 

1996.67 

504.314 

998.333 

336.231 

665  .  556  252  .  1  96  '499  .  1  67 

201.780 

399.333 

59 

1009.45 

1998.33 

504.743 

999.167 

336.518 

666.111:252.411499.583 

201.952 

399.667 

84 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

19° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

159.  8721310.  OUT 

137.055  271  .429  119.946 

237.500 

106.  641)211.  Ill 

96.0013 

190.000 

~~O~ 

160.015  316.944 

137.178271.667 

120.053 

237.708 

106.736211.296 

96.0873 

190.16? 

1 

160.158  317.222 

137.300271.905 

120.161 

237.917 

106.8*2 

211.481 

96.1734 

190.333 

o 

160.  301  1317.500 

137.423272.143 

120.268 

238.125 

106.927 

211.667 

96.2594 

190.500 

3 

160.445317.778 

137.546272.381 

120.376 

238.333 

107.023 

211.852 

96.3455 

190.667 

4 

160.588318.056 

137.  669;  272.  619 

120.484 

538.542 

107.119 

212.037 

96.4315 

190.833 

5 

160.731 

318.333 

187.  7921272.  857 

120.591 

238.750 

107.214 

212.222 

96.5176 

191.000 

6 

160.875 

318.611 

137.915;273.095 

120.699 

238.958 

107.310 

212.407 

96.6037 

191.167 

7 

161.018 

318.889 

138.038273.333 

120.806 

239.16? 

107.405 

212.593 

96.6897 

191.333 

8 

161.161 

319.167 

138.160 

273.571 

120.914 

239.375 

107.501 

212.778 

96.7758 

191.500 

9 

161.305 

319.444 

138.283 

273.810 

121.021 

239.583 

107.597 

212.963 

96.8618 

191.66? 

10 

161.448 

319.722 

138.406 

274.048 

121.129 

239.792 

107.692 

213.148 

96.9479 

191.833 

11 

161.591 

320.000 

138.529 

274.286 

121.236 

240.000 

107.788 

213.333 

97.0339 

192.000 

12 

161.735 

320.278 

138.652 

274.524 

121.344 

240.208 

107.883 

213.519 

97.1200 

192.167 

13 

161.878 

320.556 

1:38.775 

274.762 

121.451 

240.41? 

107.979 

213.704 

97.2060 

192.333 

14 

162.021 

320.833 

138.898 

275.000 

121.559 

240.625 

108.075 

213.889 

97.2921 

192.500 

15 

162.164 

321.111 

139.020 

275.238 

121.666 

240.833 

108.170 

214  074 

97.3781 

192.667 

16 

162.308 

321.389 

139.143 

275.476 

121.774 

241.042 

108.266 

214.259 

97.4642 

192.833 

17 

162.451 

321.667 

139.266 

275.714 

121.881 

241.250 

108.361 

214.444 

97.5502 

193.000 

18 

162.590 

321.944 

139.385 

275.952 

121.985 

241.458 

108.454 

214.630 

97.6334 

193.167 

19 

162.728 

322.222 

139.504 

276.190 

122.089 

241.667 

108.546 

214.815 

97.7166 

193.333 

20 

162.871 

322.500 

139.626 

276.429 

122.197 

241.875 

108.642 

215.000 

97.802? 

193.500 

21 

163.015 

322.778 

139.749 

276.667 

122.304 

242.083 

108.737 

215.185 

97.8887 

193.66? 

22 

163.158 

323.056 

139.872 

276.905 

122.412 

242.292 

108.833 

215.370 

97.9748 

193.833 

23 

163.301 

323.333 

139.995 

277.143 

122.519 

242.500 

108.929 

215.556 

98.0608 

194.000 

24 

163.445 

323.611 

140.118 

277.381 

122.627 

242.708 

109.024 

215.741 

98.1469 

194.167 

25 

163.588 

323.889 

140.241 

277.619 

122.734 

242.91? 

109.120 

215.926 

98.2329 

194.333 

20 

163.731 

324.167 

140.364 

277.857 

122.842 

243.125 

109.215 

216.111 

98.3190 

194.500 

27 

163.875 

324.444 

140.486 

278.095 

122.949 

243.333 

109.311 

216.296 

98.4050 

194.667 

28 

164.018 

324.722 

140.609 

278.333 

123.057 

243.542 

109.406 

216.481 

98.4911 

194.833 

29 

164.161 

325.000 

140.732 

278.571 

123.164 

243.750 

109.502 

216.667 

98.5771 

195.000 

30 

164.304 

325.278 

140.855 

27'8.810 

123.272 

243.958 

109.598 

216.852 

98.6632 

195.16? 

31 

164.448 

325.556 

140.978 

279.048 

123.379 

244.16? 

109.693 

217.037 

98.7493 

195.333 

32 

164.591 

325.833 

141.101 

279.286 

123.487 

244.375 

109.789 

217.222 

98.8353 

195.500 

33 

164.734 

326.111 

141.224 

279.524 

123.594 

244.583 

109.884 

217.407 

98.9214 

195.667 

34 

164.878 

326.389 

141.346 

279.762 

123.  702 

244.792 

109.980 

217.593 

99.0074 

195.833 

35 

165.021 

326.667 

141.469 

280.000 

123.809 

245.000 

110.076 

217.778 

99.0935 

196.000 

30 

165.164 

326.944 

141.592 

280.238 

123.917 

245.208 

110.171 

217.963 

09.1795 

196.167 

37 

165.308 

327.222 

141.715 

280.476 

124.024 

245".  417 

110.267 

218.148 

99.2656 

196.333 

38 

165.451 

327.500 

141.838 

280.714 

124.132 

245.  G25 

110.362 

218.333 

99.3516 

196.500 

39 

165.594 

327.778 

141.961 

280.952 

124.239 

245.833 

110.458 

218.519 

99.4377 

196.667 

4O 

165.738 

328.056 

142.084 

281.190 

124.347 

246.042 

110.554 

218.704 

99.5287 

196.833 

41 

165.881 

328.3:33 

142.206 

281  .429 

124.454 

246.250 

110.649 

218.889 

99.6098 

197.000 

42 

166.024 

328.611 

142.329 

281.667 

124.562 

246.458 

110.745 

219.074 

99.6958 

197.167 

43 

166.167 

328.889 

142.452 

281.905 

124.669 

246.667 

110.840 

219.259 

99.7819 

197.333 

44 

166.311 

329.167 

142.575 

282.143 

124.777 

246.875 

110.936 

219.444 

99.8680 

197.500 

45 

166.454 

329.444 

142.698 

282.381 

124.885 

247.083 

111.032 

219.630 

99.9540 

197.667 

46 

166.597 

329.722 

142.821 

282.619 

124.992 

247.292 

111.12? 

219.815 

100.040 

197.833 

47 

166.741 

330.000 

142.944 

282  857 

125.100 

247.500 

111.223 

220.000 

100.126 

198.000 

48 

166.884 

330.278 

143.066 

283.095 

125.207 

247.708 

111.318 

220.185 

100.212 

198.167 

49 

167.027 

330.556 

143.189 

2a3.333 

125.315 

247.917 

111.414 

220.370 

100.298 

198.333 

50 

167.171 

330.833 

143.312 

283.571 

125.422 

248.125 

111.509 

220.556 

100.384 

198.500 

51 

167.314 

331.111 

143.435 

283.810 

125.530 

248.333 

111.605 

220.741 

100.470 

198.667 

52 

167.457 

331.389 

143.558 

284.048 

125.637 

248.542 

111.701 

220.926 

100.556 

198.833 

53 

167.601 

331.667 

143.681 

284.286 

125.745 

248.750 

111.796 

221.111 

100.642 

199.000 

54 

107.744 

331.944 

143.803 

284.524 

125.852 

248.958 

111.892 

221.296 

100.728 

199.167 

55 

167.  887  1332,222 

143.9261284.762 

125.960 

249.167 

111.987 

221.481 

100.814 

199.333 

56 

168.030332.500 

144.049:285.000 

126.067 

249.375 

112.083 

221.667 

100.901 

199.500 

57 

168.174 

332.778 

144.172 

285.238 

126.175 

249.583 

112.179 

221.852 

100.987 

199.667 

58 

168.317 

333.056 

144.295 

285.476 

126.282249.792 

112.274 

222.03? 

101.073199.833 

59 

85 


TABLE   XTV. — ACTUAL   TANGENTS,    ETC. 


20° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

1010.31 

2000.01 

505.  173!  1000.  (X 

336.804 

666.667 

252.626500.000 

202.124 

400.000 

1 

1011.10 

2001.67 

505.  603  i  1000.  83 

337.091  667.222 

252  841:500.417 

202.295 

400.333 

2 

1012.03 

2003.33 

506.033 

1001.67 

337.377  667.778 

253.056  500.833 

202.467 

400.667 

3 

1012.89 

2005.00 

506.462 

1002.  5( 

337.664 

668.333 

253.271 

501.250 

202.639 

401.000 

4 

1013.75 

2006.67 

506.892 

1003.33 

337.950 

668.889 

253.486 

501  .  667 

202.811 

401  .  333 

5 

1014.61 

2008.33 

507  322 

1004.17 

338.237 

669.444 

253.701 

502.083 

202.983 

401.667 

0 

1015.47 

2010.00 

507.752 

1005.  OU 

338.523 

670.000 

253.9l6i502.500 

203.155402.000 

7 

1016.33 

2011.67 

508.181 

1005.83 

338.810 

670.556 

254.131  502.917 

203.327 

402.333 

8 

1017.18 

2013.33 

508.611  1006.67 

339.097 

671.111 

254.345503.333 

203.499 

402.667 

9 

1018.04 

2015.00 

509.041 

1007.5C 

339.383 

671.667 

254.560 

503.750 

203.671 

403.000 

1O 

1018.90 

2016.67 

509.471 

1008.33 

339.670 

672  222 

254.775 

504.167 

203.843 

403.333 

11 

1019.76 

2018.33 

509.900 

1009.17 

389'.  956 

672.778 

254.990504.583 

204.015 

403.667 

13 

1030.65 

2020.00 

510.3301010.00 

340.243 

673.333 

255.205  505.000 

204.187 

404.000 

13 

1021.48 

2021.67 

510.760  1010.83 

340.529 

673.889 

255.  420  i  505.  41  7 

204.359 

404.333 

14 

1022.34 

2023.33 

511.1891011.67 

340.816 

674.444 

255.635 

505.833 

204.531 

404.667 

15 

1023.20 

2025.00 

511.61911012.50 

341.102 

675.000 

255.850 

506.250 

204.703 

405.000 

16 

1024.06 

2026.67 

512.049  1013.33 

341.389 

675.556 

256.065 

506.667 

204.875 

405.333 

17 

1024.92 

2028.33 

512.479  1014.17 

o41.675 

676.111 

256.280 

507.083 

205.047 

405.667 

18 

1025.78 

2030.00 

512.908:1015.00 

341.962 

676.667 

256.494 

507.500 

205.219 

406.000 

19 

1026.6-1 

2031.67 

513.338 

1015.83 

342.248 

677.222 

256.709 

507.917 

205.390 

406.333 

20 

1027.50 

2033.33 

513.768 

1016.67 

342.535 

677.778 

256.924 

508.333 

205.562 

406.667 

31 

1028.36 

2035.00 

514.198 

1017.50 

342.821 

678.333 

257.139 

508.750 

205.734 

407.000 

22 

10-29.22 

2036.67 

514.627 

1018.33 

343.108 

678.889 

257.354 

509.167 

205.906 

407.333 

23 

1030.08 

2038.33 

515.057 

1019.17 

343.394 

679.444 

257.569 

509.583 

206.078 

407.667 

24 

1030.94 

2040.00 

515.48711020.00 

313.681 

680.000 

257.784 

510.000 

206.250 

408.000 

25 

1031.80 

2041.67 

515.91711020.83 

343.967 

680.556 

257.999 

510.417 

206.422 

408.333 

26 

1032.65 

2043.33 

516  346  1021.67 

344.254 

681.111 

258.214 

510.833 

206.594 

408  667 

37 

1033.51 

2045.00 

516.7761022.50 

344.510 

681.667 

258.429 

511.250 

206.766 

409.000 

38 

1034.37 

2046.67 

517.206  1023.33 

•344  827 

682.222 

258.644 

511.667 

206.938 

409.333 

39 

1035.23 

2048.33 

517.63(5 

1024.17 

345.113 

682.778 

258.858 

512.083 

207.110 

409.667 

3O 

1036.09 

2050.00 

518.065 

1025.00 

345.400 

683.333 

259.073 

512.500 

207.282 

410.000 

31 

1036.95 

2051.67 

518.495 

1025.83 

345  686 

683.889 

259.288 

512.917 

207.454 

410.333 

33 

1037.81 

2053.33 

518.925 

1026.67 

345.973 

684.444 

259.503 

513.333 

207.626 

410.667 

33 

1038.67 

2055.00 

519.355 

1027.50 

346.259 

685.000 

259.718 

513.750 

207.798 

411.000 

34 

1039.53 

2056.67 

519.784 

1028.33 

346.546 

685.556 

259.933 

514.167 

207.970 

411.333 

35 

1040.39 

2058.33 

>20.214 

1029.17 

346.832 

686.111 

260.148 

514.583 

208.142 

411.667 

36 

1041.25 

2060.00 

520.644 

1030.00 

347.119 

686.667 

260.363 

515.000 

208.313 

412.000 

37 

1042.11 

2061.67 

521.073 

1030.83 

347.405 

687.222 

260.578 

515.417 

208.485 

412.333 

38 

1042.97 

2063.33 

521  .  503 

1031.67 

347.692 

687.778 

260.793 

515.833 

208.657 

412.667 

39 

1043.83 

2065.00 

521.933 

1032.50 

347.978 

688.333 

261.007 

516.250 

208.829 

413.000 

40 

1044.69 

2066.67 

522.363 

1033.33 

348.265 

688.889 

261.222 

516.667 

209.001 

413.333 

41 

1045.55 

2068.33 

522.792 

1034.17 

348.551 

689.444 

261.437517.083 

209.173 

413.667 

43 

046.41 

2070.00 

523.222 

1035.00 

548.388 

690.000 

261.  652  1517.500 

209.345 

414.000 

43 

047.27 

2071.67 

523.652 

1035.83 

349.124 

690.556 

261.867517.917 

209.517 

414.333 

44 

048.12 

2073.33 

524.082 

1036.67 

349.411 

691.111 

262.082518.333 

209.689 

414.667 

45 

1048.98 

2075.00 

524.511 

1037.50 

349.697 

691.867 

262.297518.750 

209.861 

415.000 

46 

049.84 

2076.67 

524.941 

1038.33 

349.984 

692.222 

262.512519.167 

210.033 

415.333 

47 

050.70 

2078.33 

525.371 

1039.17 

350.270 

692.778 

262.727519.583 

210.205 

415.667 

48 

051.56 

2080.00 

525.801 

1040.00 

350.557  693.333 

262.942520.000 

210.377 

416.000 

49 

052.45 

2081.67 

526.245 

1040.83 

350.853  693.889 

263.164520.417 

210.554 

416.333 

| 

5O 

053.34 

2083.33 

526.689 

1041.67 

351.149694.444 

263.386 

520.833 

210.732 

416.667 

51 

054.20 

2085.00 

•327.118 

1042.50 

351.436695.000 

263.601  521.250 

210.904 

417.000 

53 

055.06 

2086.67 

-27.548 

1043.33 

351.722695.556 

263.816521.667 

211.076417.333 

53 

055.92 

2088.33 

527.978  1044.17 

152  i  )09  696  .  1  1  1  !  264  .  030  52'.'  .  083 

211.248417.667 

54 

056.78 

2090.00 

528  .  408  i  1  045  .  00  352  .  295  696  .  667  264  .  245  522  .  500 

211.420418.000 

55 

057.64 

2091.67 

528  .  837  1  1  045  .  S3  352  .  582  697  .  222  264  .  460  522  .917 

21  1.  592  1  41  8.  333 

56 

058.502093.33 

529.267  1046.67 

352.868  697.778 

264.675523.333 

211.764  418.667 

57 

059.  &5 

2095.00 

529  .  697  1  047  .  50  353  .  1  55  698  .  333  264  .  H90  523  .  750 

211.936419.000 

58 

060.21 

2096.67 

530  .  1  27  1  048  .  33  353  .441  698  .  889  265  .  1  05  524  .  1  67 

212.108 

419.3:33 

59 

1061.07 

2098.33 

>30.  556J  1049.  17  353.728  699.444  265.320  524.583 

212.280 

419.667 

TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

20° 

Tan. 

Arc. 
333.333 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
112.370 

Arc. 

Tan. 

Arc. 

200.000 

M. 

168.460 

144.418 

285.714 

126.390 

250.000 

222.222 

101.159 

0 

168.604 

333.611 

144.541 

285.952 

126.497 

250.208 

112.465 

222.407 

101.245 

200.167 

1 

168.747 

333.889 

144.663 

286.190 

126.605 

250.417 

112.561 

222.593 

101.331 

200.333 

2 

168.  890(334.  167 
169.034  334.444 

144.786 
144.909 

286  429 
286.667 

126.712 
126.820 

250.625 
250  833 

112.657 

112.752 

222.778 
222.963 

101.417 
101.503 

200.500 
200.667 

3 
4 

169.177 

334.722 

145.032 

286.905 

126.927 

251.042 

112.848 

223.148 

101.589 

200.833 

5 

169.320 

335.000 

145.155 

287.143 

127.035 

251.250 

112.943 

223.333 

101.675 

201.000 

6 

169.463 

335.278 

145.278 

287.381 

127.142 

251.458 

113.039 

223.519 

101.761 

201.167 

7 

169.607 

335.556 

145.401 

287.619 

127.250 

251.667 

113.134 

223.704 

101.847 

201.333 

8 

169.750 

335.833 

145.523 

287.857 

127.357 

251.875 

113.230 

223.889 

101.933 

201.500 

9 

169.893 

336.111 

145.646 

288.095 

127.465 

252.083 

113.326 

224.074 

102.019 

201.667 

10 

170.037 

336.389 

145.  7691288.  333 

127.572 

252.292 

113.421 

224.259 

102.105 

201.833 

11 

170.180 

336.667 

145.892 

288.571 

127.680 

252.500 

113.517 

224.444 

102.  191  1202.  000 

12 

170.323 

336.944 

146.015 

288.810 

127.787 

252.708 

113.612 

224.630 

102.277202.167 

13 

170.467 

337.222 

146.138 

289.048 

127.895 

252.917 

113.708224.815 

102.363202.333 

14 

170.610 

337.500 

146.261 

289.286 

128.003 

253.125 

113.804 

225.000 

102.450202.500 

15 

170.753 

337.778 

146.383 

289.524 

128.110 

253.333 

113.899 

225.185 

102.5361202  667 

16 

170.897 

338.056 

146.506 

289.762 

128.218 

253.542 

113.995 

225.370 

102.622202.833 

17 

171.040 

338.333 

146.629 

290.000 

128.325 

253.750 

114.090 

225.556 

102.708203.000 

18 

171.183 

338.611 

146.752 

290.238 

128.433 

253.958 

114.186 

225.741 

102.794 

203.167 

19 

171.326 

338.889 

146.875 

290.476 

128.540 

254.167 

114.282 

225.926 

102.880 

203.  3S3 

20 

171.470 

339.167 

146.998 

290.714 

128.648 

254.375 

114.377 

226.111 

102.966203.500 

21 

171.613 

339.444 

147.121 

290.952 

128.755 

254.583 

114.473 

226.296 

103.052203.667 

22 

171.756 

339.722 

147.243 

291.190 

128.863 

254.792 

114.568 

226.481 

103.138 

203.833 

23 

171.900 

340.000 

147.366 

291.429 

128.970 

255.000 

114.664 

226.667 

103.224 

204.000 

24 

172.043 

340.278 

147.489 

291.661 

129.078 

255.208 

114.760 

226.852 

103.310 

204.107 

25 

172.186 

340.  55G 

147.612 

291.905 

129.185 

255.417 

114.855 

227.037 

103.396 

204.333 

26 

172.330 

340.833 

147.786 

292.143 

129.293 

255.625 

114.951 

227.222 

103.482 

204.500 

27 

172.473 

341.111 

147.858 

292.381 

129.400 

255.833 

115.046 

227.407 

103.568 

204.667 

28 

172.616 

341.389 

147.980 

292.619 

129.508 

256.042 

115.142 

227.593 

103.654 

204.833 

29 

172.760 

341.667 

148.103 

292.857 

129/615 

256.250 

115.237 

227.778 

103.740 

205.000 

30 

172.903 

341.944 

148.226 

293.095 

129.723 

256.458 

115.333 

227.963 

103.826 

205.167 

31 

173.046 

342.222 

148.349 

293.333 

129.830 

256.667 

115.429 

228.148 

103.912 

205.333 

32 

173.189 

342.500 

148  472 

293.571 

129.938 

256.875 

115.524  228.333 

103.998 

205.500 

33 

173.333 

342.778 

148.595 

293.810 

130.045 

257.083 

115.620228.519 

104.085 

205.667 

34 

173.476 

343.056 

148.718 

294.048 

130.153 

257.292 

115.715228.704 

104.171 

205.833 

35 

173.619 

343.333 

148.840 

294.286 

130.260 

257.500 

115.811'i228.889 

104.257 

206.000 

36 

173.763 

343.611 

148.963 

294.524 

130.368 

257.708 

115.907229.074 

104.343i206.167 

37 

173.906 

343.889 

149.086 

294.762 

130.475 

257.917 

116.002229.259 

104.429206.333 

38 

174.049 

344.167 

149.209 

295.000 

130.583 

258.125 

116.098 

229.444 

104.515 

206.500 

39 

174.193 

344.444 

149.332 

295.238 

130.690 

258.333 

116  193  229.630 

104.601 

206.667 

40 

174.336 

344.722 

149.455 

295.476 

130.798 

258.542 

116.289229.815 

104.6871206  833 

41 

174.479 

345.000 

149.578 

295.714 

130.905 

258.750 

116.385230.000 

104  773J207.000 

42 

174.622 

345.278 

149.700 

295.952 

131.013 

258  958 

116.480230.185 

104.859 

207.167 

43 

174.766 

345.556 

149.823 

296.190 

131.121 

259.167 

116.576230.370 

104.945 

207.333 

44 

174.909 

345.833 

149.946 

296.429 

131.228 

259.375 

116.671  230  556 

105.031 

207.500 

45 

175.052 

346.111 

150.069 

296.667 

131.336 

259.583 

116.767230.741 

105.117207.667 

46 

175.196 

346.389 

150.192 

296.905 

131.443 

259.792 

116.863230.926 

105.203207.833 

47 

175.339 

346.667 

150.315 

297.143 

131.551 

260.000 

116.958231.111 

105.289208.000 

48 

175.487 

346.944 

150.442 

297.381 

131.662 

260.208 

117.057 

231.296 

105.378 

208.167 

49 

175.635 

347.222 

150.569 

297.619 

131.773 

260.417 

117.156 

231.481 

105.467 

208.333 

50 

175.778 

347.500 

150.691  297.857 

131.880 

260.625 

117.251  231.667 

105.553208.500 

51 

175.922 

347.778 

150.814298.095 

131.988 

260.833 

117.347231.852 

105.639208  667 

52 

176.065 

348.056 

150.937298.333 

132.095 

261.042 

117.442232.037 

105.  725;  208.  833 

53 

176.208 

348.333 

151.060298.571 

132.203 

261.250 

117.538232.222 

105.811i209.000 

54 

176.352348.611 

151.183298.810 

132.310 

261.458 

117.634232.407 

105.897209.167 

55 

176.495348.889 

151.306299.048 

132  418 

261.667 

117.729232.593 

105.983209.333 

56 

176.638J349.167 

151.429299.286 

132.525 

261.875 

117.825232.778 

106.069209.500 

57 

176.782349.444 

151.551  299.524 

132.633 

262.083 

117.920232.963 

106.156209.667 

58 

176.925349.722 

151.674299.762 

132.740 

262.292 

118.016233.148 

106.242209.833 

59 

87 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC/ 


81° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~o" 

1061.93 

2100.00 

530.986 

1050.00 

354.014 

?  00.  000 

265.535 

525.000 

212.452 

420.000 

1 

IOCS.  79 

2101.67 

531.416 

1050.83 

354.301 

700.556 

265.750 

525.417 

212.623 

420.333 

2 

1063.65 

2103.33 

531.846 

1051.67 

354.587 

701.111 

265.965 

525.833 

212.795 

420.  6G7 

3 

1064.51 

2105.00 

532.275 

1052.50 

354.874 

701.66? 

266.179 

526.250 

212.967 

421.  COO 

4 

1065.37 

2106.67 

532.705 

3053.33 

355.1  GO 

702.222 

266.39-1 

526.66? 

213.139 

421.333 

5 

106£.23 

2108.33 

533.135 

1054.17 

355.447 

702.778 

266.609 

527.083 

213.311 

421.067 

6 

1067.09 

2110.00 

533.565 

1055.00 

355.733 

703.333 

266.824 

527.500 

213.483 

422.000 

7 

1067.95 

2111.6? 

533.994 

1055.83 

356.020 

703.889 

267.039 

527.917 

213.655 

422.333 

8 

1068.81 

2113.33 

534.424 

1056.67 

356.  SOU 

704.444 

267.254 

528.333 

213.827 

422.667 

9 

1069.67 

2115.00 

534.854 

1057.50 

356.593 

705.000 

267.469 

528.750 

213.999 

423.000 

10 

1070.53 

2116.67 

535.284 

1058.33 

356.879 

705.556 

267.684 

529.167 

214.171 

423.  a33 

11 

1071.39 

2118.33 

535.713 

1059.17 

357.1(56 

706.111 

267.899 

529.583 

214.343 

423.667 

12 

1072.25 

2120.00 

536.143 

1060.00 

357.452 

706.667 

268.114 

530.000 

214.515 

424.000 

13 

1073.13 

2121.67 

536.587 

1060.83 

357.748 

707.222 

268.336 

530.417 

214.693 

424.333 

14 

1074.02 

2123.33 

537.031 

1061.67 

358.044 

707.778 

268.558 

530.833 

214.870 

424.667 

15 

1074.88 

2125.00 

537.461 

1062.50 

358.331 

708.333 

268.773 

531.250 

215.042 

425.000 

10 

1075.74 

2126.67 

537.891 

1063.33 

358.618 

708.889 

268.988 

531.667 

215.214 

425.333 

17 

1076.60 

2128.33 

538.320 

1064.17 

358.904 

709.444 

269.202 

532.083 

215.386 

425.667 

18 

1077.46 

2130.00 

538.750 

1065.00 

359.191 

710.000 

269.417 

532.500 

215.558 

426.000 

19 

1078.32 

2131.67 

539.180 

1065.83 

359.477 

710.556 

269.632 

532.917 

215.730 

426.333 

20 

1079.18 

2133.33 

539.610 

1066.67 

359.764 

711.111 

269.847 

533.333 

215.902 

426.667 

21 

1080.04 

2135.00 

540.039 

1067.50 

360.050 

711.667 

270.062 

533.?  50 

216.074 

427.000 

22 

1080.90 

2136.67 

540.469 

1068.33 

360.337 

712.222 

270.277 

534.167 

216.246 

427.333 

23 

1081.76 

2138.33 

540.899 

1069.17 

360.623 

712.778 

270.492 

534.583 

216.418 

427.667 

24 

1082.6-3 

2140.00 

541.329 

1070.00 

360.910 

713.333 

270.707 

535.000 

216.590 

428.000 

25 

1083.48 

2141.67 

541.758 

1070.83 

361.196 

713.889 

270.922 

535.417 

216.762 

428.333 

26 

1084.34 

2143.33 

542.188 

1071.67 

361.483 

714.444 

271.137 

535.833 

216.933 

428.667 

27 

1085.20 

2145.00 

542.618 

1072.50 

361.769 

715.000 

271.351 

536.250 

217.105 

429.000 

28 

1086.06 

2146.67 

543  047 

1073.33 

362.056 

715.556 

271.566 

536.667 

217.277 

429.333 

29 

1086.94 

2148.33 

543.492 

1074.17 

362.352 

716.111 

271.788 

537.083 

217.455 

429.667 

30 

1087.83 

2150.00 

543.930 

1075.00 

362.648 

716.667 

2?'2.011 

537.500 

217.633 

430.000 

31 

1088.69 

2151.67 

544.365 

1075.83 

362.934 

717.222 

272.225 

537.917 

217.805 

430.333 

32 

1089.55 

2153.33 

544.795 

1076.67 

363.221 

717.778 

2?  2.  440 

538.333 

217.977 

430.667 

33 

1090.41 

2155.00 

545.225 

1077.50 

363.507 

718.333 

272.655 

538.750 

218.149 

431.000 

34 

1091.27 

2156.67 

545.655 

1078.33 

363.794 

718.889 

272.870 

539.167 

218.320 

431.333 

35 

1092.13 

2158.33 

546.084 

1079.17 

364.080 

719.444 

273.085 

539.583 

218.492 

431.667 

30 

1092.99 

2160.00 

546.514 

1080.00 

364.367 

720.000 

273.300 

540.000 

218.664 

432.000 

37 

1093.85 

2161.67 

546.944 

1080.83 

364.653 

720.556 

273.515 

540.417 

218.836 

432.333 

38 

1094.71 

2163.33 

547.374 

1081.67 

364.910 

721.111 

273.730 

510.833 

219.008 

432.667 

39 

1095.57 

2165.00 

547.803 

1082.50 

365.226 

721.667 

273.945 

541.250 

219.180 

433.000 

40 

1096.43 

2166.67 

548.233 

1083.33 

365.513 

722.222 

274.160 

541.667 

219.352 

433.333 

41 

1097.29 

2168.33 

548.663 

1084.17 

365.799 

722.778 

274.374 

542.083 

219.524 

433.667 

42 

1098.14 

2170.00 

549.092 

1085.00 

366.086 

723.333 

274.589 

542.500 

219.696 

434.000 

43 

1099.03 

2171.67 

549.537 

1085.83 

366.382 

723.889 

274.811 

542.917 

219.874 

434.333 

44 

1099.92 

2173.33 

549.981 

1086.67 

366.678 

724.444 

275.033 

543.333 

220.051 

434.607 

45 

1100.78 

2175.00 

550.410 

1087.50 

366.965 

725.000 

2?5.248 

543.750 

220.2-23 

435.000 

46 

1101.64 

2176.6? 

550.840 

1088.33 

367.251 

725.556 

275.463 

544.167 

220.395 

435.333 

47 

1102.50 

2178.33 

551.270 

1089.17 

367.538 

726.111 

275.678 

5I4.5S3 

220.567 

435.667 

48 

1103.36 

2180.00 

551.7001090.00 

367.824 

726.667 

275.803545.000 

220.739 

436.000 

49 

1104.22 

2181.67 

552.129 

1090.83 

368.111 

727.222 

276.108 

545.417 

220.911 

436.333 

50 

1105.08 

2183.33 

552.559 

1091.67 

368.397 

727.778 

276.323 

545.833 

221.083 

436.667 

51 

1105.94 

8185.00 

552.  9S9 

1092.  50'  308.68  1 

728.333 

276  53S 

546.250 

221.255 

437.000 

52 

1106.80 

2186.67 

553.419 

1093.33  3H8.9TO 

728.  8S9 

276.753 

546.667 

221.427 

437.333 

53 

1107.66 

2188.33 

553.848 

1004.17369.257 

729.444 

276.968 

547.083 

221.599 

437.667 

54 

1108.52 

2190.00 

554.278 

1095.00369.543 

730.000 

277.183 

547.500 

221.771 

438.000 

55 
56 

1109.402191.67 
1110.292193.33 

554.722 
555.166 

1095.83369.839 
1096.67370.135 

730.556 
731.111 

277.405 
277.627 

547.917 
548.333 

221.948 
222.126 

438.333 

438.667 

57 

1111.152195.00 

555.596 

1097.50  370.422 

731.667 

277.842 

548.750 

222.298  439.000 

58 

1112.01 

2196.67 

556.026 

1098.33370.708 

732.222 

278.056 

549.167 

222.470439.333 

59 

1112.87 

2198.33 

556.455 

1099.17370.995 

732.778 

278.271 

549.583 

222.642  439.667 

88 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC.V 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

31° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |    Arc. 

Tan. 

Arc. 

M. 

177.008 

350.000151.797 

300.000 

132.848 

*!G2.500 

118.112^33.333 

1UG.3~28 

ZioTcoo 

~O" 

177.212 

350.278 

151.920 

300.238 

132.955 

262.708 

118.207 

233.519 

100.414 

.'10.167 

1 

177.355 

350.556 

152.043|300.476 

133.063 

262.917 

118.303 

233.704 

106.500 

210.333 

2 

177.498 

350.833 

152.  106 

300.714 

133.171 

263.125 

118.398 

233.889 

106.586 

210.500 

3 

177.641 

351.111 

152.289 

300.952 

133.278 

263.333 

118.494 

234.074 

106.672 

,210.  CG7 

4 

177.785 

351.389 

152.411 

301.190 

133.386 

263.542 

118.590 

234.259 

106.758 

210.833 

5 

177.928 

351.667 

152.534 

301.429 

133.493 

263.750 

118.685 

234.444 

106.844 

211.000 

6 

178.071 

351.944 

152.657 

301.667 

133.601 

263.958 

118.781 

234.630 

106.930 

211.167 

7 

178.215 

352.222 

152.780 

301.905 

133.708 

264.167 

118.876 

234.815 

107.016 

211.333 

8 

178.358  352.500 

152.903 

302.143 

133.816 

264.375 

118.972 

235.000 

107.102 

211.500 

9 

178.501352.778 

153.026 

302.381 

133.923 

264.583 

119.067 

235.185 

107.188 

211  667 

10 

178.645  353.  05G 

153.148 

302.619 

134.031 

264  792 

119.163 

235.370 

107.274 

211.833 

11 

178.788858.333 

153.271  302.857 

134.138 

265.000 

119.259 

235.556 

107.360 

212.000 

13 

178.936353.611 

153.398 

303.  09? 

134.249 

265.208 

119.357 

235.741 

107.449 

212.167 

13 

179.084:353.889 

153.525,303.333 

134.360 

265.417 

119.456 

235.926 

107.538 

212.333 

14 

179.227354.167 

153.648 

303.571 

134.468 

265.625 

119.552 

236.111 

107.624 

212.500 

15 

179.371 

354.444 

153.771 

303.810 

134.575 

265.833 

119.647 

236.296 

107.710 

212.667 

16 

179.514 

354.722 

153.894:304.048 

134.683 

266.042 

119.743 

236.481 

107.796 

212.833 

17 

179.657 

355.000 

154.017 

304.280 

134.790 

266.250 

119.839 

236.667 

107.882 

213.000 

18 

179.801 

355.278 

154.140 

304.524 

134.898 

266.458 

119.934 

236.852 

107.968 

213.167 

19 

179.944 

355.556 

154.262 

304.762 

135.005 

266.667 

120.030 

237.037 

108.054 

213.333 

20 

180.087 

355.833 

154.  385!  305.  000 

135.113 

266.875 

120.125 

IL'37.222 

108.141 

213.500 

31 

180.231 

356.111 

154.508 

305.238 

135.220 

267.083 

120.221 

237.407 

108.227 

213.667 

22 

180.374 

356.389 

154.631  305.476 

135.328 

267.292 

120.317 

237.593 

108.313 

213.833 

23 

180.517 

356.067 

154.754 

305.714 

135.436 

267.500 

120.412 

237.778 

108.399 

214.000 

24 

180.660 

356.944 

154.877!305.952 

135.548 

267.708 

120.508 

237.963 

108.485 

214.167 

25 

180.804 

357.222 

154.999 

306.190 

185.651 

267.917 

120.603 

238.148 

108.571 

214.333 

26 

180.947 

357.500 

155.122306.429 

135.758 

268.125 

120.699 

538.333 

108.657 

214.500 

37 

181.090 

357.778 

155.245 

306.667 

135.866 

268.333 

120.794 

238.519 

108.743 

214.667 

38 

181.238 

358.056 

155/372 

306.905 

135.977 

268.542 

120.893 

238.704 

108.832 

214.833 

39 

181.386 

358.333 

155.499 

307.143 

136.088 

268.750 

120.992 

238.889 

108.921 

215.000 

30 

181.530 

358.611 

155.622 

307.381 

136.195 

2G8.958 

121.088 

239.074 

109.007 

215.167 

31 

181.673 

358.889 

155.745j307.619 

136.303 

269.167 

121.183 

239.259 

109.093 

215.333 

33 

181.816 

359.167 

155.868 

307.857 

136.410 

269.375 

121.279 

239.444 

109.179 

215.500 

33 

181.960 

359.444 

155.990308.095 

136.518 

269.583 

121.374 

239.630 

109.265 

215.667 

34 

182.103 

359.722 

156.113 

308.333 

136.625 

269.792 

121.470 

239.815 

109.351 

215.833 

35 

182.246 

360.000 

156.236 

308.571 

136.733 

270.000 

121.566 

240.000 

109.437 

216.000 

36 

182.390 

360.278 

156.359^308.810 

136.840 

270.208 

121.661 

240.185 

109.523 

216.167 

37 

182.533 

360.556 

156.482:309.048 

136.948 

270.417 

121.757 

240.370 

109.609 

216.333 

38 

182.676 

360.833 

156.605 

309.286 

137.055 

270.625 

121.852 

240.556 

109.695 

216.500 

39 

182.820 

361.111 

156.728 

309.524 

137.163 

270.833 

121.948 

240.741 

109.781 

216.667 

40 

182  963 

361.389 

156.850 

309.762 

137.270 

271.042 

122.044 

240.926 

109.867 

216.833 

41 

183.106 

361.667 

156.973310.000 

137.378 

271.250 

122.139 

241.111 

109.953 

217.000 

43 

183.254 

361.944 

157.100 

310.238 

137.489 

271.458 

122.238 

241.296 

110.042 

217.107 

43 

183.402 

362.222 

157.  227  i  310.  476 

137.600 

271.667 

122.337 

241.481 

110.131 

217.333 

44 

183.546 

362.500 

157.350 

310.714 

137.708 

271.875 

122.432 

241.667 

110.217 

217.500 

45 

183.689 

362.778 

I57.473l310.952 

137.815 

272.083 

122.528 

241.852 

110.303 

217.667 

46 

1  S3.  832 

363.056 

157.596 

311.190 

137.923 

272.292 

122.623 

242.037 

110.389 

217.833 

47 

183.976 

363.333 

157.719 

311.429 

138.030 

272.500 

122.719 

242.222 

110.475 

218.000 

48 

184.119 

363.611 

157.841 

311.667 

138.138 

272.708 

122.815 

242.407 

110.561 

218.167 

49 

184.262 

363.889 

157.964311.905 

138.245 

272.917 

122.910 

242.593 

110.648 

218.333 

50 

184.405 

364.167 

158.087312.143 

1  38.  353  i  273.  125 

123.006 

242.778 

110.734 

218.500 

51 

184  549364.444 

158.210312.381 

138.  4  60  J273.333 

123.101 

242.963 

110.820 

218.607 

53 

184.  692  ;  364.  722 

158.333 

312.619 

138.568J273.542 

123.197 

243.148 

110.906 

218.833 

53 

184.  835  1365.000 

158.456 

312.857 

138.675i273.750 

123.293 

243.333 

110.992 

219.000 

54 

184.983365.278 

158.583313.095 

188.786273.958 

123.391 

243.519 

111.081 

219.167 

55 

185.132365.556 

158.710 

313.333 

188.898274.167 

123.490 

243.704 

111.170 

219.333 

56 

185  275365.833 

158.832 

813.  f.  71 

139.005274.375 

123.586 

243  889 

111.256 

219.500 

57 

185.418366.111 

158.955 

313.810139.113274.583 

123.681 

244.074 

111.342 

219.667 

58 

185.561  366.389 

1  59  .  C78  3  1  4  .  048  i  1  31)  .  220  274  .  792 

123.777 

244.259 

111.428 

219.833 

59 

89 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


83° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

MT 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 
733.333 

Tan. 

Arc. 

Tan. 

Arc. 

O 

1113.73 

2200.00 

556.885 

1100.00 

371.281 

278.486  550.000  222.814  440.000 

1 

1114.59 

2:201.67 

557.315 

1100.83 

371.568 

733.889 

278  .  658  550  .417  222  .  986  440  .  333 

3 

1115.45 

2203.33 

557.745 

1101.67 

371.854 

734.444 

278.916  550.833  223.158  440.667 

3 

111(5.31 

2205.00 

558.174 

1102.50 

372.141 

735.000 

279.088551.250223.330441.000 

4 

1117.17 

2206.67 

558.604 

1103.33 

372.427 

735.556 

279.  346  55t  667 

223.502441.333 

5 

1118.06 

2208.33 

559.048 

1104.17 

372.723 

736.111 

279.568552.083 

223.079441.667 

6 

1118.94 

2210.00 

559.492 

1105.00 

373.020 

736.667 

279.790552.500 

223.857 

442.000 

7 

1119.80 

2211.67 

559.922 

1105.83 

373.306 

737.222 

280.005552.917 

224.029 

442.333 

S 

1120.66 

2213.33 

560.352 

1106.67 

373.593 

737.778 

280.  220  1553.333 

224.201 

442.667 

9 

1131.62 

2215.00 

560.781 

1107.50 

373.879 

738.333 

280.435 

553.750 

224.373 

443.000 

10 

1123.38 

2216.67 

561.211 

1108.33 

374.166 

738.889 

280.650 

554.167 

224.545 

443.333 

11 

1123.24 

2218.33 

561.641 

1109.17 

374.452 

739.444 

280.865 

554.583 

224.717 

443.667 

12 

ii2i.io 

2220.00 

562.071 

1110.00 

374.739 

740.000 

281.079 

555.000 

224.889444.000 

13 

1124.96 

2221.67 

562.500 

1110.83 

375.025 

740.556 

281.294 

555.417 

225.  061  1444.333 

14 

1125.82 

2223.33 

562.930 

1111.67 

375.312 

741.111 

281.509 

555.833 

225.233444.667 

15 

1126.71 

2225.00 

563.374 

1112.50 

375.608 

741.667 

281.731 

556.250 

2-,'5.410445.000 

16 

1127.60 

2226.67 

563.818 

1113.33 

375.904 

742.222 

281.953 

556.667 

22.5.  588  '445.  333 

17 

1128.45 

2228.33 

564.248 

1114.17 

376.190 

742.778 

282.168557.083 

225.760l445.667 

18 

1129.31 

2230.00 

564.678 

1115.00 

376  .  477 

743.,  333 

282.383  557.500 

225.932 

446.000 

19 

1130.17 

2231.67 

565.107 

1115.83 

376.763 

743.889 

282.598 

557.917 

226.104 

446.333 

20 

1131.03 

2233.33 

565.537 

1116.67 

377.050 

744.444 

282.813 

558.333 

226.276 

446.667 

21 

1131.89 

2235.00 

565.967 

1117.50 

377.336 

745.000 

283.028558.750 

226.448 

447.000 

22 

1132.75 

2236.67 

566.397 

1118.33 

377.623 

745.556 

283.  243  '559.  167 

226.620 

447.333 

23 

1133.64 

2238.33 

566.841 

1119.17 

377.919 

746.111 

283.465 

559.  5S3 

226.797 

447.667 

24 

1134.53 

2240.00 

567.285 

1120.00 

378.215 

746.667 

283.687 

560.000 

226.975 

448.000 

35 

1135.39 

2241.67 

567.715 

1120.83 

•578.501 

747.222 

283.902 

560.417 

227.147 

448.333 

20 

1136.25 

2243.33 

568.144 

1121.67 

378.788 

747.778 

284.117 

560.833 

227.319 

448.667 

27 

1137.11 

2245.00 

5(58.574 

112<?.50 

379.074 

748.333 

284.332 

561.250 

227.491 

449.000 

28 

1137.97 

2246.67 

5(59.004 

1123.33 

379.361 

748.889 

284.54? 

561.667 

227.663 

449.333 

29 

1138.83 

2248.33 

569.433 

1124.17 

379.648 

749.444 

284.761 

562.083 

227.835 

449.667 

30 

1139.68 

2250.00 

569.863 

1125.00 

379.934 

750.000 

284.976 

562.500 

228.007 

450.000 

31 

1140.54 

2251.67 

570.293 

1125.83 

380.221 

750.556 

285.191 

562.917 

228.178 

450.333 

33 

1141.40 

2253.33 

570.723 

1126.67 

380.507 

751  .111 

285.406 

563.333 

228.350 

450.667 

33 

1142.29 

2255.00 

571.167 

1127.50 

380.803 

751.667 

285.628 

563.750 

228.528 

451.000 

34 

1143.18 

2256.67 

571.611 

1128.33 

381.099 

752.222 

285.850 

564.167 

228.706 

451.333 

35 

1144.04 

2258.33 

572.041 

1129.17 

381.386 

752.778 

286.065 

564.583 

228.878 

451.667 

3G 

1144.90 

2260.00 

572.470 

1130.00 

881.672 

753.333 

286.280 

505.000 

229.050 

452.000 

37 

1145.76 

2261.67 

572.900 

1130.83 

381.959 

753.889 

286.495 

565.417 

229.222 

452.333 

38 

1146.62 

2263.33 

573  330 

1131.67 

382.245 

754.444 

286.710 

565.833 

229.394 

452.667 

39 

1147.48 

2265.00 

573.760 

1132.50 

382.532 

755.000 

286.925 

566.250 

229.565 

453.000 

40 

1148.34 

2266.67 

574.189 

1133.33 

382.818 

755.556 

287.140 

566.667 

229.737 

453.333 

41 

1149.22 

2268.33 

574.633 

1134.17 

383.114 

756.111 

287.362567.083 

229.915 

453.667 

43 

1150.11 

2270.00 

575.077 

1135.00 

383  410 

756.667 

287.584567.500 

230.093 

454.000 

43 

1150.97 

2271.67 

575.507 

1135.83 

383.697 

757.222 

287.799,567.917 

280.265 

454.3:33 

44 

1151.83 

2273.33 

575.937 

1136.67 

383.983 

757.778 

288.014568.333 

230.437 

454.667 

45 

1152.69 

2275.00 

576.367 

1137.50 

384.270 

758.333 

288.229568.750 

230  609 

455.000 

40 

1153.55 

2276.67 

576.796 

1138.33 

384.556 

758.889 

288.443 

569.167 

230.781 

455.  333 

47 

1154.44 

2278.33 

577.240 

1139.17 

384.852 

759.444 

288.666 

569.583 

230.958 

455.667 

48 

1155.33 

2280.00 

577.684 

1140.00 

385.149 

760.000 

288.888 

570.000 

231  .  136 

456.000 

49 

1156.19 

2281.67 

578.114 

1140.83 

385.435 

760.556 

289.103 

570.417 

231.308 

456.333 

50 

1157.05 

2283.33 

578.544 

1141.67 

385.722 

761.111 

289.317 

570.833 

231.480 

456.667 

51 

1157.90 

2285.00 

578.974 

1142.50 

386.008 

761.667 

289.532 

571.250231.652 

457.000 

52 
53 

1158.76 
1159.62 

2286.67 
2288.33 

579.403 
579.833 

1143.33 
1144.17 

386.295 
386.581 

762.222289.747 
762.  778  '289.  962 

571.667231.824 
572.  083  !  231.  996 

457.333 

457.667 

54 

1160.48 

2290.00 

580.263 

1145.00 

386.868 

763.333  290  177 

572.500'  232.  168 

458.000 

55 

1161.37 

2291.67 

580.707 

1145.83 

387.164 

763.889^90.399 

572.917|232  345 

458.333 

50 

1162.26 

2293.33 

581.151 

1146.67 

387.4(50 

764.444j290.62l 

573.333232.523 

458.667 

57 

1163.12 

2295.00 

581.581 

1147.50 

387.746 

765.  000  1290.836 

573.750232.695 

459.000 

58 

1163.98 

2296.67 

582.011 

1148.33 

388.033 

765.556291.051 

574.167232.867 

459.333 

59 

1164.84 

2298.33 

582.440 

1149.17 

388.319 

766.  Ill  1291.  266 

574-583233.039459.667 

90 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve, 

10°  Curve. 

33° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

185.705 

366.667 

159.201 

314.286 

139.328 

275.000 

123.872 

244.444 

111.  514  220.  OuO 

~~o~ 

185.848 

306.944 

159.324 

314.524 

139.435 

275.208 

123.968 

244.630 

111.600220.167 

1 

185.991 

307.222 

159.447 

314.762 

139.543 

275.417 

124.064 

244.815 

111.686220.333 

3 

18(3.135 

367.500 

159.570 

315.000 

139.650 

275.625 

124.159 

245.000 

111.772 

220.500 

3 

180.278 

367.778 

159.692 

315.238 

139.758 

275.833 

124.255 

245.185 

111.858 

220.607 

4 

180.420 

368.050 

159.819 

315.476 

139.869 

276.042 

124.354 

245.370 

111.947 

220.833 

5 

180.574 

308.333 

159.940 

315.714 

139.980 

276.250 

124.452 

245.556 

112.030 

221.000 

6 

186.717 

308.611 

100.009 

315.952 

140.087 

276.458 

124.548 

245.741 

112.122 

221.107 

7 

180.801 

368.889 

100.192 

316.190 

140.195 

276.667 

124.644 

245.926 

112.208 

221.333 

8 

187.004 

309.167 

160.315 

316.429 

140.302276.875 

124.739 

246.111 

112.294 

221.500 

9 

| 

187.147 

369.444 

160.438 

316.667 

140.410277.083 

124.835 

246.296 

112.380 

221.667 

1O 

187.291 

309.722 

160.561 

316.905 

140.518277.292 

124.930 

246.481 

112.466 

221.833 

11 

187.484 

370.000 

160.683 

317.143 

140.625277.500 

125.026 

246.667 

112.552 

222.000 

12 

187.577 

370.278 

160.806 

317.381 

140.  733  1277.  708 

125.122 

246.852 

112.638 

222.167 

13 

187.721 

370.550 

160.929 

317.619 

140.840 

277.917 

125.217 

247.037 

112.724 

222.333 

14 

187.869 

370.833 

161.050 

317.857 

140.951 

278.125 

125.316 

247.222 

112.813 

222.500 

15 

188.017 

371.111 

101.183 

318.095 

141.062 

278.333 

125.415 

247.407 

112.902 

222.667 

16 

188.100 

371.389 

101.300 

318.333 

141.170 

278.542 

125.510 

247.593 

112.988 

222.833 

17 

188.303 

371.067 

101.429 

318.571 

141.277 

278.750 

125.600 

247.778 

113.074 

223.000 

18 

188.447 

371.944 

161.552 

318.810 

141.385 

278.958 

125.701 

247.963 

113.160 

223.167 

19 

188.590 

372.222 

161.674 

319.048 

141.492 

279.167 

125.797 

248.148 

113.246 

223.333 

30 

188.733 

372.500 

161.797 

319.286 

141.600 

279.375 

125.893 

248.333 

113.332 

223.500 

31 

188.877 

372.778 

161.920 

319.524 

141.707 

279.583 

125.988 

248.519 

113.418 

223.667 

33 

189.025 

373.056 

102.047 

319.762 

141.818 

279.792 

126.087 

248.704 

113.507 

223.833 

33 

189.173 

373.333 

102.174 

320.000 

141.930 

280.000 

126.186 

248.889 

113.596 

224.000 

34 

189.310 

373.611 

162.297 

320.238 

142.037 

280.208 

126.281 

249.074 

113.682 

221.167 

35 

189.459 

373.889 

162.420. 

320.476 

142.145 

280.417 

126.377 

249.259 

113.768 

224.333 

36 

189.  003 

374.167 

162.543 

320.714 

142.252 

280.625 

126.473 

249.444 

113.854 

224.500 

37 

189.740 

374.444 

102.060 

320.952 

142.300 

280.833 

126.568 

249.630 

113.941 

224.667 

38 

189.889 

374.722 

102.788 

321.190 

142.467 

281.042 

126.664 

249.815 

114.027 

224.833 

39 

190.033 

375.000 

162.911 

321.429 

142.575 

281.250 

126.759 

250.000 

114.113 

225.000 

3O 

190.170 

3:5.278 

163.034 

321.667 

142.682 

281.458 

126.855 

250.185 

114.199 

225.167 

31 

190.319 

375.550 

163.157 

321.905 

142.790 

281.607 

126.951 

250.370 

114.285 

225.333 

33 

190.467 

375.833 

163.284 

322.143 

142.901 

281.875 

127.049 

250.556 

114.374 

225.500 

33 

190.615 

376.111 

163.411 

322.381 

143.012 

282.083 

127.148 

250.741 

114.463 

225.667 

34 

190.759 

376.389 

103.534 

322.619 

343.119 

282.292 

127.244 

250.926 

114.549 

225.833 

35 

190.902 

376.667 

163.657 

322.857 

143.227 

282.500 

127.339 

251.111 

114.635 

226.000 

36 

191.045 

376.944 

163.779 

323.095 

143.334 

282.708 

127.4:35 

251.296 

114.721 

226.167 

37 

191.189 

377.222 

103.902 

323.333 

143.442 

282.917 

127.530 

251.481 

114.807 

226.333 

38 

191.332 

377.500 

164.025 

323.571 

143.549 

283.125 

127.626 

251.667 

114.893 

226.500 

39 

191.475 

377.778 

164.148 

323.810 

143.657 

283.333 

127.722 

251.852 

114.979 

226.667 

4O 

191.623 

378.056 

164.275 

324.048 

143.768 

283.542 

127.820 

252.037 

115.068 

226.833 

41 

191.771 

37'8.333 

164.402 

324.286 

143.879 

283.750 

127.919 

252.222 

115.157 

227.000 

43 

191.915 

378.611 

164.525 

324.524 

143.987 

283.958 

128.015 

252.407 

115.243 

227.167 

43 

192.058 

378.889 

1  64.  648  :  324.  702 

144.094 

284.107 

128.110 

252.593 

115.329 

227.333 

44 

192.201 

379.167 

164.7703,55.000 

144.202 

284.375 

128.206 

252.778 

115.415 

227.500 

45 

192.345 

379.444 

164.893325.938 

144.309 

284.583 

128.302 

252.963 

115.501 

227.667 

46 

192.493 

379.722 

105.020325.476 

144.420 

284.792 

128.400 

253.148 

115.590 

227.833 

47 

192.641 

380.000 

105.147325.714 

144.531 

285.000 

128.499 

253.3-33 

115.679 

228.000 

48 

192.784 

380.278 

165.270 

325.952 

144.639 

285.208 

128.595 

253.519 

115.765 

228.167 

49 

192.927 

380.556 

165.393 

326.190 

144.747 

285.417 

128.690 

253.704 

115.851 

228.333 

50 

193.071  880.833 

165.516326.429 

144.854 

285.625 

128.786 

253.889 

115.937 

228.500 

51 

193.214381.111 

165.639326.667 

144.962 

285.833 

128.881 

254.074 

116  023 

228.667 

53 

193.357381.389 

165.761  326.905 

145.069 

286.042 

128.977 

254.259 

116.109 

228.833 

53 

193.501:381.667 

165.884327.143 

145.177 

286.250 

129.073 

254.444 

116.195 

229.000 

54 

193.  649  i  38  1.944 

166.011  327.381 

145.288 

286.458 

129.171 

254.630 

116.284 

229.167 

55 

193.797382.222 

166.138327.619 

145.399 

286.667 

129.270 

254.815 

116.373 

229.333 

56 

193.940382.500 

166.261  327.857 

145.506 

286.875 

129.306 

255.000 

116.459 

229.500 

57 

194.  083;  382.  778 

166.384  328.095 

145.614 

287.083 

129.461 

255.185 

116.545 

229.667 

58 

194.227383.056 

166.507,328.333 

145.721 

287.292 

129.557 

255.370 

116.631 

229.833 

59 

91 


TABLE   XIV. — ACTUAL   TANGEKTS,    ETC. 


33° 
M. 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~o" 

1165770 

2300.00 

582.870 

1150.00 

388.606766.667 

291.481 

575.000 

233.211 

460.000 

1 

1166.59 

2301.67 

583.314 

1150.83 

388.902767.22-3 

291.703 

575.417 

233.388 

460.333 

g 

1167.47 

2303.33 

683.758 

1151.67 

389.198767.778 

291.925 

575.833 

233.566 

460.667 

3 

1168.33 

2305.00 

584.188 

1152.50 

389.484768.333 

•392.140 

576.250 

2:33.738 

461.000 

4 

1169.19 

2303.67 

584.618 

1153.33 

389.771  768.889 

293.355 

576.667 

233.910 

461.333 

5 

1170.05 

2308.  33 

585.047 

1154.17 

390.057769.414 

292.570 

577.083 

234.082 

461.667 

6 

1170.91 

2310.00 

585.477 

1155.00 

390.344770.000 

292.785 

577.500 

234.254 

462.000 

7 

1171.77 

2311.67 

585.907 

1155.83 

390.630770.556 

292.999 

577.917 

234.426 

462.333 

8 

1172.63 

2313.33 

586.337 

1156.67 

390.917,771.111 

•393.214 

578.333 

234.598 

463.667 

9 

1173.52 

2315.00 

586.781 

1157.50 

391.213 

771.667 

293.436 

578.750 

234.775 

463.000 

1O 

1174.41 

2316.67 

587.225 

1158.33 

391.509 

772.222 

293.658 

579.167 

234.953 

463.333 

11 

1175.27 

2318.33 

587.654 

1159.17 

391.796 

772.778 

293.873 

579.583 

235.1  25  403.  067 

13 

1176.13 

2320.00 

58S.084 

1160.00 

393.082 

773.333 

294.088 

580.000 

235.297464.000 

13 

1176.98 

2321.67 

588.514 

1160.83 

392.369 

773.889 

294.303 

580.417 

235.469 

464.333 

14 

1177.84 

2323.33:588.944 

1161.67 

392.655 

774.444 

294.518 

580.833 

235.641 

464.667 

15 

1178.73 

2325.00 

589.388 

1162.50 

392.951 

775.000 

294.740 

581.250 

235.818 

465.000 

16 

1179.6v> 

2326.67 

589.832 

1163.33 

393.247 

775.556 

294.962 

581.667 

235.996 

465.333 

17 

1180.48 

2328.33 

590.262 

1164.17 

393.534 

7:6.111 

,395.177 

582.083 

236.168 

465.  6G7 

18 

1181.31 

2330.00 

590.691 

1165.00 

393.820 

776.  66  1' 

295.392 

582.500 

226.340 

466.000 

19 

1182.20 

,'331.67 

591.121 

1165.83 

394.107 

777.222 

295.607 

582.917 

236.512 

466.333 

20 

1183.06 

2333.33 

591  .  551 

1166.67 

394.393 

777.778 

295.822 

583.333 

236.684 

466.667 

21 

1183.95 

2335.00 

591.995 

1167.50 

394.689 

778.333 

2UG.044 

583.750 

336.862 

467.000 

22 

1184.83 

2336.67 

592.439 

1168.33 

394.985 

778.889 

296.266 

584.167 

337.039 

467.333 

23 

118.5.69 

2338.33 

592.869 

1169.17 

395.272 

779.444 

296.481 

584.583 

237.211 

467.667 

34 

1186.55 

2340.00 

593.298 

1170.00 

395.558 

780.000 

,'96.696 

585.000 

237.  3S3 

168.000 

25 

1187.41 

2341.67 

593.728 

1170.83 

395.845 

780.556 

296.911 

585.417 

'337  555 

468.3.33 

36 

1188.27 

2343.33 

594.158 

1171.67 

396.131 

781.111 

297.126 

585.833 

337  727 

468.667 

37 

1189.10 

3345.00 

594.602 

1172.50 

396.428 

781.667 

297.348 

586.250 

337.905 

469.000 

38 

1190.05 

234<>.G7 

595  046 

1173.33 

396.724 

782.222 

297.570 

586  667 

338.082 

469.333 

39 

1190.91 

2348.33 

595  476 

1174.17 

397.010 

782.778 

297.785 

587.083 

238.254 

469.667 

3O 

1191.77 

2350.00 

595.905 

1175.00 

397.297 

783.333 

?38.000 

587.500 

238.426 

470.000 

31 

1192.63 

2351.67 

596  335 

1175.83 

397.583 

783.889 

298.214 

587.917 

238  598 

470.333 

33 

1193.49 

#53.33 

598.765 

1176.67 

397.870 

784.444 

298.429 

588.333 

238.770 

470.667 

33 

1194.37 

2355.00 

597.209 

1177.50 

398.166 

785.000 

298.651 

588.750 

238.948 

471.000 

34 

1195.26 

2356.67 

597.653 

1178.33 

39S.462 

785.556 

298.873 

589.167 

239.125 

471.333 

35 

1196.12 

2358.33 

598.083 

1179.17 

398.748 

786.111 

299.088 

589.583 

339.297 

471.667 

36 

1196.98 

2360.00 

598.513 

1180.00 

399.035 

786.667 

299.303 

590.000 

239.469 

472.000 

37 

1197.84 

3351.67 

598.942 

1180.83 

399.321 

787.222 

299.518 

590.417 

339.641 

472.333 

38 

1198.70 

2363.33 

599.37-3 

1181.67 

399.603 

787.778 

299.733 

590.833 

339.813 

472.667 

39 

1199.59 

3365.00 

599.816 

1182.50 

399.904 

788.333 

299.955 

591.250 

239.991 

473.000 

4O 

1200.48 

2366.67 

600.260 

1183.33 

(00.200 

788.889 

300  177 

591.667 

240.169 

473.333 

41 

1201.34 

2368.33 

6)0.690  1184.17 

100.486 

789.  44  < 

300.  3£8 

592.083 

240.341 

473.667 

43 

1202.20 

2370.00 

601.120 

1185.00 

+00.773 

790  000 

300.607 

592.500 

240.512 

474.000 

43 

1203.08 

2371  67 

601.561 

1185.83 

401.069 

790.556 

300.829 

592.917 

240.690 

474.333 

44 

1203.97 

2373.33 

602.008 

1186.67 

401.365 

791.111 

301.051 

593  333 

340.868 

474.667 

45 

1204.83 

2375.00 

602.437 

1187.50 

101.652 

791.667 

301.266 

593.750 

241.010 

475.000 

46 

1205.69 

2376.67602.867 

1188.33 

401.938 

792.222 

301.481 

594.167 

241.212 

475.333 

47 

1206.55 

2378.33603.297 

1189.17 

402.225 

792.  77S 

301.696 

594.583 

241.384 

475.667 

48 

1207.41 

2380.00 

603.727 

1190.00 

402.511 

793.333 

301.911 

595.000 

241.556 

476.000 

49 

1208.30 

2381.67 

604.171 

1190.83 

402.807 

793.889 

302.133 

595.417 

241.733 

476.333 

5O 

1209  19 

2383.33 

604.615 

1191.67 

403.103 

794.444 

302.355 

595.833 

241.911 

476.667 

51 

1210.04 

2385  00 

605.045 

1192.50 

403.390 

795.000 

302.570 

596.250 

242.083 

477.000 

53 

1210.90 

2386.67 

605.474 

1193.33 

403.676 

795.556 

302.785 

596.667 

242.255 

477.333 

53 

1211.76 

2388.33 

605.904 

1194.1: 

403.963 

796.111 

303.000 

597.083 

342.427 

477.667 

54 

1212.62 

2390.00 

606.3341195.00 

404.249 

796.667 

303.215 

597  500 

342.599 

478.000 

55 

1213.51 

2391.67 

606.778  1195.83 

404.545 

797.223 

303.437 

597.917 

342.776 

478.3:33 

56 

1214.40 

2393.33 

607.222  1196.67 

404.841 

797.778 

303.659 

598.333 

242.  954  1  478.  667 

57 

1215.26 

2395.00 

607.6521197.50 

405.128 

798.333 

303.874 

598.750 

243.126479.000 

58 

1216.12 

2396.67 

608.081  1198.33 

405.414 

798.889 

304.088 

599.167 

243.298479.333 

59 

1217.01 

2398.33608.525:1199  17 

405.7111799.444 

304.311 

599.583 

243.  476  J479.667 

92 


TABLE   XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve, 

9°  Curve, 

1O°  Curve. 

23° 
M? 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.       Arc. 

194.370383.333 

166.630 

328.571 

145.829 

287.500 

129.653 

255.556 

116.717230.000 

O 

194.518383.011 

166.757 

328.810 

145.940 

287.708 

129.751 

255.741 

116.806230.167 

1 

194.660383.889 

166.883 

329.048 

146.051 

287.917 

129.850 

255.926 

116.895230.333 

2 

194.809384.107 

167.000 

329.280 

146.159 

288.125 

129.946 

256.111 

116.981  230.500 

3 

194.  953;  384.  444 

167.129 

329.524 

146.206 

288.3:33 

130.041 

256.296 

117.067230.667 

4 

195.096,384.722 

167.252 

329.762 

146.374 

288.542 

130.137 

256.481 

117.153230.833 

5 

195.  239  385.  000 

167.375 

330.000 

140.4cSl 

288.750 

130.232 

256.667 

117.239231.000 

6 

195.383385.278 

167.498 

330.238 

146.589 

288.958 

130.328 

256.852 

117.325231.167 

7 

195.526385.556 

167.621 

330.476 

146.696 

289.167 

130.424 

257.037 

117.41li231.333 

8 

195.674 

385.833 

167.748 

330.714 

146.807 

289.375 

130.522 

257.222 

117.500 

231.500 

9 

195.822 

386.111 

167.874 

330.952 

146.918 

289.583 

130.621 

257.407 

117.589 

231  .667 

10 

195.965386.389 

107.997 

331.190 

147.026 

289.792 

130.717 

257.593 

117.675 

231.833 

11 

196.109386.667 

168.120331.429 

147.138 

290.000 

130.812 

257.778 

117.761 

232.000 

13 

196.252380.944 

168.243331.667 

147.241 

290.208 

130.908 

257.963 

117.  847j232.167 

13 

196.395:387.222 

108.366 

331.905 

147.348 

290.417 

131.004 

258.148 

117.933232.333 

14 

196.  543  '387.  500 

168.493 

332.143 

147.460 

290.625 

131.102 

258.333 

118.  022  '  232.  500 

15 

196.692 

387.778 

168.620 

332.381 

147.571 

290.833 

131.201 

258.519 

118.  Ill  1232.667 

16 

196.835 

388.056 

168.743 

332.619 

147.678 

291.042 

131.297 

258.704 

118.197 

232.833 

17 

196.978 

388.333 

168.866 

332.857 

147.780 

291.250 

131.392 

258.889 

118.283 

233.000 

18 

197.121 

388.611 

168.988 

333.095 

147.893 

291.458 

131.488 

259.074 

118.369 

233.167 

19 

197.265 

388.889 

169.111 

333.333 

148.001 

291.667 

131.583 

259.259 

118.455 

233.333 

30 

197.413 

389.167 

169.238 

333.571 

148.112 

291.875 

131.682 

259.444 

118.544 

233.500 

31 

197.561 

389.444 

169.365 

333.810 

148.223 

292.083 

131.781 

259.630 

118.633 

233.667 

33 

197.704 

389.722 

169.488 

•334.048 

148.330 

292.292 

131.877I259.815 

118.719 

233.833 

33 

197.848 

390.000 

169.611 

334.286 

148.438 

292.500 

131.97'2!260.000 

118.805 

234.000 

24 

197.991 

390.278 

169.734 

334.524 

148.545 

292.708 

132.068 

200.185 

118.891 

234.167 

25 

198.134 

390.556 

169.857 

334.76-> 

148.653 

292.917 

132.163 

260.370 

118.978 

234.  a33 

36 

198.282 

390.833 

169.983 

335.000 

148.7'64 

293.125 

132.262 

260.556 

119.066 

234.500 

37 

198.430 

391.111 

170.110 

335.238 

148.875 

293.333 

132.361 

260.741 

119.155 

234.667 

28 

198.574 

391.389 

170.233 

335.476 

148.983 

293.542 

132.457 

260.926 

119.241 

234.833 

29 

198.717 

391.667 

170.356 

335.714 

149.090 

293.750 

132.552 

261.111 

119.327 

235.000 

30 

198.860 

391.944 

170.479 

335.952 

149.198 

293.958 

132.648 

261.296 

119.414 

235.167 

31 

199.004 

392.222 

170.602 

336.190 

149.305 

294.167 

132.743 

261.481 

119.500 

235.333 

32 

199.152 

392.500 

170.729 

336.429 

149.416 

294.375 

132.842 

261.667 

119.589 

235.500 

33 

199.300 

392.778 

170.856 

336.667 

149.527 

294.583 

132.941 

261  .852 

119.677 

235.667 

34 

199.443 

393.056 

170.979 

336.905 

149.635 

294.792 

133.036 

262,037 

119.763 

235.  a33 

35 

199.586 

393.333 

171.101 

337.143 

149.742 

295.000 

133.132 

262.222 

119.850 

236.000 

36 

199.730 

393.611 

171.224 

337.381 

149.850 

295.208 

133.228 

262.407 

119.936 

236.167 

37 

199.873 

393.889 

171.347 

337.619 

149.957 

295.417 

133.323 

262.593 

120.022 

236.333 

38 

200.021 

394.167 

171.474 

337.857 

150.069 

295.625 

133.422 

262.778 

120.111 

236.500 

39 

200.169 

394.444 

171.601 

338.095 

150.180 

295.833 

i  as.  521 

262.963 

120.199 

236.667 

4O 

200.312 

394.  782 

171.724 

338.333 

150.287 

296.042 

133.616 

263.148 

120.286 

236.833 

41 

;  200.456 

395.000 

171.847 

338.571 

150.395 

296.250 

133.712 

263.333 

120.372 

237.000 

43 

200.  604  1  395.  278 

171.974 

S38.810 

150.506 

296.458 

133.811 

263519 

120.461 

237.167 

43 

200.752 

395.556 

172.101 

339.048 

150.617 

296.667 

133.909 

263.704 

120.549 

237.333 

44 

200.895 

895.833 

172.223 

339.286 

150.724 

296.875 

134.005 

263.889 

120.636 

237.500 

45 

201.038396.111 

172.346 

339.524 

150.832 

297.083 

134.101 

264.074 

120.722 

237.667 

46 

201.182396.389 

172.469 

339.762 

150.939 

297.292 

134.196 

264.259 

120.808 

237.833 

47 

201.325396.667 

172.592 

340.000 

151.047 

297.500 

134.292 

264.444 

120.894 

238.000 

48 

201.473 

396.944 

172.719 

340.238 

151.158 

297.708 

134.391 

264.630 

120.983 

238.167 

49 

201.621 

397.222 

172.846 

340.476 

151.269 

297.917 

134.489 

264.815 

121.071 

238.333 

50 

201.765 

397.500 

172.969 

340.714 

151.377 

298.125 

134.585 

265.000 

121.158 

238.500 

51 

201.908397.778 

173.092 

MO.  952 

151.484 

298.333 

134.681 

265.185 

121.244 

238.667 

53 

202.051  398.056 

173.2141341.  190 

151.592 

298.542 

134.776 

265.37'0 

121.330 

238.833 

53 

202.194398.333 

173.337 

341.429 

151.699 

298.750 

134.872 

265.556 

121.416 

239.000 

54 

202.343398.611 

173.461 

341.667 

151.810 

298.958  134.971 

265.741 

121.505 

239.167 

55 

202.491  398.889 

173.591 

341  .905 

151.921 

299.167135.069 

265.926 

121.594 

239.3:33 

56 

202.634399.167 

173.714342.143 

152.029 

299.375135.165266.111 

121.680 

239.500 

57 

202.777399.444 

173.  837  342.  381 

152.137 

299.583  135.261  266.296 

121.766 

239.667 

58 

202.925399.722 

173.964  342.619 

152.248 

299.7921135.359266.481 

121.855 

239.833 

59 

TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


24° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5*  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

1217.89 

2400.00 

608.  97011200.  00'406.  007 

800.000 

304.533 

600.000 

243.053 

480.000 

1 

1218.75 

2401.67 

609  .  399  1200  .  83  :  406  .  293 

800.556 

304.747 

600.417 

243.825 

480.333 

2 

1219.61 

2403  33 

609  .  829  i  1201  .  67  406  .  580  HO  1  .  1  1  1 

304.9(8 

600.833 

243  5)97 

480.007 

3 

1220.4V 

2405.00 

310.259  1202.50406.866 

801.66? 

305  .  1  77 

601.250 

244.109 

481.000 

4 

1221.33 

2406.67 

610.688 

1203.33 

407.153 

802.222 

305.31)2 

601  .  607 

244.341 

481.333 

5 

1222.22 

2408.33 

611.133 

1204.17 

407.449 

802.  7,  "8 

-505.614 

002  .  083 

244  519 

481.007 

6 

1223.11 

2410.00 

611.577  1205.00 

407.745 

803.333 

DU5.M38 

002.500 

244.690 

482.KX) 

7 

12-23.97 

2411.67 

612.0061205.83 

408.031 

803.88!) 

306.051 

00-2.917 

244.868 

482.333 

8 

1224.83 

2413  33 

612.436  1206.67 

408.318 

804.444 

306.260 

t)03.333 

245.040 

482.007 

9 

1225.72 

2415.00 

612.880 

1207  50 

408.614 

805.000 

306.488 

003.750 

245.218 

483.000 

1O 

1226.60 

2416.67 

613.324 

1208.33 

408.910 

805.556 

306.710 

604.167 

245.396 

483.333 

11 

I227.4G 

2418.33 

613.754 

1209.17 

409.196 

806.111 

"306.925 

604.583 

245.508 

483.067 

12 

1228.32 

2420.00 

614.184 

1210.00 

409.483 

806.667 

307.140 

605.000 

245.740 

484.000 

13 

1229.21 

2421.67 

614.628 

1210.83 

409.779 

807.222 

307.363 

605.417 

245.917 

484.333 

14 

1230.10 

2423.33 

615.072 

1211.67 

410.075 

807.778 

307.584 

605.833 

246.095 

484.667 

15 

1230.96 

2425.00 

615.502 

1212.50 

410.365 

808.333 

'307.799 

606.250 

246.267 

485.000 

16 

1231.82 

2426.67 

615.931 

1213.33 

410.618 

808.889 

308.014 

606.667 

246.439 

485.333 

17 

1232.68 

2428.33 

616.361 

1214.17410.935 

809.444 

308.229 

607.083 

246.611 

485.667 

18 

1233.54 

2430.00 

616.791 

1215.00 

411.221 

810.000 

308.444 

607.500 

246.783 

480.000 

19 

1234.42 

2431.67 

617.235 

1215.83 

411.517 

810.550 

308.666 

607.917 

246.960 

486.333 

2O 

1235.31 

2433.33 

617.679 

1216.67 

411.813 

811.111 

308.888 

608.333 

247.138 

486.667 

21 

1236.17 

2435.00 

618.109 

1217.50 

412.100 

811.667 

109.108 

608.750 

247.310 

487.000 

22 

1237.03 

24:}6.67 

618.538 

1218.33 

412.386 

812.222 

309.318 

009.167 

247.482 

487.  333 

23 

1237.92 

2438.33 

618.982 

1219.17 

412.682 

812.778 

'309.540 

609.583 

247.660 

487.667 

24 

1238.81 

2440.00 

619.427 

12-20.00 

412.978 

813.333 

309.762 

610.000 

247.837 

488.000 

25 

1259.67 

2441.67 

619.856 

1220.85 

413.265 

813.889 

309.977 

610.417 

248.009 

488.333 

26 

1240.53 

2443.33 

620.286 

1221.67 

413.551 

814.444 

310.192 

610.833 

248.181 

488.667 

27 

1241.41 

2445.00 

620.730 

1322.50 

413.847 

815.000 

310.414 

611.250 

248.359 

489.000 

28 

1242.30 

2446.67 

621.174 

1223.33 

414.144 

815.556 

310.636 

611.667 

248.536 

489.333 

29 

1243.16 

2448.33 

621.604 

1224.17 

414.430 

816.111 

310.851 

612.083 

248.708 

489.667 

30 

1244.02 

2450.00 

622.034 

1225.00 

414.717 

816.667 

311.066 

612.500 

248.880 

490.000 

31 

1244.91 

2451.67 

022.478 

1225.83 

415.013 

817.222 

311.288 

612.917 

249.058 

490.333 

32 

1245.80 

2453.33 

622.922 

1226.67 

415.309 

817.778 

311.510 

613.333 

249.236 

490.667 

33 

1246.66 

2455.00 

623.351 

1227.50 

415.595 

818.333 

311.725 

613.750 

249.408 

491.000 

34 

1247.52 

2456.67 

623.781 

12-28.33 

415.882 

818.889 

311.940 

614.167 

249.580 

491.333 

35 

1248.40 

2458.33 

624.225 

1229.17 

416.178 

819.444 

312.162 

614.583 

249.757 

491.667 

36 

1249.29 

2460.00 

624.669 

1230.00 

416.474 

820.000 

312.384 

615.000 

249.935 

492.000 

37 

1250.15 

2461.67 

625.099 

1230.83 

416.760 

820.556 

312.599 

615.417 

250.107 

492.333 

38 

1251.01 

2463.33 

625.529 

1231.67 

417.047 

821.111 

312.814 

615.833 

250.279 

492.667 

39 

1251.87 

2465.00 

625.959 

1232.50 

417.333 

821.667 

313.028 

616.250 

250.451 

493.000 

40 

1252.73 

2466.67 

626.388 

1233.33 

417.620 

822  222 

313.243 

616.667 

250.623 

493.333 

41 

1253.622468.33 

626.832 

1234.17 

417.916 

822  '.178 

313.465 

617.083 

250.800 

493.607 

42 

1-J54.  51  2470.00 

627.276 

1235.00 

418.212 

823.333 

313.687 

617.50T 

250.978 

494.000 

43 

1255.3712471.67 

627.706|  1235.  83 

418.499 

823.889 

313.902 

617.917 

251.150 

494.333 

44 

1256.  23  '24?  3.  33 

628.136 

1236.67 

418.785 

824.444 

314.117 

618.333 

251.322 

494.007 

45 

1257.11  2175.00 

628.580 

1237.50 

419.081 

825.000 

314.339 

618.7-50 

251.500 

495.000 

46 

1258.002476.67 

629.021 

1238.33 

419.377 

825  .  5oC 

314.561 

019.167 

251.677 

495.  S33 

47 

1258.86  2478.  as 

629.454 

1239.17 

419.664)826.  Ill 

314.776 

619.583 

251.849 

495.607 

48 

1259.  72  '2480.  00 

629.884 

1240.00 

419.950l826.667 

314.991 

620.000 

252.021 

496.000 

49 

1260.61:2481.67 

630.328 

1240.83 

420.  246  j  827.  222 

315.213 

620.417 

252.199 

496.333 

50 

1261.502483.33 

630.772 

1241  67 

420.542 

827.778 

315.435 

620.833 

•252.376 

496.667 

51 

1262.362185.00 

631.201 

1242.50 

420.829 

828.333 

315.650 

621.250 

252.548 

497.000 

52 

1263.222486.67 

631.631 

1243.33 

421.115 

828.889 

315.  R65 

621.667 

252.720 

497.333 

53 

1264.102488.33 

632.075 

1244.17 

421.411 

829.444 

316.087 

622.083 

252.898 

497.667 

54 

1204.  99  2490.  00 

632.519 

1245.00 

421.707 

830.000 

316.309 

622.500 

253.076 

498.000 

55 

1265.  85  12491.  67 

632.949 

1245.83 

421.994 

830.556 

316.524 

622.917 

253.248 

498.333 

56 

1266.71  2493.33 

633.379 

1246.67 

422.280 

831.111 

316.739 

623.333 

253.420 

498.667 

57 

1267.602495.00 

633.823 

1247.50 

422.577 

831.667 

316.961 

023.750 

253.597 

499  000 

58 

1268.492496.67 

634.267 

1248.33 

422.873 

832.222 

317.183 

624.167 

253.775 

499.333 

59 

1269.  35  2  198.  33 

634.697 

1249.17 

423.159 

832.778 

317.398 

624.583 

253.947 

499.667 

94 


TABLE  XIV. — ACTUAL  TANGENTS,   ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

24° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

203.073 

00.  000  174.  OK  I  34'-'.  857 

52.359 

300.000 

35.458)266.667 

21.943 

240.000 

"~o~ 

80S.  21  7 

00.278 

174.214343.095 

52.466 

300.208 

35.554 

266.852 

22.030 

240.167 

i 

203.360 

00.556 

174.337  343.333 

52.574 

300.417 

35.649 

267.037 

22.116 

240.333 

2 

203.503 

00.833 

174.459343.571 

52.681 

300.625 

35.745 

-267.222 

22.202 

240.500 

3 

203.647 

01.111 

174.  5S2 

43.810 

52.789 

300.833 

35.840 

267.407 

122.288 

240.667 

4 

203.795 

01.389 

174.709 

£44.048 

52.900 

301.042 

35.939 

267.593 

122.377 

240.8:33 

5 

203.943 

401.667 

174.836 

344.286 

53.011 

301.250 

36.038 

267.77'8 

122.466 

241.000 

6 

204.086 

401.944 

174.959 

344.524 

53.118 

301.458 

36.134 

267.963 

122.552 

241.167 

7 

204.229 

402.222 

175.082 

344.762 

53.226 

301.667 

36.229 

268.148 

122.638 

241.  333 

8 

204.377 

02.500 

175.209 

345.000 

53.337 

301.875 

36.328 

,268.333 

122.727 

241.500 

9 

204.526 

402.778 

175.336 

345.238 

53.448 

302.083 

36.427 

268.519 

122.816 

241.667 

10 

204.669 

403.  056 

175.459 

345.476 

53.55(5 

302.29s! 

36.522 

268.704 

122.902 

241.833 

11 

204.81:2 

03.333 

175.581 

345.714 

53.663 

302.500 

136.618 

268.889 

122.988 

242.000 

12 

204.960 

03.611 

175.708 

345.952 

53.774 

302.708 

36.717 

269.074 

123.077 

242.167 

13 

205.108 

403.889 

175.835 

346.190 

53.885 

302.917 

36.815 

269.259 

123.165 

242.333 

14 

205.252 

404.167 

175.958 

346.429 

153.993 

303.125 

136.911 

269.444 

123.252 

242.500 

15 

205.395 

404.444 

176.081 

346.667 

154.100 

303.333 

137.007 

269.630 

123.338 

24-2.667 

16 

205.  538 

404.722 

176.204 

346.905 

154.208 

303.542 

137.  102 

269.815 

123.424 

242.833 

17 

205.682 

405.000 

176.327 

347.143 

54.316 

303.750 

137.198 

270.000 

123.510 

243.000 

18 

205.830 

405.278 

176.454 

347.381 

154.427 

303.958 

137.297 

270.185 

123.599 

243.167 

19 

205.978 

405.556 

176.581 

347.619 

154.538 

304.167 

137.395 

270.370 

123.688 

243.333 

20 

206.121 

405.833 

176.704 

347.857 

154.645 

304.375 

137.491 

270.556 

123.774 

243.500 

21 

206.264 

406.111 

176.826 

348.095 

154.753 

304.583 

137.587 

270.741 

123.860 

243.667 

22 

206.412 

406.389 

176.953 

348.333 

154.864 

304.79:2 

137.685 

270.926 

1*23.949 

243.833 

23 

206.561 

406.667 

177.080 

348.571 

154.975 

305.000 

137.784 

271.111 

124.037 

244.000 

24 

206  704 

406.944 

177.203 

348.810 

155.082 

305.208 

187.880 

271,296 

124.124 

244.167 

25 

206  .347 

407.222 

177.326 

349.048 

155.190 

305.417 

137  975 

271.481 

124.210 

244.333 

26 

206.995 

407.500 

177.453 

349.280 

155.301 

305.625 

138.074 

271.667 

124.298 

244.500 

27 

207.143 

407.778 

177.580 

349.524 

155.412 

305.833 

138.173 

•271.852 

124.387 

244.667 

28 

207.287 

408.056 

177.703 

349.  70S 

155.520 

306.042 

138.268 

272.037 

124.473 

244.833 

29 

207.430 

408.  333 

177.826 

a50.00f 

155.627 

306.250 

138.364 

272.222 

124.560 

245.000 

30 

207.578 

408.611 

177.953 

350.238 

155.738 

306.458 

138.463 

272.407 

124.648 

245.167 

31 

207.726 

408.889 

178.079 

350.476 

155.849 

306.667 

138.502 

272.593 

124.737 

245.333 

32 

207.869 

409.167 

178.202 

&50.714 

155.957 

306.875 

138.657 

272.778 

124.823 

245.500 

33 

208.013 

409.444 

178.325 

350.952 

156.064 

307  083 

138.753 

272.963 

124.909 

245.667 

34 

208.161 

409.722 

178.452 

351.190 

156.176 

307.292 

138.  a52 

273.148 

124.998 

245.833 

35 

208.309 

410.000 

178  579 

351  .429 

156.287 

307.500 

138.950 

•273.333 

125.087 

246.000 

36 

208.452 

410.278 

178.702 

351.667 

156.394 

307.708 

139.046 

273.519 

125.173 

246.167 

37 

208.595 

410.556 

178.825 

351.905 

156.502 

307.91" 

139.141 

273.704 

125.259 

246.333 

38 

208.739 

410.833 

178.948 

352.143 

156.609 

308.125 

139.237 

273.889 

125.345 

246.500 

39 

208.882 

411.111 

179.070 

352.381 

156.717 

308.333 

139.333 

274.074 

125.432 

246.667 

40 

209.030 

411.389 

179.197 

352.619 

156.828 

308.542 

139.431 

274.259 

125.520 

246.833 

41 

209.178 

411.667 

179.324 

352.85" 

156.939 

308.750 

139.530 

274.444 

125.609 

247.000 

42 

209.  32!^ 

411.944 

179.447 

353.  095 

157.046 

308.958 

139.626 

274.630 

125.695 

247.16" 

43 

209.465 

412.22V 

179.570 

353.333 

157.154 

309.16" 

139.721 

274.81F 

125.781 

247.333 

44 

209.613 

412.500 

179.697 

353.57 

157.265 

309.375 

139.820 

275.000 

125.870 

247.500 

45 

209.761 

412.778 

179.824 

353.810 

157.376 

309.583 

139.919 

275.18. 

125.959 

247.66" 

46 

209.904 

413.056 

179.947 

354.048 

157.484 

309.792 

140.015 

275.  37C 

126.045 

247.833 

47 

210.048 

413.333 

180.070 

354.  28C 

157.59 

310.000 

140.110 

275.55 

126.13 

248.000 

48 

210.196 

413.611 

180.197 

354.524 

157.702 

310.208 

140.209 

275.74 

126.220 

248.16" 

49 

210.344 

413.889 

180.324 

354.762 

157.813 

310.41" 

140.308 

275.926 

126.309 

248.333 

50 

210.48" 

414.167 

180.446 

355.000 

157.921 

310.62. 

140.403 

276.11 

126.395 

248.500 

51 

210.630 

414.444 

180.569 

355.238 

158.  02F 

310.  as, 

140.499 

276.296 

126.48 

248.66' 

52 

210.77 

414.722 

180  69f 

355.47 

158.140 

311.042 

140.598 

276.48 

126.570 

248.833 

53 

210.92 

415.000 

180.82: 

,355.714 

158.25 

311.250 

140.696 

276.66 

126.65S 

249.00(1 

54 

211.070 

415.27* 

180.  94< 

355.952 

158.35 

311.45 

140.792 

276.  &5 

126.745 

249  16" 

55 

211.21 

415.556 

ISl.Oflfl 

356.19 

158.466 

311.66 

140.888 

277.03 

126.83 

249.333 

56 

211.36 

415.833 

181.106 

356.42<1 

158.5r 

311  .87. 

140.986 

277.22* 

126.  9& 

249.500 

57 

211.50 

416.111 

181.323 

356.66 

158.  68? 

312.08. 

141.085 

277.40 

127.009 

249.66" 

58 

811.663 

416.889  181.446 

356.90 

158.79 

312.29 

141.181 

277.  5& 

127.095 

249.833 

59 

95 


TABLE  XIV.— ACTUAL   TANGENTS,    ETC. 


25° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

BiT 
~~o~ 

Tan. 
1270.21 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

83^333 

Tun. 
317.613 

Arc. 

G25.000 

Tan. 

Arc. 

2500.00 

635.126 

1250.00 

423.446 

254.119 

500.000 

i 

1271.09 

2501.67 

635.570 

1250.83 

423.742 

833.889 

sir.  835 

(525.417 

254.296 

500.333 

2 

1271.98 

2503.33 

636.014 

1251.67 

424.038 

834.444 

318.057 

625.833 

254.474 

500.667 

3 

1272.87 

2505.00 

636.459 

1252.50 

424.  a34 

835.000 

318.279 

626.250 

254.652 

501.000 

4 

1273.76 

2506.67 

636.903 

1253.33 

424.630 

835.556 

318.501 

626.667 

254.830 

501.333 

5 

1274.62 

2508.33 

637.332 

1254.17 

424.916 

836.111 

318.716 

627.083 

255.001 

501  .  6(57 

6 

1275.48 

2510.00 

637.762 

1255.00 

425.203 

836.667 

318.931 

627.500 

255.173 

502.000 

7 

1276.37 

2511.67 

638.206 

1255.83 

425.499 

837.222 

319.153 

627.917 

255.351 

502.333 

8 

1277.25 

2513.33 

638.650 

1256.67 

425.795 

837.778 

319.375 

628.333 

255.529 

502.667 

9 

1278.11 

.2515.00 

639.080 

1257.50 

426.082 

838.333 

319.590 

628.750 

255.701 

503.000 

10 

1278.97 

2516.67 

639.510 

1258.33 

426.368 

838.889 

319.805 

629.167 

255.873 

503.333 

11 

1279.86 

2518.33 

639.954 

1259.17 

426.664 

839.444 

320.027 

629.583 

256.050 

503.667 

12 

1280.75 

2520.00 

640.398 

1260.00 

426.960 

840.000 

320.249 

630.000 

256.228 

504.000 

13 

1281.61 

2521.67 

640.828 

1260.83 

427.247 

840.556 

320.464 

630.417 

256.400 

504.333 

14 

1282.47 

2533.33 

641.257 

1261.67 

427.533 

841.111 

320.679 

630.833 

256.572 

504.667 

15 

1283.86 

2525.00 

641.701 

1262.50 

427.829 

841.667 

320.901 

631.250 

256.750 

505.000 

16 

1284.24 

2526.67 

642.145 

1263  33 

428.125 

842.222 

321.123 

631.667 

256.927 

505.333 

17 

1285.10 

2528.33 

642.575 

1264.17 

428.412 

842.778 

321.338 

632.083 

257.099 

505.667 

18 

1285.96 

2530.00 

643.005 

1265.00 

428.698 

843.333 

321.553 

632.500 

257.271 

506.000 

19 

1286.85 

2531.6? 

643.449 

1265.83 

428.994 

843.889 

321.775 

632.917 

257.449 

506.333 

2O 

1287.74 

2533.33 

643.893 

1266.67 

429.290 

844.444 

321.997 

633.333 

257.626 

506.667 

21 

1288.60 

2535.00 

644.323 

1267.50 

429.577 

845.000 

322.212 

633.750 

257.798 

507.000 

22 

1289.46 

2533.67 

644.752 

1268.33 

429.864 

845.556 

322.427 

634.167 

257.970 

507.333 

23 

1290.35 

2538.33 

645.197 

1269.17 

430.160 

846.111 

32-2.040 

634.583 

258.148 

507.667 

24 

1291.23 

2540.00 

645.641 

1270.00 

430.456 

846.667 

322.871 

635.000 

258.326 

508.000 

25 

1292.12 

2541.67 

646.085 

1270.83 

430.752 

847.222 

323.093 

635.417 

258.503 

508.333 

26 

1293.01 

2543.33 

646.529 

1271.67 

431.048 

847.778 

323.315 

635.833 

258.681 

508.667 

27 

1293.87 

2545.00 

646.958 

1272.50 

431  .334 

848.333 

323.530 

636.250 

258.853 

509.000 

28 

1294.73 

2546.67 

647.388 

1273.33 

431.621 

848.889 

323.745 

636.667 

259.025 

509.333 

29 

1295.62 

2548.33 

647.832 

1274.17 

431.917 

849.444 

323.967 

637.083 

259.203 

509.667 

3O 

1296.51 

2550.00 

648.276 

1275.00 

432.213 

850.000 

324.189 

637.500 

259.380 

510.000 

31 

1297.36 

2551.67 

648.706 

1275.83 

432.499 

850.556 

324.404 

637.917 

259.552 

510.333 

32 

1298.22 

2553.33 

649.136 

1276.67 

432.786 

851.111 

324.619 

638.333 

259.724 

510.667 

33 

1299.11 

2555.00 

649.580 

1277.50 

433.082 

851.667 

324.841 

638.750 

259.902 

511.000 

34 

1300.00 

2556.67 

650.024 

1278.33 

433.378 

852.222 

325.063 

639.167 

260.079 

511.333 

35 

1300.86 

2558.33 

650.454 

1279.17 

433.665 

852.778 

325.278 

639.583 

260.251 

511.667 

36 

1301.72 

2560.00 

650.883 

1280  00 

433.951 

853.333 

325.493 

640.000 

260.423 

512.000 

37 

1302.61 

2561.67 

651.328 

1280.  83 

434.247 

853.889 

325.715 

640.417 

260.601 

512.333 

38 

1303.50 

2563.33 

651.772 

1281.67 

434  543 

a54.444 

325  937 

640.833 

260.779 

512.667 

39 

1304.38 

2565.00 

652.216 

1282.50 

434.839 

855.000 

326.159 

641.250 

260.956 

513.000 

40 

1305.27 

2566.67 

652.660 

1283.33 

435.135 

855.556 

326  381 

641.667 

261.134 

513.333 

41 

1300.13 

2568  33 

653.089 

1284.17 

435.422 

856.111 

326.596 

642.083 

261.306 

513.667 

42 

1306.99 

2570.00 

653.519 

1285.00 

435.708 

856  667 

326.811 

642.500 

261.478 

514.000 

43 

1307.88 

2571.67 

053.963 

1285.83 

436.004 

857.222 

327.033 

642.917 

261.656 

514.333 

44 

1308.77 

•2573.33 

654.407 

1286.67 

436.300 

857.778 

327.255 

643.333 

261.833 

514.667 

45 

1309.63 

2575.00 

654.837 

1287.50 

436.587 

&78.3S3 

327.470 

643.750 

262.005 

515.000 

46 

1310.49 

2576.67 

655.267 

1288.33 

436.873 

858.889 

327.685 

644.167 

262.177 

515.383 

47 

1311.37 

2578.33 

655.711 

1289.17 

437.170 

859.444 

327.907 

644.583 

202.355 

515.667 

48 

1312.26 

2580.00 

656.155 

1290.00 

437.466 

S60.000 

328.129 

645.000 

262.533 

516.000 

49 

1313.15 

2581.67 

656.599 

1290.83 

437.762 

860.556 

328.351 

645.417 

262.710 

516.333 

5O 

1314.04 

2583.33 

657.043 

1291.67 

438.058 

8(51.111 

328.573 

645.833 

262.888 

516  667 

51 

1314.90 

2585.00 

657.473 

1292.50 

438.344 

^61.007 

328.788 

646.250 

263.060 

517.000 

52 

1315.76 

2586.67 

657.903 

1293.33 

438.631 

862.222 

329.003 

646.667 

203.232 

517.333 

53 

1316.64 

2588.33 

658.347 

1294.17 

438.927 

802.778 

329.225 

647.083 

263.409 

517.607 

54 

1317.53 

2590.00 

658.791 

1295.00 

439.223 

863.333 

329.447 

647.500 

263.587 

518.000 

55 

1318.4-2 

2591.67 

659.235 

1295.83 

439.519 

863.889 

329.669 

647.917 

263.765 

518.383 

56 

1319.31 

2593.33 

659.679 

1296.67 

439.815 

864.444 

3-29.891 

648.833 

263.942 

518.007 

57 

1320.17 

2595.00 

660.1  OS 

1297  50 

440.102 

865.000 

380.106 

648.750 

204.114 

519.000 

58 

1321.03 

2596.67 

660.538 

1298.33 

440.388 

865.556 

330.321 

649.167 

264.286 

519.333 

59 

1321.92 

2598.33 

660.982 

1299.17 

440.684 

866.111 

33).  543 

649.583 

264.464 

519.  667  - 

96 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9*  Curve. 

1O°  Curve. 

25° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

211.796 

416.667 

181.568 

357.143  158.903 

312.500 

141.27(3 

277.778 

127.181 

250.000 

O 

211.944 

416.944 

181.695 

357.381 

159.014 

312.708 

141.375 

277.903 

127.270 

250.167 

1 

212.092 

417.222 

181.822 

357.619159.125 

312.917 

141.474 

278.148 

127.359 

250.333 

2 

212.240 

417.500 

181.949 

357.857 

159.236 

313.125 

141.573 

278.333 

127.448 

250.500 

3 

212.388 

417.778 

182.076 

358.095 

159.347 

313.333 

141.671 

278.519 

127.537 

250.667 

4 

212.532 

418.056 

182.199 

358.333 

159.455 

313.542 

141  767 

278.704 

127.623 

250.833 

5 

212.675 

418.333 

182.322 

358.571 

159.562 

313.750 

141.863 

278.889 

127  709 

251.000 

6 

212.823 

418.611 

182.449 

358.810 

159.673 

313.958 

141.961 

279.074 

127.798 

251.167 

7 

212.971 

418.889 

182.576 

359.048 

159.785 

314.167 

142.060 

279.259 

127.887 

251.333 

8 

213.114 

419.167 

182.699 

359.286 

159.892 

314.375 

142.156 

279.444 

127.973 

251.500 

9 

213.258 

419.444 

182.822 

359.524 

160.000 

314.583 

142.251 

279.630 

128.059 

251.667 

1O 

213.40(5 

419.722 

182.949359.762 

160.111 

314.792 

142.350 

279.815 

128.148 

251.833 

11 

213.554 

420.000 

183.075360.000 

160.222 

315.000 

142.449 

280.000 

128.237 

252.000 

12 

213.697 

420.278 

183.198360.238 

160.329 

315.208 

142.545 

280.185 

128.323 

252.167 

13 

213.840 

420.556 

183.321  360.476 

160.437 

315.417 

142.640 

280.370 

128.409 

252.333 

14 

213.988 

420.833 

183.448360.714 

160.548 

315.625 

142.739 

280.556 

128.498 

252.500 

15 

214.137 

421.111 

183.575360.952 

160.659 

315.833 

142.838 

280.741 

128.587 

252.667 

16 

214.280 

421.389 

183.698361.190 

160.767 

316.042 

142.933 

280.926 

128.673 

252.833 

17 

214.423 

421.667 

183.  821  '361.  429 

160.874 

316.250 

143.029 

281.111 

128.759 

253.000 

18 

214.571 

421.944 

183.948 

361.667 

160.985 

316.458 

143.128 

281.296 

128.848 

253.167 

19 

214.719 

422.222 

184.075 

361.905 

161.096 

316.667 

143.226 

281.481 

128.937 

253.333 

20 

214.863 

422.500 

184.198362.143 

161.204 

316.875 

143.322 

281.667 

129.023 

253.500 

21 

215.006 

4522.778 

184.320362.381 

161.311 

317.083 

143.418 

281.852 

129.109 

253.667 

22 

215.154 

423.056 

184.4471  362.  619 

161.422 

317.292 

143.516 

282.037 

129.198 

253.833 

23 

215.302 

423.333 

184.574362.857 

161.533 

317.500 

143.615 

282.222 

129.287 

254.000 

24 

215.450 

423.611 

184.701363.095 

161.645 

317.708 

143.714 

282.407 

129.376 

254.167 

25 

215.598 

423.889 

184.  828  1363.333 

161.756 

317.917 

143.813 

282.593 

129.465 

254.333 

26 

215.742 

424.167 

184.951  363.571 

161.863 

318.125 

143.908 

282.778 

129.551 

254.500 

27 

215.885 

424.444 

185.074 

363.810 

161.971 

318.333 

144.004 

282.963 

129.637 

254.667 

28 

216.033 

424.722 

185.201 

364.048 

162.082 

318.542 

144.103 

283.148 

129.726 

254.833 

29 

216.181 

425.000 

185.328 

364.286 

162.193 

318.750 

144.201 

283.333 

129.815 

255.000 

30 

216.324 

425.278 

185.451 

364.524 

162.300 

318.958 

144.297 

283.519 

129.901 

255.167 

31 

216.468 

425.556 

185.574 

364.762 

162.408 

319.167 

144.393 

283.704 

129.987 

255.333 

32 

216.616 

425.833 

185.700 

365.000 

162.519 

319.375 

144.491 

283.889 

130.076 

255.500 

33 

216.764 

426.111 

185.827 

365.238 

162.630 

319.583 

144.590 

284.074 

130.164 

255.667 

34 

216.907 

426.389 

185.950 

365.470 

162.738 

319.792 

144.686 

284.259 

130.251 

255.833 

35 

217.050 

426.667 

186.073 

365.714 

162.845 

320.000 

144.781 

284.444 

130.337 

256.000 

36 

217.199 

426.944 

186  200 

365.952 

162.956 

320.208 

144.880 

284.630 

130.426 

256.167 

37 

217.347 

427.222 

186.327 

366.190 

163  067 

320.417 

144.979 

284.815 

130.514 

256.333 

38 

217.495 

427.500 

186.454 

366.429 

163.179 

320.625 

145.078 

285.000 

130.603 

256.500 

39 

217.643 

427.778 

186.581 

366.667 

163.290 

320.833 

145.176 

285.185 

130.692 

256.667 

4O 

217.786 

428.056 

186.704 

366  905 

163.397 

321.042 

145.272 

285.370 

130.778 

256.833 

41 

217.929 

428.333 

186.827 

367.143 

163.505 

321.250 

145.368 

285.556 

130.864 

257.000 

42 

218.077 

428.611 

186.954 

367.381 

163.616 

321.458 

145.466 

285.741 

130.953 

257.167 

43 

218.226 

428.889 

187.080 

367.619 

163  727 

321.667 

145.565 

285.926 

131.042 

257.333 

44 

218.369 

429.167 

187.203 

367.857 

163.834 

321.875 

145.661 

286.111 

131.128 

257.500!  45 

218.512 

429.444 

187.326 

368.095 

163.942 

322.083 

145.756 

286.296 

131.214 

257.  667  '  46 

218.660l429.72:> 

187.4531368.333 

164.053 

322.292 

145.855 

286.481 

131.303 

257.833  47 

218.808430.000 

187.580368.571 

164.164 

322.500 

145.954 

286.667 

131.392 

258.000  48 

218.956 

430.278 

187.707 

368.810 

164.275 

322.708 

146.053 

286.852 

131.481 

258.  1G7  49 

219.105 

430.556 

187.834 

369.048 

164.386 

322.917 

146.151 

287.037 

131.570 

258.3.°3  50 

219.248 

430.833 

187.957309.286 

1  64.  494  !  323.  125 

146.247 

287.222 

131.656 

258.500  51 

219.391 

431.111 

188.080369.524 

164.  601  1323.  333 

146.343 

287.407 

131.742 

258.6(57  52 

219.539 

431.389 

188.2078fi9.762 

164.712323.542 

146.441 

287.593 

131.831 

258.833  53 

219.687 

431.667 

188.33*  370.000 

164.824323.750 

146.540 

287.778 

131.920 

259.000  54 

219.835 

431.944 

188.4(Jl  370.238 

164.935323.958 

146.639 

287.963 

132.009 

259.167  55 

219.983 

482.222 

1S8.5K7-370.476 

165.046324.167 

146.738 

288.148 

132.098 

259.333  56 

220.127 

432.500 

188.  710:370.  714 

165.153324.375 

146.833 

288.333 

132.184 

259.500  57 

220.270 

432.778 

188.  8153  370.  952 

165.261  324  583 

146.929 

288.519 

132.270 

259.667  58 

220.418 

433.056 

188.9601371.190 

165.372324.792ll47.028 

288.704 

132.359 

259.833  59 

97 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


26° 

1°  Carve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~0~ 

1322.802600.00 

661.426 

1300.00 

440.980 

866.667 

330.765 

650.000 

264.642 

520.000 

1 

1  323.  66  (  2601.  67 

661.856 

1300.83 

441.267 

867.222 

330.  9SO|  650.  41  7 

2(54.814 

520.333 

2 

1324.522603.33 

662.286 

1301.67 

441.553 

867.778 

33  1.1  95650.  833 

264.986 

520.667 

3 

1325.41  2605.00 

662.7:30 

1302.50 

441.849 

868.333 

331.417 

651.250 

265  163 

521.000 

4 

1326.30J2606.6? 

663.174 

1303.33 

442.145 

868.889 

881.889 

651.667 

265.341 

521.333 

5 

1327.19 

2608.33 

663.618 

1304.17 

442.441 

869.444 

331.861 

652.083 

265.519 

521.66? 

6 

1328.08 

2610.00 

(564.062 

1305.00 

442.737 

870.000 

332.083 

652.500 

2(55.696 

522.000 

7 

1328.94 

2611.67 

664.492 

1305.83 

443.024 

870.556 

332.298 

652.917 

265.868 

522  333 

8 

1329.79 

2613.33 

664.922 

1306.67 

443.310 

871.111 

332.513 

653.333 

266.040 

522.667 

9 

1330.68 

2615.00 

665.366 

1307.50 

443.607 

871.66? 

332.735 

653.750 

266.218 

523.000 

10 

1331.57 

2616.67 

665.810 

1308.33 

443.903 

872.222 

332.957 

654.16? 

266.395 

523.333 

11 

1332.46 

2618.33 

666.254 

1309.17 

444.199 

872.778 

333.179 

654.583 

266.573 

523.667 

12 

1333.352620.00 

666.698 

1310.00 

444.495 

873.333 

333.401  655.000 

2(56.751 

524.000 

13 

1334.21 

2621.67 

667.128 

1310.83 

444.781 

873.889 

333.616I655.  417 

266.923 

524.3:33 

14 

1335.07 

2623.33 

667.557 

1311.67 

445.068 

874.444 

333.831  655.833 

267.095 

524.667 

15 

1335.95 

2625  00 

668.001 

1312.50 

445.364 

875.000 

334.053656.250 

267.272 

525  000 

16 

1336.84 

2626.67 

668.445 

1313.  as 

445.660 

875.556 

334.2751656.667 

267.450 

525.333 

17 

1337.73 

2628.33 

568.890 

1314.17 

445.956 

876.111 

334.497 

657.083 

267.628 

525.667 

18 

1338.62 

2630.00 

(569.334 

1315.00 

446.252 

876.667 

334.719 

657.500 

267.805 

526.000 

19 

1339.48 

2631.67 

669.763 

1315.83 

446.539 

877.222 

334.934 

657.917 

267.977 

526.333 

20 

1340.34 

2633  33 

670.193 

1316.67 

446.825 

877.778 

335.149 

658.333 

268.149 

526.667 

21 

1341.23 

2635.00 

670.637 

1317.50 

447.121 

878.333 

335.371 

658.750 

268.32? 

527.000 

22 

1342.11 

2636  67 

671.081 

1318  33 

447.417 

878.889 

335.593 

659.167 

268.505 

527.333 

23 

1343.00 

2638.33 

671.525 

1319.17 

447.713 

879.444 

335.815 

659.583 

268.682 

527.667 

24 

1343.89 

2640.00 

671.969 

1320.00 

448.009 

880.000 

336.037 

660.000 

268.860 

528.000 

25 

1344.75 

2641.67 

672.399 

1320.83 

448.296 

880.556 

336.252 

660.417 

269.032 

528.333 

26 

1345.61 

2643.33 

672.829 

1321.67 

448.582 

881.111 

336.467 

660.833 

269.204 

528.667 

27 

1346.50 

2645.00 

673.273 

1322.50 

448.878 

881.667 

336.689 

661.250 

269.382 

529.000 

28 

1347.38 

2646.67 

673.717 

1323.33 

449.174 

882.222 

336.911 

661.66? 

269.559 

529.333 

29 

1348.27 

2648.33 

674.161 

1324.17 

449.47'0 

882.778 

337.133 

662.083 

269.73? 

529.667 

30 

1349.16 

2650.00 

674.605 

1325.00 

449.767 

^83.333 

337.356 

662.500 

•269.915 

530.000 

31 

1350.05 

2651.67 

675.049 

1325.  a3 

450.063 

^83.889 

337  578 

662.917 

270.092 

530.333 

32 

1350.94 

2653.33 

675.493 

1326.67 

450.359 

884.444 

337.800 

663.333 

•270.270 

530.667 

33 

1351.80 

2655.00 

675.923 

1327.50 

450.645 

885.000 

338.015 

663.750 

270.442 

531.000 

34 

1352.66 

2656.67 

676.353 

1328.33 

450.932 

885.556 

338.229 

664.167 

270.614 

531.333 

35 

1353.54 

2658.33 

676  797 

1329.17 

451  .  228 

886.111 

338.452 

664.583 

270.791 

531.667 

36 

1354.43 

2660.00 

677.241 

1330.00 

451.524 

886.667 

338.674 

665.000 

270.969 

532000 

37 

1355.32 

2661.67 

677.685 

1330.83 

451.820 

887.222 

338.896 

665.417 

271.147 

532.333 

38 

1356.21 

9688.81 

678.189 

1331.67 

452.116 

887.778 

339.118 

665.833 

271.324 

532.667 

39 

1357.07 

2665.00 

678.559 

1332.50 

452.402 

888.333 

339.3:33 

666.250 

271.496 

533.000 

4O 

1357.93 

2666.67 

678.988 

1333.33 

452.689 

888.889 

339.548 

666.667 

271.668 

533.333 

41 

1358.82 

2668.33 

679.432 

1334.17 

452.985 

S89.444 

339.770 

667.083 

271.846 

533.667 

42 

1359.70 

2670.00 

679.877 

1335  00 

453.281 

S90.000 

339.992 

667.500 

272.024  534.000 

43 

1360.59 

2671.67 

080.321 

1335.83 

453.577 

^90.556 

340.214 

667.917 

272.201  534.333 

44 

1361.48 

2673.33 

680.765 

1336  67 

453.873 

891.111 

340.436 

668.333 

272.379 

534.667 

45 

1362.37 

2675.00 

681.209 

ia37.50 

454.169 

891.66? 

340.658 

668.750 

272.557 

535.000 

46 

1363.26 

2676.67 

681.653 

1338.33 

454.465 

892.222 

340.880 

660.167 

272.734 

535.333 

;47 

1364.12 

2678.33 

682.083 

1339.17 

454  752 

892.778 

341.095 

669.583 

272.906:535.667 

48 

1364.97 

2680.00 

682.512 

1340.00 

455.038 

893.333 

341.310 

670.000 

273.078536.000 

49 

1365.86 

2681.67 

682.956 

1340.83 

455.334 

893.889 

341  532 

670.417 

273.256 

536.333 

50 

1366.75 

2683.33 

683.400 

1341.67 

455.630 

804.444 

341.754 

670.833 

273.434 

536.667 

51 

1367.64 

2685.00 

683.844 

1342.50 

455.927 

895.000 

341.976 

671.250 

273.611  537.000 

52 

1368.53 

2686.67 

684.289  1343.33 

456.223 

H95  556 

342.198 

671.667 

273.789537.333 

53 

1369.41 

2688  33 

684.733  1314.17 

456.519 

896.111 

3  42.  420  672.  OR3 

273.967537.667 

54 

1370.30 

2690.00 

685.1771345.00 

456.815 

896.667 

342.642672.500 

274.144538.000 

55 

1371.16 

2691.67 

685.6061345.83 

457.101 

897.222 

34-2.  857  072.  91  7 

274.316538.333 

56 

1372.02 

2693  .  33;  686  .  03fi  1  346  .  67 

457.388 

897.778 

343.  072!  673.  &33 

274.488588.667 

57 

1372  91 

2695  .  00  .  686  .  480  1  347  .  50 

457.6,84 

^98.333 

243.294673.750 

274.666539.000 

58 

1373.80 

2696.  67  686.  924  11348.  33 

457.980 

898.889 

343.516674.167 

274.844539.333 

59 

1374.69 

2698.  33:  687.  368  '1349.  17 

458.276 

899.444 

343.738674.583 

275.021  539.667 

TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

36° 

Tan. 

220.5(56 

Arc. 
433  333 

Tan. 

18-J.087 

Arc. 

371.429 

Tan. 

Arc. 

Tail. 

Arc. 

Tan. 
132T448 

Arc. 

260.000 

M7 
O 

165.483 

325.000 

147.126 

288.889 

&J0.710 

433.611 

189.210371.667 

165.590325.208 

147.222 

289.074 

132.534 

260.167 

1 

220.853 

433.889 

189.333371.905 

165.698 

325.417 

147.318 

289  259 

132.620 

260.333 

3 

221.001 

434.167 

189.460,372.143 

165.809 

325.  62£ 

147.416 

289  444 

132.709 

260.500 

3 

221.  149 

431.444 

189.587 

372.381 

1*55.920 

325.833 

147.515 

289.630 

132.798 

260.667 

4 

221.297 

434.722 

189.714 

372.619 

166.031 

326.042 

14-7.614 

289.815 

132.887 

260.833 

5 

221.445 

435.000 

189.841 

372.857 

166.142 

326.250 

147.713 

290.000 

132.976 

261.000 

6 

221.588 

435.278 

189.963 

373.095 

166.250 

326.458 

147.808 

290.185 

133.062 

261.167 

7 

221.732 

435.556 

190  086 

373.333 

166.357 

326.667 

147.904 

290.370 

133.148 

261.333 

8 

221.880 

4:35.833 

190.213 

373.571 

166.469 

326.875 

148.003 

290.556 

133.237 

261.500 

9 

222.028 

436.111 

190.340 

373.810 

166.580 

327.083 

148.101 

290.741 

133.326 

261.667 

10 

222.170 

436.389 

190.467 

374.048 

166.691 

327.292 

148.200 

290.926 

133.414 

261.833 

]  1 

222.324 

436.667 

190.594 

374.286 

166.802 

327.  500 

148.299 

291.111 

133.503 

262.000 

12 

222.467 

436.944 

190.717 

374.524 

166.909 

327.708 

148.395 

291.296 

133.  5S9 

262.167 

13 

222.611 

437.222 

190.840 

374.762 

167.017 

327.917 

148.490 

291  .481 

133.675 

262.333 

14 

222.759 

437.500 

190.967 

375.000 

167.128 

328.125 

148.589 

291.667 

133.764 

262.500 

15 

222.907 

437.778 

191.094 

375.238 

167.239 

328  333 

148.688 

291.852 

133.853 

262.667 

16 

223.055 

438.056 

191.221 

375.476 

167.350 

328.542 

148.787 

292.037 

133.942 

262.833 

17 

223.203 

4:38.333 

191.348 

375.714 

167.461 

328.750 

148.8R5 

292.222 

134.031 

263.000 

18 

223.340 

438.  Gil 

191.470 

375.952 

167.569 

328.958 

148.981 

292.407 

134.117 

263.167 

19 

223.490 

438.889 

191.593 

376.190 

167  676 

329.167 

149.077 

292.593 

134.203 

263.33:3 

2O 

223.6:38 

439.167 

191.720 

376.429 

167.787 

329.375 

149.175 

292.778 

134.292 

263.500 

21 

223.786 

439.444 

191.847 

376.667 

167.898 

329.583 

149.274 

292.963 

K34.381 

263.667 

22 

223.934 

439.722 

191.974 

376.905 

168.010 

329.792 

149.373 

293.148 

134.470 

263.833 

23 

224.082 

440.000 

192.101 

377.143 

168.121 

330.000 

149.472 

293.3:33 

134.559 

264.000 

24 

224.225 

440.27'8 

192  224 

377.381 

168.228 

330.208 

149.567 

293.519 

134.645 

264.167 

25 

224.369 

440.556 

19.5.347 

377.619 

168.336 

330.417 

149.603 

293.704 

134  731 

264.333 

26 

224.517 

440.833 

192.474 

377.857 

168.447 

330.625 

149.762 

293.889 

134.820 

264.500 

21 

224.665 

441.111 

192.601 

378.095 

168.558 

330.833 

149.8(50 

294.074 

134.909 

264.667 

28 

224.813 

441.389 

192.728 

378.333 

168.669 

331.042 

149.959 

294.259 

134.998 

264.833 

29 

224.961 

441.667 

192.855 

378.571 

168.780 

331.250 

150.058 

294.444 

135.087 

265.000 

30 

225.109 

441.944 

192.982 

378.810 

168  891 

1331.458 

150.157 

294.630 

135.176 

265.167 

31 

225.257 

442.222 

193.108 

379.048 

169.002 

33  1.667 

150.255 

294.815 

135  265 

265.333 

32 

225.400 

442.500 

193.231 

379.286 

169.110 

331.875 

150.351 

295.000 

135.351 

265.500 

33 

225.544 

442.778 

193.354 

379.524 

169.217 

332.083 

150.447 

295.185 

135.437 

265.667 

34 

225.692 

443.056 

193.481 

379.762 

169.328 

332  292 

150.545 

295.370 

1,35.526 

265.833 

35 

225.840 

443.333 

193.608 

380.000 

169.440 

332.500 

150.644 

295.556 

135.615 

266.000 

36 

225.988 

443.611 

193.735 

380  238 

169.551 

332.708 

150.743 

295.741 

ia5.703 

066.167 

37 

226.136 

443.889 

193.862 

380.476 

169.662 

332.917 

150.842 

295.926 

1:35.790 

266.  3a3 

38 

226.279 

444.167 

193.985 

380.714 

169.769 

333.125 

150.937 

296.111 

135.878 

266.500 

39 

226.423 

444.444 

194.108 

380.952 

169.877 

333.338 

151.033 

296.296 

135.964 

266.667 

40 

226.571 

444.722 

194.235 

381.190 

169.988 

333.542 

151.132 

296.481 

136.053 

266.833 

41 

226.719 

445.000 

194  362 

381.429 

170.099 

333.750 

151.230 

296.667 

136.142 

267.000 

4=2 

226.867 

445.278 

194.489 

381.667 

170.210 

333.958 

151.329 

296.852 

136.231 

267.167 

43 

227.015 

445.556 

194.615 

381.905 

170.321 

334.167 

151  428 

297.037 

136.320 

267.333 

44 

227.163 

445.  833 

194.742 

•382.143 

170.432 

334.375 

151  .527 

297.222 

136.409 

267.500 

45 

227  311 

446.111 

194.869j382.38l 

170.543 

334.583 

151.626 

297.407 

136.498 

067.667 

46 

227.454 

446.389 

194.992382.619 

170.651 

3:34.792 

151.721 

297.593 

136.584 

267  833 

47 

227.598 

446.667 

195.115382.857 

170.758 

335.000 

151.817 

297.778 

136.670 

268.000 

48 

227.746 

446.944 

195.242 

383.095 

170.870 

335.208 

151.916 

297.963 

136.759 

268.167 

49 

227.894 

417.222 

195.3M 

383.333 

170.981 

335.417 

152.014 

29^.148 

136.848 

268.333 

50 

228.042 

447.500 

195.  49(1383.  571 

171.092 

335.625 

152.113 

298.333 

136.9-37 

268.500 

51 

228.190 

447.778 

195.623383.810 

171  203 

335.833 

152.212 

298.519 

137  026 

268.667 

52 

228.338 

418.056 

195.7f)03K4.048 

171  314 

33(5.042 

152.311 

298.704 

137.115 

068  833 

53 

228.486 

448.  333  195.  87  7  3S4.  280 

171.42:. 

336.250 

152.405) 

298.889 

137.204 

269.000 

54 

208.  (>:>,<) 
228  77  3 

4  J  8.  611  196.000384.524 
4  18.  889'  196.  122  38  4.  762 

171.533 
171.640 

336.458 
336.  f  ,67 

152.505 
152.601 

299.074 
299.259 

137.290 
137.376 

269.167 
269.333 

55 
56 

228.901  449.167)196.249  3S5.000 

171.751 

336.875 

152.699 

099.444 

137.465 

269.500 

57 

229  069  449.444  19(5.376  3S5.238 

171  862 

337.083 

152.798 

299.630 

137.554 

069  667 

r>8 

229.2l7i4l9  722  190.503  385.476 

171.973 

337.292 

152.897 

299.815 

137.643 

269.  833 

59 

99 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


37° 
M. 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tail. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~cT 

1375.57 

2700.00 

687.812 

1:350.00 

458.572 

900.000 

3437960 

(3?5.000 

275.199 

540.000 

1 

1376.46 

2701.67 

688.256 

1350.83 

458.  H6H 

900.556 

344.182 

675.417 

275.377 

540.  ai3 

2 

1377.35 

2703.33 

688.701 

1351  67 

459.161 

901.111 

344.404 

675.833 

275.5M 

540.607 

3 

1378.21 

2705.00 

689.130 

1352.50 

459.451 

U01.0G7 

344.619 

676.250 

275.726 

541.000 

4 

1379.0? 

2706  67 

689.560 

1353.33 

459.737 

9U2.222 

344.834 

370  .  667 

275.898 

541.333 

5 

1379.96 

2708.33 

690.004 

1354.17 

460.033 

U02.778 

345.050 

077.083 

276.070 

541.607 

6 

1380.85 

2710.00 

690.448 

1355.00 

460.329 

903.  sas 

345.278 

677.500 

276.253 

542.000 

7 

1381.73 

2711.67 

690.892 

1:355.83 

4(50.625 

903.889 

345.500 

677.91? 

276.431 

542.333 

8 

1382.62 

2713.33 

691.336 

1356.67 

460.921 

904.444 

345.722 

078.33:3 

<J?'O.C09 

542.007 

9 

1383.51 

2715.00 

691.780 

1357.50 

461.217 

9U5.000 

345.914 

678.750 

276.787 

543.000 

1O 

1384.40 

2716.67 

692.224 

ia58.33 

461.514 

905.556 

34G.16? 

679.107 

27-6.964 

543.333 

11 

1385.29 

2718.  as 

692.608 

^359.1? 

461.810 

906.111 

S46.389 

679.583 

277.142 

543.007 

12 

1386.17 

2720.00 

693.113 

1:360.00 

462.106 

906.667 

S46.611 

680.000 

277.320 

544.000 

13 

1387.03 

2721.67 

69-].  542 

1360.83 

462.392 

907.222 

S46.826 

680.417 

277.491 

544.333 

14 

1387.89 

2723.33 

693.972 

1361.67 

462.679 

907.778 

347.040 

080.833 

277.003 

544.667 

15 

1388.78 

2725.00 

694.416 

1362.50 

462.975 

908.  333 

S47.263 

681.250 

277.841 

545.000 

16 

1389.67 

2726.67 

694  860 

1363.33 

463.271 

908.  h89 

347.485 

681.06? 

278.019 

545.333 

17 

1390.56 

2728.33 

695.304 

1364.17 

463.567 

909.444 

347.707 

682.083 

278.196 

545.66? 

18 

1391.45 

27:30.00 

695.748 

1365.00 

463.863 

910.000 

S47.929 

682.500 

278.374 

546.000 

19 

1392.33 

2731.67 

696.192 

1365.83 

464.159 

910.556 

S48.151 

682.917 

278.552 

546.333 

20 

1393.22 

2733.33 

696.636 

1366.67 

464.455 

911.111 

348.373 

683.333 

278.729 

546.667 

21 

1394.11 

2735.00 

697.080 

1367.50 

464.751 

911.667 

348.595 

683.750 

278.90?' 

547.000 

22 

1395.00 

2736.67 

697.525 

1368.a3 

465.047 

912.222 

S48.817 

084.107 

279.085 

547.333 

23 

1395.86 

2738.33 

697.954 

1369.17 

465.334 

912.778 

349.032 

684.583 

279.257 

547.607 

24 

1396.72 

2740.00 

698.384 

1370.00 

465.620 

913.  3:3:3 

S49.24? 

685.000 

2?  9.  429 

548.000 

25 

1397.60 

2741.67 

698.828 

1370.83 

465.916 

913.889 

349.469 

685.417 

279.006 

548.333 

26 

1395.49 

2743.  33 

699.272 

1371.67 

466  212 

914.444 

'349.691 

685.833 

279.784 

548.667 

27 

1399.38 

2745.00 

699.716 

1372.50 

466.508 

915.000 

349.913 

086.250 

279.902 

549.000 

28 

1400.27 

2746.67 

700.160 

1373.33 

466.804 

915.556 

350.135 

086.00? 

280.139 

549.333 

29 

1401.16 

2748.33 

700.604 

1374.17 

467.101 

916.111 

350.35? 

687.083 

2^0.317 

549.667 

3O 

1402.05 

2750.00 

701.048 

1375.00 

467  397 

916.66? 

350.579 

687.  5PO 

280.495 

550.000 

31 

1402.93 

2751.67 

701.492 

1375.83 

467.693 

917.222 

350.801 

687.917 

280.072 

550.333 

32 

1403.82 

2753.33 

701.936 

1376.67 

467.989 

917.778 

351.023 

088.3:33 

280.850 

550.607 

33 

1404.71 

2755.00 

702.381 

1377.50 

468.285 

918.333 

351.245 

688.750 

281.028 

551.000 

34 

1405.60 

2756.67 

702.825 

1378.33 

468.581 

918.889 

351.468 

689.167 

281.205 

551.333 

35 

1406.46 

2758.  a3 

703.254 

1379.17 

468.867 

919.444 

a(31.G82 

089.583 

281.377 

551.667 

36 

1407.32 

2760.00 

703  684 

1380.00 

469.154 

920.000 

351.897 

690.000 

281.549 

552.000 

37 

1408.20 

2761.67 

704.128 

1380.83 

469.450 

920.556 

352.119 

690.417 

281.727 

552.  333 

38 

1409.09 

2763.33 

704.572 

1381.67 

469.746 

921.111 

352.341 

690.833 

281.905 

552.667 

39 

1409.98 

2765.00 

705.016 

1382.50 

470.042 

921.667 

352.564 

691.250 

282.082 

553.000 

40 

1410.87 

2766.67 

705.460 

1383.  as 

470.338 

922.22v> 

352.786 

691.667 

282.260 

553.333 

41 

1411.76 

2768.33 

705.904 

1384.17 

470.634 

922.778 

353.008 

092.083 

282.438 

553.667 

42 

1412.65 

2770.00 

706.348 

1385.00 

470.930 

923.3:33 

353.230 

692.500 

282.615 

554.000 

43 

1413.53 

2771.67 

706.793 

1385.83 

471.226 

923.889 

353.452 

692.917 

282.793 

554.333 

44 

1414.42 

2773.  as 

707.237 

1386.67 

471.522 

924.444 

353.674 

693.333 

282.971 

554.667 

45 

1415.31 

2775.00 

707.681 

1387.50 

471.818 

925.000 

353.896 

693.750 

283.148 

555.000 

46 

1416.20 

2776.67 

708.125 

1388.33 

472.114 

925.556 

354.118 

694.16? 

283.326 

555.  a33 

47 

1417.06 

2778.33 

708.554 

1389.17 

472.401 

926.111 

354.  .333 

694.583 

283.498 

555.667 

48 

1417.92 

2780.00 

708.984 

1390.00 

472.687 

9*6.667 

354.548 

695.000 

283.670 

556.000 

49 

1418.80 

2781.67 

709.428 

1390.83 

472.984 

927.222 

354.770 

695.417 

283.848 

556.333 

50 

1419.69 

2783.33 

709  872 

1391.67 

473.280 

927.778 

354.992 

695.833 

284.025 

556.667 

51 

1120.58 

2785.00 

710.316 

1392.50 

473.576 

928.333 

355.214 

096.250 

284.2(3 

557.000 

52 

1121.47 

2786.67 

710.760 

1393.33 

473.872 

928.889 

355.436 

696.607 

284.381 

557.33;3 

53 

1422.36 

2788.33 

711.205 

1394.17 

474.168 

929.444 

355.658 

697.083 

284.558 

557.667 

54 

1423.25 

2790.00 

711.649 

1395.00 

474.464 

930.000 

355.880 

697.500 

284.730 

558.000 

55 

1424  13 

2791.67 

712.093 

1395.83 

474.760 

930.556 

356.102 

097.917 

284.914 

558.333 

56 

1425.02 

2793.33 

712.537 

1396.67 

475.  050 

931.111 

356.324 

698.  333 

285.091 

558.667 

57 

1425.91 

2795.00 

712.981 

1397.50 

475.352 

931.667 

356.546 

098.750 

285.269 

559.000 

58 

1426.80 

2796.67 

713.425 

1398.  as 

475.648 

932.222 

356.768 

699.167 

285.44? 

559.333 

59 

1427.69 

2798.33 

713.869 

1399.17 

475.914 

932.  7781356.  9'J1 

099.583 

2a5.624 

559.667 

100 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

27° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

337  500 

Tan. 

Arc. 

300.000 

Tan. 

137.731 

Arc. 

M. 

&J9.365 

450.000 

196.630 

385.714 

172.084 

152.996 

270.000 

a 

229.513 

450.278 

196.757 

385.952 

172.196 

337.708 

153.095 

300.185 

137.820270.167 

i 

229.661 

450.556 

196.884 

386.190 

172.307 

337.917 

153.193 

300.370 

137.909  ^70.333 

2 

229.805 

450.833 

197.007 

386.429 

172.414 

338.125 

153.289 

300.556 

137.995270.500 

3 

229.948 

451.111 

197.130 

386.667 

172.522 

338.333 

153.384 

300.741 

138.081 

270.607 

4 

230.096 

451.389 

197.257 

386.905 

172.633 

338.542 

153.483 

300.926 

138.170 

27'0.833 

5 

230.244 

-151.667 

197.384 

387.143 

172.744 

338.750 

153.582 

301.111 

138.259271.000 

G 

230.392 

451.944 

197.511 

387.381 

172.855 

338.958 

153.681 

301.296 

138.348 

271.167 

7 

230.540 

452.222 

197.638 

387.619 

172.966 

339.167 

153.780 

•301.481 

138.437 

271.333 

8 

230.688 

452.500 

197.765 

387.857 

173.077 

339.375 

153.878 

301.667 

138.526 

271.500 

9 

230.836 

452.778 

197.892 

388.095 

173.188 

339.583 

153.977 

301.852 

138.615 

271.667 

10 

230.985 

453.056 

198  019 

388.333 

173.299 

339.792 

154.076 

302.037 

138.704 

271  833 

11 

231.133 

453.333 

198.145 

388.571 

173.411 

340.000 

154.175 

302.222 

138.793 

272.000 

12 

231.276 

453.611 

198.268 

888.810 

173.518 

340.208 

154.270 

302.407 

138.879 

272  167 

13 

231.419 

453.889 

198.391 

389.048 

173.626 

340.417 

154.366 

302.593 

138.965 

272.3:33 

14 

231.567 

454.167 

198.518 

389.286 

173.737 

340  625 

154.465 

302.778 

139.054 

272.500 

15 

231.715 

454.444 

198.645 

389.524 

173.848 

340.833 

154.563 

302.963 

139.143 

272  667 

16 

231.863 

454.722 

198.772 

389.762 

173.959 

341.042 

154.662 

303.148 

139.232 

272.833 

17 

232.012 

455.000 

198.899 

390.000 

174.070 

341.250 

154.761 

303.333  139.321 

273.000 

18 

232.160 

455.278 

199.026 

390.238 

174.181 

341.458 

154.860 

303.519 

139.409 

273.167 

19 

232.308 

455.556 

199.153 

390.476 

174.292 

341.667 

154.959 

303.704 

139.498 

273.333 

20 

232.456 

455.833 

199.280 

390.714 

174.403 

341.875 

155.057 

303.889 

139.587 

273.500 

21 

232.004 

456.111 

199.407 

390.952 

174.514 

342.083 

155.156 

304.074 

139.676 

273.667 

22 

232.747 

456,389 

199.530 

391.190 

174.622 

342.292 

155.252 

304.259 

139.762 

273.833 

23 

232.  b90 

456.667 

199.652 

391.429 

174.729 

342.500 

155  347 

304.444 

139.848 

274.000 

24 

233.039 

456.944 

199.779 

391.667 

174.841 

342.708 

155.446 

304.630 

139.937 

274.167 

25 

233.197 

457.222 

199.906 

391.905 

174.952 

342  917 

155.545 

304.815 

140.026 

274.333 

26 

233.335 

457.500 

200.033 

392.143 

175.063 

343.125 

155.644 

305.000 

140.115 

274.500 

27 

233.483 

457.778 

200.160 

392.381 

175.174 

343.333 

155.742 

305.185 

140.204 

274.667 

28 

233.631 

458.056 

200.287 

392.619 

175.285 

343.542 

155.841 

305.370 

140.293 

274.833 

29 

233.779 

458.333 

200.414 

392.857 

175.396 

343.750 

155.940 

305.556 

140.382 

275.000 

30 

233.927 

458.611 

200.541  393.095 

175.507 

343.958 

156.039 

305.741 

140.471 

275.167 

31 

234.075 

458.889 

200.  668  j  393.  333 

175.618 

344.167 

156.137 

305.926 

140.560 

275.333 

32 

234.223 

459.167 

200.795  393.571 

175.729 

344.375 

156.236306.111 

140.649 

275.500 

33 

234.371 

459.444 

200.922393.810 

175.840 

344.583 

156.335306.296 

140.738 

275.667 

34 

894.515 

459.722 

201.045:394.048 

175.948 

344.792 

156.431  306.481 

140  824 

275.833 

35 

384.658 

460.000 

201.168394.286 

176.055 

345.000 

156.526306.667 

140.910 

276.000 

36 

234.  806  '400.  27  8 

201.295394.524 

176.167 

345.208 

156.6251306.852 

140.999 

276.167 

37 

234.  954  1460.  556 

201.422394.762 

176.278 

345.417 

156.724 

307.037 

141.088 

276.333 

38 

235.102J460.833 

201.548395.000 

1 

176.389 

345.625 

156.823 

307.222 

141.176 

276.500 

39 

235.250461.111 

201.675395.238 

176.500 

345.833 

156.921 

307.407 

HI.  265 

276.667 

40 

235.398461.389 

201.802395.476 

176.611 

346.04? 

157.020 

307.593 

141.354 

276.  8S3 

41 

235.546461.667 

201.929395.714 

176.722 

346.250 

157.119307.778 

141.443 

277.000 

42 

235.695461.944 

202.056395.952 

176.833 

346.458 

157.2181307.963 

141.532 

277.167 

43 

235  843462.222 

202.183396/190 

176.944 

346.667 

157.  316*308.  148 

141.621 

277.333 

44 

235.991  462.500 

202.310396.429 

17   .055 

346.875 

157.415308.333 

141.710 

277.500 

45 

23(5.139 

462.778 

202.437396.667 

17  .166 

347.083 

157.514308.519 

141.799 

277.007 

46 

236.282 

463.056 

202.560396.905 

17  .274 

347.292 

157.610 

308.704 

141.885 

277.833 

47 

236.425 

463.333 

202.683397.143 

17  .381 

347.500 

157.705 

308.889 

141.971  278.000 

48 

236.573 

463.611 

202.810 

397.381 

177.493 

347.708 

157.804 

309.074 

142.060 

278.167 

49 

236.722 

463.889 

202.937 

397.619 

17~.604 

347.917 

157.903 

309.259 

142.149 

278.333 

50 

230.870 

464.167 

203.064397.857 

17^.715 

348.125 

158.001 

309.444 

142.23F  278.500 

51 

237.018 

464.444 

203.191  398.095 

17  .826 

348.333 

158.100 

309.630 

142.3-.7278.667 

52 

237.166 

464.722 

203.3183D8.333 

177.937 

348.542 

158.199 

309.815 

142.410  278.833 

53 

237.314 

465.000 

203.445  398  571 

178.048 

348.750 

158.298 

310.000 

142.505  27'9.000 

54 

237.462 

465.278 

203.571 

398.810 

178.159 

348.958 

158.397 

310.185 

142.593279.167 

55 

237.610 

4R5.556 

203.698 

399.048 

178.270 

349.167 

158.495 

310.370 

142.682:279.333 

56 

237.758 

465.833 

203.825 

399.286 

178.381 

149.375 

158.594 

310.556 

142.771,27'9.500 

57 

237.906 

166.111 

203.952 

399.524 

178.493 

349.583 

158.693 

310.741 

142.  860  1279.  607 

58 

238.054 

466.389 

204.079 

399.762 

178.604 

349.792 

158.792 

310.926 

142.  949  |279.  833 

59 

101 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


28° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tau. 

Arc. 

Tan. 

Arc. 

Tan.      Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

1428.57 

2800.00 

714.313 

1400.00 

476.240933.333 

357.213 

700.000 

285.802 

560.000 

1 

14-29.46 

2801.67 

714.757 

1400.83 

476.536933.889 

357.435 

700.417 

285.980 

500.333 

2 

1430.35 

2803.33715.201 

1401.67 

476.832934.444 

357.057 

700.833 

286.157 

560.607 

3 

1431.24 

2805.00 

715.645 

1402.50 

477.128935.000 

357.879 

701.250 

286  335 

5(11.000 

4 

1432.13 

2806.67 

716.089 

1403.33 

477.424  935.556 

358.101 

701.607 

286.513 

561.333 

5 

1433.01 

2808.33 

716.533 

1404.17 

477.721  936.111 

358.323 

702.083 

286.690 

501.667 

6 

1433.90 

2810.00 

716.977 

1405.00 

478.017936.667 

358.545 

702.500 

286.868 

562.000 

7 

1434.76 

2811.67 

717  407 

1405.83 

478.303937.222 

358.760 

702.917 

287.040 

562.333 

8 

1435.62 

2813.33 

717.837 

1406.67 

478.590937.778 

358.975 

703.333 

287.212 

562.667 

9 

1436.51 

2815.00 

718.281 

1407.50 

478.886938.333 

359.197 

703.750 

287.390 

563.000 

10 

1437.40 

2816.67 

713.725 

1408.33 

479  182938.889 

359.419 

704.167 

287.567 

563  333 

11 

1438.29 

2818.33,719.169 

1409.17 

479.478939.444 

359.641 

704.583 

287.745 

563  667 

13 

1439,17 

2820.00  719  613 

1410.00 

479.774940.000 

359.863 

705.000 

287.923 

564.000 

13 

1440.06 

5821.67 

720.057 

1410.83 

480.070940.556 

360.085 

705.417 

288.100 

564.333 

14 

1410.05 

2823  33 

720.501 

1411.67 

480  366  941.1  11 

360.307 

705.833 

288.278 

564.667 

15 

1441.84 

2825.00 

720.94') 

1412.50 

480  662941.667 

360.529 

706.250 

288.456 

565.000 

16. 

144-2.  73 

2826.67 

721.389 

1413.33 

480.958942.222 

360.751 

706.667 

288.633 

565.333 

17   1443.61 

2828,33 

721.833 

1414.17 

481.254942.778 

360.973 

707.083 

288.811 

565.667 

18 

1444.50 

2830.00 

722.278 

1415.00 

481.550943.333 

361.195 

707.500 

288.989 

566  000 

19 

1445.39 

2831.67 

722.722 

1415.83 

481.846:943.889 

361.418 

707.917 

289.160 

566.333 

20 

1446.28 

2833.33 

723.166 

1416.67 

482.142944.444 

361.640 

708.333 

289.344 

566.667 

21 

1447.17 

2835.00 

723.610 

1417.50 

482.438945.000 

361.802 

708.750 

289.522 

567.000 

22 

1448.05 

2836.67 

724.054 

1418  33 

482.735945.556 

362.084 

709.167 

289.699 

567.333 

23 

1448.94 

2838.33 

724.498 

1419.17 

483.031  946.111 

362.306 

709.583 

289.877 

567.667 

24: 

1449.83 

2840.00 

724.942 

14-20.00 

483.327946.667 

36-2.528 

710.000 

290.055 

508.00!) 

25 

1450.72 

2841  67 

725.186 

1420  83 

483.  6.  >:{  947.  222 

362.750 

710.41? 

290.232 

568.333 

26 

1451.61 

3843  .33 

725.830 

14-21.67 

483.919947.778 

362.972 

710.833 

290.410 

568.667 

27 

1452  49 

2845.00 

726.274 

1422.50 

484.215948.333 

363.194 

711  250 

290.588 

5(59.000 

28 

1453.38 

2846.67 

726.718 

1423.33 

484.511  948.889 

363.416 

711.667 

290.765 

569.333 

29 

1454.2? 

2848.33 

727.162 

1424.17 

484,807949.444 

363.638 

712.083 

290.943 

569.  C67 

30 

1455,  16 

2850.00 

727.606 

1425.00 

485.103950.000 

363.860 

712.500 

291.121 

570.000 

31 

1456.05 

2851  ,67 

728  050 

1425.83 

485.399950.556 

364.082 

712.917 

291.298 

570.333 

32 

1456.94 

2853.33 

728.494 

14-26.67 

485.  695951.  Ill 

304.304 

713.333 

291.470 

570.667 

33 

1457.82 

2855.00 

728.938 

1427.50 

485.991:951.667 

364.526 

713.750 

291  654 

571.000 

34 

1458.71 

2856.67 

729.383 

1428.33 

486.287952.222 

364  749 

714.167 

291.831 

571.333 

35 

1459.60 

2858.33 

729  827 

1429.17 

486.  583  952.  77H 

364.971 

714.583 

292.009 

571.667 

36 

1460.49 

2860.00 

730.271 

1430.00 

486.879953.333 

365.193 

715.000 

292.187 

572.000 

37 

1461.38 

2861.67 

730.715 

1430.83 

487.175-953.889 

365.415 

715.417 

292.364 

572.333 

38 

1462.26 

2803.33 

731.159 

14-51.67 

487.472i'954.444 

305.637 

715.838 

292.542 

572.667 

39 

1463.  15 

2865.00 

731.603 

1432.50 

487.768955.000 

365.859 

716.250 

292.720 

573.000 

40 

1464,04 

2866.67 

732.017 

1433.33 

488.064:955.556 

366.081 

716.667 

292  897 

573.333 

41 

14(54.93 

2868,33 

732.491 

1434.17 

488.360556.111 

366.303 

717.083 

293.075 

573.667 

42 

1465.  8:> 

2870,00 

732.9% 

1435.00 

488.656956.667 

366.525 

717.500 

293.253 

574.000 

43 

1466.70 

2871.67 

733.379 

1435.83 

488  952-957.222 

366'.  747 

717.917 

293.430 

574.333 

44 

1467.59 

•2873.33 

733.8231436.67 

489.248957.778 

366.969 

718.333 

293.608 

574.667 

45 

1468.48 

2875.00 

734.  2(37(1437.50 

489.544  958.333 

367.191 

718.750 

295.786 

575.000 

46 

1469.57 

•2876.67 

734.71111438.33 

489.840958.889 

367.413 

719.167 

293.964 

575.333 

47 

1470.26 

2878.33 

735.155J1439.17 

490.136959.444 

367.635 

719.583 

294.141 

575.667 

48 

1471,14 

2880.00 

735.  599!  1440.  00 

190.  432  '960.  000 

367.857 

720.000 

294.319 

576.000 

49 

1472.03 

2881.67 

736.043 

1440.83 

490.728.960.556 

368.080 

720.417 

294.497 

576.333 

50 

1472.92 

2883.33 

736.  4H8 

1441.67 

491.624961.111 

368.302 

720.833 

294.674 

576.667 

51 

1473.81 

2385.00 

736.932 

1442.50 

491.  320%  1.66? 

368.524 

721.250 

294.852 

577.000 

52 

1474.70 

2886.67 

737.376 

1443.33 

491  .-61  6  962.  222 

368.746 

721.667 

295.030 

577.333 

53 

1475.59 

2888.33 

737.820 

1444.17 

491J912962.778 

308.968 

722.083 

295.207 

577.607 

54 

1476.47 

2890.00 

738.264 

H45.00 

492  .209  -963.333 

309.190 

722.500 

295.385 

578.000 

35 

1477.36 

2891.  .67 

788.708 

1445.83 

492.505963.889 

369.412 

722.917 

295  563 

578.333 

56 

1478.25 

2893.33 

739.152 

1446.67 

492.  flOl  964,444 

369.634 

723.333 

295.740 

578.667 

57 

1479..14 

2895.00 

739.596 

1447.50 

493.097965.000 

369.856 

723.750 

295.918 

579.000 

58 

1480.03 

2896.07 

740.040 

1418.33 

4  03.  393  965.550 

370  078 

724.167 

290.096 

579.333 

59 

1480.91 

2898.33 

740.484 

1449.17 

4D3.6S9  906.1  11 

370.300 

724.  5831  296.  273 

579.667 

102 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

28° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

288.202 

466.667 

204.206 

400.000 

178.715 

350.000 

158.890 

311.111 

143.038 

280.000 

O 

238.350 

466.944 

204.333 

400.238 

178.826:350  208 

158.989 

311.296 

143.127 

280.167 

1 

238.499 

467.222 

204.460 

400.476 

178.937 

350.417 

159.088 

311.481 

143.216 

280.333 

2 

238.  64T 

467.500 

204.587 

400.714 

179.048 

350.625 

159  187 

311.667 

143.305 

280.500 

3 

238.795 

467.778 

204.714 

400.952 

179.159 

350.833 

159.286 

311.852 

143.394 

280.667 

4 

238.943 

468.056 

204.841 

401.190 

179.270 

351.042 

159.384 

312.037 

143.483 

280.833 

5 

239.091 

4(58.  333 

204.968 

401.429 

179.381 

351.250 

159.483 

312.222 

143.572 

281.000 

6 

239.234 

468.611 

205.091 

401.667 

179.489 

351.458 

159.579 

312.407 

143.658 

281.167 

7 

239.377 

468.889 

205.214 

401.905 

179.596 

351.667 

159.674 

312.593 

143.744 

281.333 

8 

239.526 

469.167 

205.341 

402.143 

179.707 

351.875 

159.773 

312.778 

143.833 

281.500 

9 

239.674 

469.444 

205.467 

402.381 

179.819 

352.083 

159.872 

312.963 

143.922 

281.667 

1O 

239.822 

469.722 

205.594 

402.619 

179.930 

352.292 

159.971 

313.148 

144.010 

281.833 

11 

239.970 

470.000 

205.721 

402.857 

180.041 

352.500 

160.069 

313.333 

144.099 

282.000 

12 

240.118 

470.278 

205.848 

403.095 

180.152 

353.708 

160.168 

313.519 

144.188 

282  167 

13 

240.266 

470.556 

205.975 

403  333 

180.263 

352.917 

160.267 

313.704 

144.277 

282.333 

14 

240.414 

470.833 

206.102 

403.571 

180.374 

353.125 

160.366 

313.889 

144.366 

282.500 

15 

240.562 

471.111 

206.229 

403.810 

180.485 

353.333 

160.465 

314.074 

144.455 

282.667 

16 

240.710 

471.389 

206.356 

404.048 

180.596 

353.542 

160.563 

314.259 

144.544 

282.833 

17 

240.858 

471.667 

206.483 

404.286 

180.707 

353.750 

160.662 

314.444 

144.633 

283.000 

18 

241.006 

471.944 

206.610 

404.524 

180.818 

353.958 

160.761 

314.630 

144.722 

283.167 

19 

241.154 

472.222 

206.737 

404.762 

180.930 

354.167 

160.860 

314.815 

144.811 

283.333 

2O 

241.303 

472.500 

206.864 

405.000 

181.041 

354.375 

160.958 

315.000 

144.900 

283.500 

21 

241.451 

472.778 

206.991 

405.238 

181.152 

354.583 

161.057 

315.185 

144.989 

283.667 

22 

241.59:> 

473.056 

207.118 

405.476 

181.263 

354.792 

161.156 

315.370 

145.078 

283.833 

23 

241.747 

473.333 

207.245 

405.714 

181.374 

355.000 

161.255 

315.556 

145.166 

284.000 

24 

241.895 

473.611 

207.372 

405.952 

181.485 

355.208 

161.354 

315.741 

145.255 

284.167 

25 

242.043 

473.889 

207.499 

406.190 

181.596 

355.417 

161.45-2 

315.926 

145.344 

284.333 

26 

242.191 

474.167 

207.626 

406.429 

181.707 

355.625 

161.551 

316.111 

145.433 

284.500 

27 

242.339 

474.444 

207.753 

406.667 

181.818 

355.833 

161.650 

316.296 

145.522 

284.667 

28 

242.487 

474.722 

207.880 

400.905 

181.929 

356.042 

161.749 

316.481 

145.611 

284.883 

29 

242.635 

475.000 

208.006 

407.143 

182.041 

356.250 

161.847 

316  667 

145.700 

285.000 

30 

242.783 

475.278 

208.133 

407.381 

182.152 

356  458 

161.946 

31  G.  852 

145.789 

285.167 

31 

242.931 

475.556 

208.260 

407.619 

182.263 

356.667 

162.045 

317.037 

145.878 

285.333 

32 

243.080 

475.833 

208.387 

407.857 

182.374 

356.875 

162.144 

317.222 

145.967 

285.500 

33 

243.228 

476.111 

208.514 

408.095 

182.485 

357.083 

162.243 

317.407 

146.056 

285.667 

34 

243.376 

476.389 

208.641 

408.333 

182.596 

357.292 

162.341 

317.593 

146.145 

•285.833 

35 

243.524 

476.667 

208.768 

408.571 

182.707 

357.500 

162.440 

317.778 

146.234 

286.000 

36 

243.672 

476.944 

208.895 

408.810 

182.818 

357.708 

162.539 

317.963 

146.322 

286.167 

37 

243.820 

477.222 

209.022 

409.048 

182.929 

357.917 

162.638 

318.148 

146.411 

286.333 

38 

243.968 

477.500 

209.149 

409.286 

183.040 

358.125 

162.736 

318.333 

146.500 

286.500 

39 

244.116 

477.778 

209.276 

409.524 

183.152 

358.333 

162.835 

318.519 

146.589 

286.667 

40 

244.264 

478.056 

209.403 

409.762 

183.263 

358.542 

162.934 

318.704 

146.678 

286.833 

41 

244.412 

478.333 

209.530 

410.000 

183.374 

358.750 

163.033 

318.889 

146.767 

287.000 

42 

244.560 

478.611 

209.657 

410.238183.485 

358  958 

163.132 

319.074 

146.856 

287.167 

43 

244.708 

478.889 

209.784 

410.476  183.596 

359.167 

163.'230 

319.259 

146.945 

287.333 

44 

244.857 

479.167 

209.911 

410.714183.707 

359.375 

163.329 

319.444 

147.034 

287.500 

45 

245.005 

479.444 

210.038 

410.952  183.818 

a^9.583 

163.428 

319.630 

147.123 

287.667 

46 

245.153 

479.722 

210.165 

411.190183.929 

359.792 

163.527 

319.815 

147.212 

287.833 

47 

245.301 

480.000 

210.292 

411.  429  j  184.  040 

360.000 

163.625 

320.000 

147.301 

288.000 

48 

245.449 

480.278 

210.418 

411.667 

184.151 

360.208 

163.724 

320.185 

147.390 

288.167 

49 

245.597 

480.556 

210.545 

411.905 

184.263 

360  417 

163.823 

320.370 

147.478 

288.333 

50 

245  .  745 

480.833 

210.672 

412.143 

184.374 

360.625 

163.92-2 

320.556 

147.567 

288.500 

51 

245.893 

481.111 

210.799 

412.381 

184  4a5 

360.833 

164.0-21 

320.741 

147  656 

288  667 

52 

246.041 

481.389 

210.926 

412.619184.596 

8(51.042 

164.119 

320.926 

147.745 

288.833 

53 

246.189 

481.667 

•211.053 

412.857184.707 

361.250 

164.218 

321  111 

147.834 

•289.000 

54 

246.337 

481.944 

•211.180 

413.095184.818 

361.458 

164.317321.296 

147.9-23 

289.107 

55 

246.485 

482.222 

211.307 

4  13.  333  184.  929  '361.667 

164  416321  481 

148.012 

289.333 

56 

246.633 

482.500 

•211.434 

413.571  185.  040i361.875 

164.514 

321.667 

148.101 

289.500 

57 

246.782 

482.778 

211.561 

413.810185.151 

362.083 

164.613 

321.852 

148.190 

289.667 

58 

246.930 

483.056 

211.688 

414.048  185.262 

362.292 

164.71-2 

3-22.037 

148.279 

289.833 

59 

103 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


3<>° 

~M^ 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Are. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

1481.80 

2900  .  00 

740.  92b 

1450.00 

493.985 

966.667 

370.522 

725.000 

296.451 

580.000 

i 

1482  69 

2901.67 

741.372 

1450.8) 

494.281 

967.222 

370.744 

725.417 

296.629 

580.  3.« 

2 

1483.58 

2903.33 

741.816 

1451.67 

494.577 

967.778 

370.966 

725.833 

296.806 

580.007 

3 

1484.47 

2905.00 

742.260 

1452.50 

494.873 

968.333 

371.188 

726.250 

296.984 

581.000 

4 

1485.35 

2906.67 

742.704 

1453.33 

495.169 

968.889 

371.411 

726.667 

297.162 

581.3:33 

5 

1486.24 

2008.33 

743.149 

1454.17 

495.465 

969.444 

371.633 

727.083 

297.339 

581.667 

6 

1487.13 

2910.00 

743.593 

1455.00 

495.761 

970.000 

371.855 

727.500 

297.517 

582.000 

7 

1488.  OJ 

2911.67 

744.037 

1455.83 

496.057 

970.556 

372.077 

727.917 

S97.695 

582.3:33 

8 

1488.91 

2913.33 

744.481 

1456.67 

496.353 

971.111 

372.299 

728.333 

297.872 

582.667 

9 

1489.79 

2915.00 

744.925 

1457.50 

496.649 

971.667 

372.521 

728.750 

298.050 

583.000 

10 

1490.68 

2916  67 

745.369 

1458.33 

496.946 

972.222 

372.743 

729.167 

298.228 

583.333 

11 

1491.57 

2918.33 

745.813 

1459.17 

497.242 

972.778 

372.965 

729.583 

298.405 

583.667 

13 

1492.46 

2920.00 

746.257 

1460.00 

497.538 

973.333 

373.187 

730.000 

298.583 

584.000 

13 

1493.35 

2921.67 

746.701 

1460.83 

497.834 

973.889 

373.409 

730.417 

298.761 

584.333 

14 

1494.24 

2923.33 

747.145 

1461.67 

498.130 

974.444 

373.631 

730.8313 

298.938 

584.667 

15 

1495.12 

2925.00 

747.589 

1462.50 

498.426 

975.000 

373.853 

731.250 

299.116 

585.000 

16 

1496.01 

2926.67 

748.033 

1463.33 

498.722 

975.556 

374.075 

731.667 

299.294 

585.333 

17 

1496.90 

2928.33 

748.477 

1464.17 

499.018 

976.111 

374.297 

732.083 

299.  471  1  585.  667 

18 

1497.79 

2930.00 

748.921 

1465.00 

199.314 

976.667 

374.  51  9  ^32.  500 

299.649 

586.000 

19 

1498.68 

2931.67 

749.305 

1465.83 

499.610 

977.222 

374.742 

732.917 

299.827 

586,333 

20 

1499.56 

2933.33 

749.809 

1466.67 

499.906 

977.778 

374.964 

733.333 

300.004 

586.667 

31 

1500.45 

2935.00 

750.254 

1467.50 

500.202 

978.333 

375.186 

733.750 

300.182 

587.000 

22 

1501.34 

2936.67 

750.698 

1468.33 

500.498 

978.889 

375.408 

734.167 

300.360 

587.333 

23 

1502.26 

2938.33 

751.156 

1469.17 

500.801 

979.444 

375  .  637 

734.583 

300.543 

587.667 

34 

1503.17 

2940.00 

751.614 

1470.00 

501.109 

980.000 

375.866 

735.000 

300.727 

588.000 

35 

1504.06 

2941.67 

752.058 

1470.83 

501.406 

980.556 

376.088 

735.417 

300.904 

588.333 

36 

1504.95 

2913.33 

752.503 

1471.67 

501.702 

981.111 

376.310 

735.833 

301.082 

588.667 

37 

1505.84 

2945.00 

752.947 

1472.50 

501.998 

981.667 

376.532 

736.250 

301.260 

589.000 

38 

1506.73 

2946.67 

753.391 

1473.33 

502.294 

982.222 

376.754 

730.667 

301.437 

589.333 

39 

1507.61 

2948.33 

753.835 

1474.17 

502.590 

982.778 

376.977 

737.083 

301.615 

589.667 

30 

1508.50 

2950.00 

754.279 

1475.00 

502.886 

983.333 

377.199 

737.500 

301  793 

590.000 

31 

1509.39 

2951.67 

754.723 

1475.83 

503.182 

983.889 

377.421 

737.917 

301.970 

590.333 

33 

1510.28 

2953.33 

755.167 

1476.67 

503.478 

984.444 

377.643 

738.333 

302.148 

590.667 

33 

1511.17 

2955.00 

755.611 

1477.50 

503.774 

985.000 

377.865 

738.750 

302.326 

591.000 

34 

1512.05 

2956.67 

756.055 

1478.33 

504.070 

985.556 

378.087 

739.167 

302.503 

591.333 

35 

1512.94 

2958.33 

756.499 

1479.17 

504.366 

986.111 

378.309 

739.583 

302.681 

591  .  6(57 

36 

1513.  as 

2960.00 

756.943 

1480.00 

504.662 

986.667 

378.531 

740.000 

302.859 

592.000 

37 

1514.72 

2961.67 

757.387 

1480.83 

504.958 

987.222 

378.753 

740.417 

303.036 

592.333 

38 

1515.61 

2963.33 

757.831 

1481.67 

505.254 

987.778 

378.975 

740.8:33 

303.214 

592.667 

39 

1516.50 

2965.00 

758.275 

1482.50 

505.550 

988.333 

379.197 

741.250 

303.392 

593  000 

40 

1517.38 

2966.67 

758.719 

1483.33 

505.846 

988.889 

379  419 

741.667 

303.569 

593.333 

41 

1518.30 

2968.33 

759.178 

1484.17 

506.152 

989.444 

379.649 

742.083 

303.753 

593.607 

43 

1519.22 

2970.00 

759.636 

1485.00 

506.458 

990.000 

379.878 

742.500 

303.930 

594.000 

43 

1520.10 

2971.67 

760.080 

1485.83 

506.754 

990.556 

380.100 

742.917 

304.114 

594.333 

44 

1520.99 

2973.33 

760.524 

1486.67 

507.050 

991.111 

380.322 

743.333 

304.291 

594.607 

45 

1521.88 

2975.00 

760.968 

1487.50 

507.346 

991.667 

380.544 

743.750 

304.469 

595.000 

46 

1522.77 

2976.67 

761.412 

1488.33 

507.642 

992.222 

380  766 

744.167 

304.647 

595.333 

47 

1523.66 

2978.33 

761.857 

1489.17 

507.938 

992.778 

380.988 

744.583 

304.825 

595.667 

48 

1524.55 

2980.00 

762.301 

1490.00 

508.234 

993.  a33 

381.210 

745.000 

305.002 

596.000 

49 

1525.43 

2981.67 

762.745 

1490.83 

508.530 

993.889 

381.432 

745.417 

305.180 

596.333 

50 

1526.32 

2983.33 

763.189 

1491.67 

508.826 

994.444 

381.054 

745.833 

305.358 

596.667 

51 

1527.21 

2985.00 

763.633 

1492.50 

509  122 

995.000 

381.876 

746.250 

305.535 

507.000 

53 

1528.10 

2986.67 

764.077 

1493.33 

509.418 

995.556 

382.098 

746.667 

305.713 

597.33:3 

53 

1528.99 

2988.33 

764.521 

1494.17 

509.714 

996.111 

382.320 

747.083 

305.891 

59r.6'i7 

54 

1529.87 

2990.00 

764.965 

1495.00 

510.010 

996.667 

382.  543  !  747.  500 

306.068 

598.000 

55 

1530.79 

2991  .  67 

765.4231495.83 

510.316 

997.222 

382.772 

747.917 

806.253 

598.333 

50 

1531.71 

2993.33 

765.882 

1496.67 

510.622 

997.778 

388.001 

748.333 

306.43559S.Gf,7 

57 

1532.60 

2995.00 

766.326 

1497.50 

510.918 

998.333 

383.223 

748.750 

306.613509.000 

58 

1533.48 

2996.67 

766.77'0 

1498.33 

511  214 

998.889 

383.445 

749.167 

306  790  590  .  333 

59 

153  4.  371-2998.  33 

767.  21411499.  17 

511.510 

999.444 

383.667749.583 

306.968599.007 

104 


TABLE   XTV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

29° 

Tan. 

2477078 

Arc. 

483.333 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

161.811 

Arc. 
322.222 

Tan. 

1487368 

Arc. 

M7 

211.815 

414.286 

185.374 

302.500 

•390.00(i 

o 

247.226 

483.611 

211.942 

414.524 

185.485 

362.  70S 

164.909 

322.407 

148.457 

290.107 

1 

247.374 

483.889 

212.069 

414.762 

185.596 

362.917 

165.008 

322.593 

148.546 

•390.333 

2 

247.522 

484.167 

212.196 

415.000 

185.707 

303.125 

165.107 

322.778 

148.634 

•390.500 

3 

247.670 

484.444 

212.323 

415.238 

185.818 

363.333 

165.206 

322.963 

148.723 

290.607 

4 

247.818 

484.722 

212.450 

415.476 

185.929 

363  542 

165.305 

323.148 

148.812 

-390.833 

5 

247.966 

485.000 

212.577 

415.714 

186.040 

363.750 

165.403 

323.333 

148.901 

291.000 

6 

248.114 

485.278 

212.704 

415.952 

186.151 

363.958 

165.502 

3-33.519 

148.990 

291.167 

7 

248.262 

485.556 

212.830 

416.190 

186.202 

364.167 

165.601 

323.704 

149.079 

291.333 

8 

248.410 

485.833 

212.957 

416.429 

186.374 

364.375 

165.700 

323.889 

149.168 

291.500 

9 

248.559 

486.111 

213.084 

416.667 

186.485 

364.583 

165.798 

324  074 

149.257 

291.667 

10 

248.707 

486.389 

213.211 

416.905 

186.590 

364.792 

165.897 

324.259 

149.346 

291.833 

11 

248.855 

486.667 

213.338 

417.143 

186.707 

365.000 

165.996 

324.444 

149.435 

292.000 

13 

249.003 

486.944 

213.465 

417.381 

186.818 

365.208 

166.095 

3-34.630 

149.524 

292.167 

13 

249.151 

487.222 

213.592 

417.619 

186.929 

365.417 

166.194 

824.815 

149.613 

292.333 

14 

249.299 

487.500 

•313.719 

417.857 

187.040 

365.625 

166.292 

325.000 

149.701 

292.500 

15 

249.447 

487.778 

213.846 

418.095 

187.151 

365.833 

166.391 

325.185 

149.790 

292.667 

16 

249.595 

488.056 

213.973 

418.333 

187.262 

366.042 

166.490 

325.370 

149.879 

292.833 

17 

249.743 

488.333 

214.100 

418.571 

187.373 

306.250 

166.589 

325.556 

149.968 

293.000 

18 

249.891 

488.611 

•314.227 

418.810 

187.485 

366.458 

166.687 

325.741 

150.057 

293.167 

19 

250.030 

488.889 

214.354 

419.048 

187.596 

366.667 

166.780 

325.926 

150.146 

293  333 

20 

250.187 

489.167 

214.481 

419.286 

187.707 

366  875 

166.885 

326.111 

150.235 

293.500 

21 

1350.336 

489.444 

214.608 

419.524 

187.818 

367.083 

166.984 

326.296 

150.324 

293.667 

22' 

250.488 

489.722 

214.739 

419.762 

187.93-3 

367.292 

167.086 

3-36.481 

150.416 

293.833 

23 

250.641 

490.000 

214.870 

420.000 

188.047 

367.500 

167.188 

326.667 

150.508 

294.000 

24 

250.789 

490.  27S 

214.997 

420.238 

188.158 

367.708 

167.287 

3-36.852 

150.596 

294.167 

25 

2£0.937 

490.556 

215.124 

420.476 

188.269 

307.917 

167.385 

327.037 

150.685 

294.333 

26 

251.  C80 

490.833 

215.251 

420.714 

188.380 

368.125 

167.484 

327.222 

150.774 

294.500 

27 

251.2J34 

491.111 

215.378 

420.952 

188.492 

368.333 

167.583 

327.407 

150.863 

294.667 

28 

251.382 

491.389 

215.505 

421.190 

188.603 

368.542 

167.682 

327.593 

150.952 

294.633 

29 

251.530 

491.667 

215.63-3 

421.429 

188.714 

368.750 

167.780 

327.778 

151.041 

295.000 

3O 

251.678 

491.944 

215.758 

421.667 

188.825 

368.958 

167.879 

327.963 

151.130 

295.167 

31 

251.826 

492.222 

215.885 

421.905 

188.936 

369.167 

167.978 

328.148 

151.219 

295.333 

33 

251.974 

492.500 

216.012 

422.143 

189.047 

369.375 

168.077 

328.333 

151.308 

295.500 

33 

252.1-32 

492.778 

216.139 

422.381 

189.158 

369.583 

168.176 

3-38.519 

151.397 

295.667 

34 

252.270 

493.056 

216.266 

422.619 

189.269 

369.792 

168.274 

328.704 

151.486 

295  >33 

35 

252.418 

493.333 

216.393 

422  857 

189.380 

370.000 

168.373 

328.889 

151.575 

296.000 

36 

252.506 

493.611 

216.520 

423.095 

189.491 

370.208 

168.472 

329.074 

151.664 

296.167 

37 

25-3.714 

493.889 

216.647 

423.333 

189.603 

370.417 

168.571 

329.259 

151.752 

296.333 

38 

252.863 

494.167 

216.774 

423.571 

189.714 

370.625 

168.609 

329.444 

151.841 

296.500 

39 

253.011 

494.444 

216.901 

423.810 

189.825 

370.833 

168.768 

329.630 

151.930 

296.667 

40 

253.163 

494.722 

217.032 

424.048 

189.939 

371.042 

168.870 

329.815 

152.022 

296.833 

41 

253.316 

495.000 

217.163 

424.286 

190.054 

371.250 

168.972 

330.000 

152.114 

297.  COO 

42 

253.464 

495.278 

217.290 

424.524 

190.165 

371.458 

169.071 

330.185 

152.203 

297.167 

43 

253.612 

495.556 

217.417 

424.762 

190.276 

371.667 

169.170 

330.370 

152.292 

297.333 

44 

253.761 

495.833 

217.544 

425.000 

190.387 

371.875 

169.268 

330.556 

152.381 

297.500 

45 

253.909 

496.111 

217.671 

425.238 

190.499 

372.083 

169.367 

330.741 

152.470 

297.667 

46 

254.057 

496.389 

217.798 

425.476 

190.610 

372.292 

169.466 

330.926 

152.558 

297.833 

47 

254.205 

490  607 

217.925 

425.714 

190.721 

372.500 

169.565 

331.111 

152.647 

298.000 

48 

254.353 

496.944 

•318.052 

425.952 

190.832 

372.708 

169.664 

331.296 

152.736 

298.167 

49 

254.501 

497.22-3 

218.179 

426.190 

190.943372.917 

169.76-3 

331.481 

152.825 

298.333 

50 

254.649 

497.500 

218.306 

426.429 

191.054373.125 

169.861 

331.667 

152.914 

298.500 

51 

254.797 

497.778 

218.433 

426.667 

191.165373.333 

169.960 

331.852 

153.003 

298.667 

52 

254.945 

498.056 

218.560 

426.905 

191.276373.542 

170.059 

332.037 

153.092 

298.833 

53 

255.093 

498.333 

218.686 

427.143 

191.387373.750 

170.157 

332.222 

153.181 

299.000 

54 

255.246 

498.611 

218.818 

427.381 

191.502373.958 

170.259 

33-3.407 

153.273 

299.167 

55 

255.399 

498.889 

218.949 

427.619 

191.617374.167 

170.361 

332.593 

153.364 

299.333 

5(5 

255.547 

499.167 

219.076 

427.857 

191.728374.375 

170.460 

332  778 

153.453 

299.500 

57 

255.695 

499.444 

219.202 

428.095 

191.839374.583 

170.  559  1332.  963 

153.542 

299.607 

58 

255.843 

499.722 

219.3-39 

428.333 

191.950374.79-3 

170.6581333.148 

153.  631  1299.833|  59 

105 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


30° 

1°  Curve. 

2°  Curve. 
Tan.  |    Arc. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Are 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.       Arc. 

O 

1535.26 

3000.00 

767.658 

1500.00 

511.806 

1000.00 

383.889 

750.  000  307.  146  (500.  000 

1 

1586.15 

3001.67 

768  .  102 

1500.83 

512.102 

1000.5(5 

884.  HI 

750.417:307.323000.333 

2 

1537.04 

3003.33 

7(58.546 

1501.67 

512.3*$ 

1001.11 

>:8  1.333 

750.833307.501  600.667 

3 

1587.92 

3005.00 

768.990 

1502.50 

512.091 

10(11.07 

384..  555 

751.250307.679601.000 

4 

1538.81 

3006.67 

769.434 

1503.33 

512.99(1 

1  002.2,  ! 

384.778 

751.667 

307.856601.333 

5 

1539.70 

3008.33 

769.878 

1504.17 

513.280 

1002.78 

385.000 

752.083 

308.034601.607 

6 

1540.59 

3010.00 

770.322 

1505.00 

513.582 

1003.33 

385.222 

752.500 

308.212602.000 

7 

1541  51 

3011.67 

770.781 

1505.83 

513.888 

1003.89 

385.451 

752.917 

308.395602.333 

8 

1542.42 

3013.  M 

771.239 

1506.67 

514.194 

1004.44 

385  680 

753.333 

308.579602.067 

9 

1543.31 

3015.00 

771.683 

1507.50 

514.490 

1005.00 

385.902 

753.750 

308.756  603.000 

| 

10 

1544.20 

3016.67 

772.127 

1508.33 

514.786 

1005.56 

386.124 

754.167 

308.934603.333 

11 

1545.09 

3018.33 

772.571 

1509.17 

515.082 

1006.11 

386.346 

754.583 

309.112603.667 

12 

1545.97 

3020.00 

773.015 

1510.00 

515.378 

1006.67 

886.568 

755.000 

309.289,604.000 

13 

1546.8(5 

3021.67 

773.459 

1510.  as 

515.674 

1007.22 

386.790 

755.417 

309.467604.333 

14 

1547.75 

3023.33 

773  904 

1511.67 

515.970 

1007.78 

387.013 

755.8.33 

309.645604.667 

15 

1548.64 

3025.00 

774.348 

1512.50 

516.266 

1008.33 

387.235 

756.250 

309.822605.000 

16 

1549.53 

3026.67 

774.792 

1513.33 

516.562 

1008.89 

387.457 

756.007 

310.000:605.333 

17 

1550.44 

-J028.33 

775.250 

1514.17 

516.868 

1009.44 

387.686 

757.083 

310.183 

605.667 

18 

1551.3(5 

3030.00 

775.708 

1515.00 

517.173 

1010.00 

387.915 

757.500 

310.307 

606.000 

19 

1552.25 

3031.67 

776.153 

1515.83 

517.469 

1010.56 

388.137 

757.917 

310.544 

606.333 

20 

1553.14 

3033.33 

776.597 

1516.67 

517.765 

1011.11 

388.359 

758.333 

310.722 

606.667 

21 

1554.02 

3035.00 

777.041 

1517.50 

518.061 

1011.67 

388.581 

758.750 

310.900 

607.000 

22 

1554.91 

3036.6; 

777.485 

1518.33 

518.358 

1012.22 

388.803 

759.167 

311.077 

607.333 

23 

1555.80 

3038.33 

777.929 

1519.17 

518.654 

1012.78 

389.025 

7'59.583 

311.255 

607.667 

24 

1556.69 

3040.00 

778.37'3 

1520.00 

518.950 

1013  33 

389.248 

760.000 

311.488 

008.000 

25 

1557.61 

3041.  (57 

778.831 

1520.83 

519.255 

1013.89 

389.477 

760.417 

311.616 

608.333 

26 

1558.52 

W43.33 

779.290 

1521.67 

519.561 

1014.44 

389.706 

760.833 

311.800 

608  667 

27 

1559.41 

3045.00 

779.734 

1522.50 

519.857 

1015.00 

389.928 

761.250 

311.977 

609.000 

28 

1560.30 

3046.67 

780.178 

1523.33 

520.153 

1015.56 

390.150 

761.067 

312.155 

609.333 

29 

1561.19 

3048.33 

780.622 

1524.17 

520.449 

1016.11 

390.372 

762.083 

312.333 

609.607 

30 

1562.07 

3050.00 

781.066 

1525.00 

520.745 

1016.67 

390.594 

762.500 

312.510 

010.000 

31 

1562.96 

3051.67 

781.510 

1525.83 

521.041 

1017.22 

390.816 

762.917 

312.688 

610.333 

32 

1563.85 

3053.33 

781.954 

1526.67 

521.337 

1017.78 

391.038 

763.  aS3 

312.866 

610.667 

33 

1564.77 

3055.00 

782.412 

1527.50 

521.643 

1018.33 

391.268 

763.750 

313.049 

611.000 

34 

1565.68 

3056.67 

782.871 

1528.  as 

521.948 

1018.89 

391.497 

764.167 

313.232 

611.333 

35 

1566.57 

3058.33 

783.315 

1529.17 

522.245 

1019.44 

391.719 

764.583 

313.410 

611.667 

36 

1567.46 

3060.00 

783.759 

1530.00 

522.541 

1020.00 

391.941 

765.000 

313.588 

612.000 

37 

1568.35 

3061.67 

784.203 

1530.83 

522.837 

1020.56 

392.163 

765.417 

313.765 

612.333 

38 

1569.24 

3063.33 

784.647 

1531.67 

523.1  as 

1021.11 

392.385 

765.833 

313.943 

612.667 

39 

1570.12 

3065.00 

785.091 

1532.50 

523.429 

1021.87 

392.607 

766.250 

314.121 

613.000 

40 

1571.01 

3066.67 

785.535 

1533.33 

523.725 

1022.22 

392.829 

766.667 

314.299 

613.333 

41 

1571.93 

3068.33 

785.994 

1534.17 

o24.030 

1022.78 

393.059 

767.083 

314.482 

613.667 

42 

1572.85 

3070.00 

786.452 

1535.00 

524.336 

1023.33 

393.288 

767.500 

314.665 

614.000 

43 

1573.73 

3071.67 

786.896 

1535.83 

524.632 

1023.89 

393.510 

767.917 

3M.843 

614.333 

44 

1574.62 

3073.33 

787.340 

1536.67 

524  928 

1024.44 

393.73* 

768.383 

315.021 

614.007 

45 

1575.51 

3075.00 

7'87.784 

1537.50 

525.224 

1025.00 

393.954 

768.750 

315.198 

615.000 

46 

1576.40 

3076.67 

788.228 

1538.33 

525.520 

1025.56 

394.176 

769.167 

315.376,615.333 

47 

1577.32 

3078.33 

788.687 

1539.17 

525.826 

1026.11 

304.405 

769.583 

315..  559:  6  15.  007 

48 

1578.23 

3080.00 

789.145 

1540.00 

5-26.132 

1026.67 

394.634 

770.000 

315.743  010.000 

49 

1579.12 

3081.67 

789.589 

1540.83 

526.428 

1027.22 

394.857 

770.417 

315.920 

616.333 

50 

1580.01 

3083.33 

790.033 

1541.67 

526.724 

1027.78 

395.079 

770.833 

:<1  0.008 

010  007 

51 

1580.90 

3085.00 

790.477 

1542.50 

527.020 

1028.33 

395.301 

771.250 

3H>  276 

(517  000 

52 

1581.78 

3086.67 

790.921 

15-13.33 

527.316 

1028.89 

395.523 

771.607 

3;  6.  454 

017.333 

53 

1582.67 

30S8.33 

791.365 

1544.17 

527.012 

1029  44 

305.745 

77..  083 

3  Hi.  031 

017.007 

54 
55 

1583.56 
1584.48 

3090.00 
3091.67 

791.809 

792.268 

1545.00 
1545.83 

527.908 
528.214 

1030.00 

1030.56 

395.967772.500 
390.196772.917 

316.800 
310  002 

518  000 
51  K.  333 

56 

15S5.39 

3093.  33 

792.726 

154(5.67 

528.519 

J031.11 

300  425  7  73.  333!  3  1  7J7<; 

sis.  007 

57 

1586.28 

3095.00 

793.170 

1547.50 

528.815 

1031.67 

39(U)47  77  3.  7'.5()  3  17.  3:.:! 

519.000 

58 

1587.17 

•3096.67 

793.614 

1548.33 

529.111 

1032.22 

390.869  774.1(17 

317.531 

>19.3:-:3 

59 

1588.06 

3098.33 

794.058  1549.17 

529  407 

1032.78 

397.092774.583 

317.709 

019.067 

106 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

3O° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
1  92.061 

Arc. 

375.000 

Tan. 
170.756 

Arc. 
333.333 

Tan. 
153.720 

Arc. 

M. 

255.991 

500.000 

219.456 

428.571 

300.000 

O 

250.139 

500.278 

219.583 

428.810 

192.172 

375.208 

170.855 

3:33.519 

153.809 

300.167 

1 

250.288 

500.556 

219.710 

429.048 

192.283 

375.417 

170.954 

333.704 

153.898 

300.333 

2 

256.436 

500.833 

219.837 

429.286 

192.394 

375.625 

171.053 

333.889 

153.987 

300.500 

3 

256.584 

501.111 

219.964 

429.524 

192.506 

375.833 

171.152 

334.074 

154.076 

300.667 

4 

256.732 

501.389 

220.091 

429.762 

192.617 

376.042 

171.250 

334.259 

154.165 

300.833 

5 

256.880 

501.667 

220.218 

430.000 

192.728 

376.250 

171.349 

334.444 

154.254 

301.000 

6 

857.083 

501.944 

220.349 

430.2138 

192.842 

376.458 

171.451 

334.630 

154.346 

301.167 

7 

257.186 

502.222 

220.480 

430.476 

192.957 

376.667 

171.553 

334.815 

154.437 

301.333 

8 

257.334 

502.500 

220  ..607 

430.714 

193.068 

376.875 

171.652 

335.000 

154.526 

301.500 

9 

257.482 

502.778 

220.734 

430.952 

193.179 

377.083 

171.751 

335.185 

154.615 

301.667 

1O 

257.630 

503.056 

220.861 

431.190 

193.290 

377.292 

171.849 

335.370 

154.704 

301.833 

11 

257.778 

503.333 

220.988 

431.429 

193.402 

377.500 

171.948 

335.556 

154.793 

302.000 

12 

257.926 

503.611 

221.115 

431.667 

193.513 

377.708 

172.047 

335.741 

154.882 

302.167 

13 

258.074 

503.889 

221.242 

431  .  905 

193.624 

377.917 

172.146 

335.926 

154.971 

302.333 

14 

258.222 

504.167 

221.369 

432.143 

193.735 

378.125 

172.244 

336.111 

155.060 

302.500 

15 

258.370 

504.444 

221.496 

432.381 

193.846 

378.333 

172.343 

336.296 

155.149 

302.667 

16 

258.523 

504.72^ 

221.627 

432.619 

193.961 

378.542 

172.445 

336.481 

155.240 

302.833 

17 

258.676 

505.000 

221.758 

432.857 

194.075 

378.750 

172.547 

336.667 

155.332 

303.000 

18 

258.824 

505.278 

221.885 

433.095 

194.186 

378.958 

172.646 

336.852 

155.421 

303.167 

19 

258.972 

505.556 

222.012 

433.333 

194.298 

379.167 

172.745 

337.037 

155.510 

303.333 

20 

259.120 

505.833 

222.139 

433.571 

194.409 

379.375 

172.844 

337  222 

155.599 

-303.500 

21 

259.268 

506.111 

222.266 

433.810 

194.520 

379.583 

172.942 

33?!  407 

155.688 

303.667 

22 

259.416 

506.389 

222  393 

434.048 

194.631 

379.792 

173.041 

337.593 

155.777 

303.833 

23 

259  564 

506.667 

222.519 

434.286 

194.  742 

380.000 

173.140 

337.778 

155.866 

304.000 

24 

259.717 

506.944 

222.651 

434.524 

194.857 

380.208 

173.242 

337.963 

155.958 

304.167 

25 

259.870 

507.222 

222.782 

434.762 

194.971 

380.417 

173.344 

338.148 

156.049 

304.333 

26 

260.018 

507.500 

222.909 

435.000 

195.082 

380.625 

173.443 

338.333 

156.138 

304.500 

27 

260.166 

507.778 

223.035 

435.238 

195.193 

380.833 

173.541 

338.519 

156.227 

304.667 

28 

260.314 

508.056 

223.162 

435.476 

195.305 

381.042 

173.640 

338.704 

156.316 

304.833 

29 

260.462 

508.333 

223  289 

435.714 

195.416 

381.250 

173.739 

338.889 

156.405 

305.000 

30 

260.611 

508.611 

223.416 

435.952 

195.527 

381.458 

173.838 

339.074 

156.494 

305.167 

31 

260.759 

508.889 

223.543 

436.190 

195.638 

381.667 

173.936 

339.259 

156.583 

305.333 

32 

260.911 

509.167 

223.674 

436.429 

195.753 

381.875 

174.038 

339.444 

156.675 

305.500 

33 

261.064 

509.444 

223.805 

436.667 

195.867 

382.083 

174.140 

339.630 

156.766 

305.667 

34 

261.212 

509.722 

223.932 

436.905 

195.978 

382.292 

174.239 

339.815 

156  855 

305.833 

35 

261.361 

510.000 

224.059 

437.143 

196.089 

382.500 

174.338 

340.000 

156.944 

306.000 

36 

261.509 

510.278 

224.186 

437.381 

196.201 

382.708 

174.437 

340.185 

157.033 

306.167 

37 

261.657 

510.556 

224.313 

437.619 

1%  312 

382.917 

174.535 

340.370 

157.122 

306.333 

28 

261.805 

510.833 

224.440 

437.857 

196.423 

383.125 

174.634 

340.556 

157.211 

3C6.500 

39 

261.953 

511.111 

224  567 

438.095 

196.534 

383.333 

174.733 

340.741 

157.300 

306.667 

40 

262.106 

511.389 

224.698 

438.  333 

196.649 

383.542 

174.835 

340.926 

157.392 

306  833 

41 

262.259 

511.667 

224.829 

438.571 

196.763 

383.750 

174.937 

341.111 

157.484 

307.000 

42 

262.407 

511.944 

224.956 

438.810 

196.874 

383  958 

175.036 

341.296 

157.573 

307.167 

43 

262.5.55 

512.222 

225.083 

439.048 

196.985 

384.167 

175.134 

341.481 

157.661 

307.333 

44 

262.703 

512.500 

225.210 

439.286 

197.097 

384.375 

175.233 

341.667 

157.750 

307.500 

45 

262.851 

512.778 

225.337 

439.524 

197.208 

384.583 

175.332 

341.852 

157.839 

307.667 

46 

263.004 

513.056 

225.468 

439.762 

197.322 

384.792 

175.434 

342.037 

157.931 

307.833 

47 

263.157 

513.333 

225.599 

440.000 

197.437 

385.000 

175.536 

342  222 

158.023 

308.000 

48 

263.305 

513.611 

225.726 

440.238 

197.548 

385.208 

175.635 

342.407 

158.112 

308.167 

49 

263.453 

513.889 

225.  853 

440.476 

197.659 

385.417 

175.734 

342.593 

158.201 

308.333 

50 

263.601 

514.167 

2:25.980 

440  714 

197.770 

385.625 

175.832 

342.778 

158.290 

308.500 

51 

263.749 

514.444 

226.107 

440.952 

197.881 

385.833 

175.931 

342.963 

158.379 

308.667 

52 

263  897 

514.722 

226.234 

441.190 

197.993 

386.042 

176.030 

343.148 

158.467 

'308.833 

53 

264.045 

515.000 

226.361 

441.429 

198.104 

386.250 

176.129 

343.333 

158.556 

309.000 

54 

264.198 

515.278 

226.492 

441.667 

198.218386.458 

176.231 

343.519 

158.648 

309.167 

55 

264.351 

515.556 

226.623 

441.905 

198.  333  1386.  667 

176  333 

343.704 

158.740 

309.333 

56 

264.499 

515.833 

226.750 

442.143 

198.444336.875 

176.431 

343.889 

158.829 

309.500 

57 

264.647 

516.111 

226.877 

442.381 

198.555387.083 

176.530 

344.074 

158.918 

309.667 

58 

264.795 

516.389 

227.004 

442.619 

198.666387.292 

176.629 

344.259 

159.007 

309.833 

59 

107 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


31° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

1588.95 

3100.00 

794.502  1550.00 

529.103 

1033.33 

397.314 

715.000 

317.8S6  6^U.OOO 

1 

1  589.  8(5 

3101.67 

794.961 

1550.83 

530.009 

1033.89 

397.543 

775.417 

318.070 

020.333 

2 

1590.78 

3103.33 

795.419 

1551.67 

530.315 

1034.44 

397.772 

775.833 

318.253 

620.667 

3 

1591.07 

3105.00 

795.863 

1552.50 

530.611 

1035.00 

397.994 

776.250 

318.431 

621.000 

4 

1593.56 

3106.67 

796.307 

1553.33 

530.907 

1035.56 

398.216 

776.667 

318.609 

621.333 

5 

1593.44 

3108.33 

796  751 

1554.17 

531.203 

1036.11 

398.438 

777.083 

318.786 

021.667 

6 

1594.33 

3110.00 

797^195 

1555.00 

531.499 

1036.67 

398.600 

777.500 

318.964 

G--22.000 

7 

1595.25 

3111.67 

797.654 

1555.83 

531  .  804 

1037.22 

398.890 

777.917 

319.147 

622.333 

8 

1596.17 

3113.33 

798.112 

1556.67 

532.110 

1037.78 

399.119 

778.333 

319.331 

622.607 

9 

1597.05 

3115.00 

798.556 

1557.50 

532.406 

1038.33 

399.341 

778.750 

319.508 

623.000 

1O 

1597.94 

3116.67 

799.000 

1558.33 

532.702 

1038.89 

399.563 

779.167 

319.686 

623.333 

11 

1598.86 

3118.33 

799.459 

1559.17 

533  COS 

1039.41 

399.792 

779.583 

319.869 

623.667 

12 

1599.78 

3120.00 

799.91? 

1560.00 

533.313 

1040.00 

400.021 

780.000 

3-20.053 

624.000 

13 

1600.66 

3121.67 

800.3(51 

1560.83 

533.609 

1040.56 

400.243 

780.417 

320.231 

624.333 

14 

1601.55 

3123.33 

800.805 

1561.67 

533.906 

1041.11 

400.406 

780.833 

320.408 

624.667 

15 

1602.44 

3125.00 

801.249 

1562.50 

53  1.  202 

1011.67 

400.688 

781.250 

320.586 

625.000 

16 

1603.33 

3126.67 

801.693 

1563.33 

534.498 

1012.22 

400.910 

781  .  667 

320.764 

625.333 

17 

1604.24 

3128.33 

802.152 

1564.17 

534.803 

1042.78 

401  .  139 

782.083 

320.947 

625.667 

18 

1605.16 

3130.00 

802.610 

1565.00 

535.109 

1043.33 

401  .  368 

782.500 

321.130 

626.000 

19 

1606.05 

3131.67 

803.054 

1565.83 

535.405 

1013.89 

401.590 

;  82.  917 

321.308 

626.333 

20 

1606.91 

3133.33 

803.498 

1566.67 

535.701 

1044.41 

401.812 

783.333 

321.486 

626.667 

21 

1607.83 

3135.00 

803  942 

1567.50 

535.997 

1015.00 

403.031 

783.750 

321.663 

627.000 

22 

1608.71 

3136.67 

804.386 

1568.33 

536.293 

1045.56 

402  250 

1-84.161 

321.841 

627.333 

23 

1609.63 

3138.33 

804.845 

1569.17 

536.599 

1046.11 

402.486 

784.583 

322.024 

627.667 

34 

1610.55 

3140.00 

805.303 

1570.00 

536.  90  J 

1040.07 

402.715 

785.000 

322.208 

628.000 

25 

1611.44 

3141.67 

805.747 

1570.83 

387.300 

1047.22 

402.937 

785.417 

322.386 

628.333 

26 

1612.32 

3143.33 

806.191 

1571.67 

537.497 

1047.78 

403.159 

785.833 

322.563 

628.667 

21 

1613.24 

3145.00 

806.650 

1572.50 

537.802 

1048.33 

103.388 

786.250 

322.747 

629.000 

28 

1614.16 

3146.67 

807.108 

1573.33 

538.108 

1048.89 

403.617 

786.667 

322.930 

629.333 

29 

1615.05 

3148.33 

807.552 

1574.17 

538.404 

1049.44 

403.839 

787.083 

323.108 

629.667 

3O 

1615.93 

3150.00 

807.996 

1575.00 

538.700 

1050.00 

404.06-2 

787.500 

323.285 

630.000 

31 

1616.82 

3151.67 

808.440 

1575.83 

533.996 

1050.56 

404.284 

787.917 

323  463 

630.333 

32 

1617.71 

3153.33 

808.884 

1576.67 

539.292 

1051.11 

404.506 

788.333 

323.641 

630.667 

33 

1618.63 

3155.00 

809.343 

1577.50 

539.598 

1051.67 

404.735 

788.750 

323.824 

631.000 

34 

1619.54 

3156.67 

809.801 

1578.33 

539.903 

1052.22 

404.964 

789.107 

324.008 

631.333 

35 

1620.43 

3158.33 

810.245 

1579.17 

540.199 

1052.7H 

405.186 

789.583 

324.185 

631.667 

36 

1621.32 

3160.00 

810.689 

1580.00 

540.495 

1053.33 

405.408 

790  000 

324.363 

632.000 

37 

1622.24 

3161.67 

811.148 

1580.83 

540.801 

1053.89 

405.638 

790.41? 

3-24.546 

032.333 

38 

1623.15 

3163.33 

811.606 

1581.67 

541.10"7 

1054.44 

405.867 

790.832 

324.730 

632.667 

39 

1624.04 

3165.00 

812.050 

1582.50 

541.403 

1055.00 

\  06.  089 

791.250 

324.907 

033.000 

40 

1624.93 

3166.67 

812.491 

15S3.P.3 

541.699 

1055.56 

406.311 

791.667 

325.085 

033.333 

41 

1625.82 

3168.33 

81  2.  93  s 

1584.17 

541.995 

1056.11 

406.533  792.083 

3-25.263 

033.667 

43 

1626.70 

3170.00 

813.382 

1585.00 

542.291 

1056.67 

406.755792.500 

325.440 

034.000 

43 

1627.62 

3171.67 

813.841 

1585.83 

542.596 

1057.22 

406.  984  '792.  91  7 

325.624 

034.333 

44 

1628.54 

3173.33 

814.299 

1586.67 

542.902 

1057.78 

407.213:793.333 

325.807 

034.607 

45 

1629.43 

3175.00 

814.743 

1587.50 

543.198 

1058.33 

407.436,793.750 

325.985 

035.000 

46 

1630.31 

3176.67 

815.187 

1588.33 

543.494 

1058.89 

407.  058i  794.  167 

326.108 

035.333 

47 

1631.23 

3178.33 

815.646 

1589.17 

543.800 

1059.44 

407.  887!  794.  583 

326.346 

035.007 

48 

1632.15 

3180.00 

816.104 

1590.00 

544.105 

1060.00 

408.  1  16  '  795.  000 

326.529 

036.000 

49 

1633.04 

3181.67 

816.548 

1590.83 

544.401 

1060.56 

408.  338:795.  417 

326.707 

636.333 

50 

1633.92 

3183.33 

816.992 

1591.67 

544.698  1061.11 

408.560795.833 

326.885 

636.667 

51 

1634.84 

3185.00 

817.450 

1592.50 

545.003  1061.67 

408.789 

79G.250 

327.068 

037.000 

52 

1635.76 

3186.67 

817.  909  11593.  33 

545.309  1062.22 

409.019 

796.607 

327.251 

037.333 

53 

1636.65 

3188.33 

818.35311594.17 

545.605  1062.78 

409.241  797.083 

327.429 

037.007 

54 

1637.53 

3190.00 

S18.797'  1595.00 

545.901  1063.33 

409.  463  5  797.  500 

227.607 

038.000 

55 

1638.45 

3191.67 

319.255  1595.83 

546.20(5  1063.89 

409.692:797.917 

327.790 

038.333 

56 

1639.37 

3193.33 

819.714  1596.67 

546.512  1064.44 

409  92  1  798  .  333  327  .  974 

038.607 

57 

1640.26 

3195.00 

820.15811597.50 

546.808  1065.00 

410.143  T98.  750  328.  151 

039.000 

58 

1641.14 

3196.67 

820.602 

1598.33 

547.104  1005.56 

410.305  799.167 

328.329039.333 

59 

1642.06 

3198.33 

821.060 

1599.17 

547.410  1066.11 

410.595,799.583 

328.  512  1039.  607 

108 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

31° 

Tan. 
204.943 

Arc. 
516.667 

Tan. 

227.131 

Arc. 

Tan. 

Are. 

Tan. 

Arc. 

Tan. 

15970~96 

Arc. 

310.000 

M. 

~o 

442.857 

198.777 

387.500 

176.758 

344.444 

265.096 

516.944 

227.262 

443.095 

198.892 

387.708 

176.830 

344.630 

159.187 

310.167 

i 

265.249 

517.222 

227.393 

443.333 

199.007 

387.917 

176.932 

344.815 

159.279 

310.333 

2 

265.397 

517.500 

227.520 

443.571 

199.118 

388.125 

177.030 

345.000 

159.368 

310.500 

3 

265.545 

517.778 

227.647 

443.810 

199.229 

388.333 

177.129 

345.185 

159'.  457 

310.667 

4 

265.693 

518.056 

227.774 

444.048 

199.340 

388.542 

177.228 

345.370 

159  546 

310  833 

5 

965.841 

518.333 

227.900 

444.286 

199.451 

388.750 

177.327 

345.556 

159.635 

311.000 

6 

265.994 

518.611 

228.031 

444.524 

199.566 

388.958 

177.429 

345.741 

159.727 

311.167 

7 

266.147 

518.889 

228.163 

444.762 

199.681 

389.167 

177.531 

345.926 

159.819 

311.333 

8 

266.295 

519.167 

228.289 

445.000 

199.792 

389.375 

177.629 

346.111 

159.907 

311.500 

9 

266.443 
266.596 

519.441 
519.722 

228.416 
228.547 

445.238 
445.476 

199.903 
200.017 

389.583 
389.792 

177.728 
177.830 

346.296 
346.481 

159.996 
160.088 

311  667 
311.833 

10 
11 

266.749 

520.000 

228.679 

445.714 

200.132 

390.000 

177.932 

346.667 

160.180i312.000 

12 

266.89? 

52  J.  278 

228.805 

445.952 

200.243 

390.208 

178.031 

346.852 

160.269 

312.167 

13 

267.045 

520.556 

228.932 

446.190 

200.354 

390.417 

178.130 

347.037 

160.358 

312.333 

14 

267.193 

520.833 

229.059 

446.429 

200.465 

390.625 

178.228 

347.222 

160.447 

312.500 

15 

267.341 

521.111 

229.186 

446.667 

200.  57( 

390.833 

178.327 

347.407 

160.536 

312.667 

16 

267.494 

521.389 

229.  31  7!  446.  905 

200.691 

391.042 

178.429 

347.593 

160.627 

312.833 

17 

267.647 

521.667 

2^9.448 

447.143 

200.806 

391.250 

178.531 

347.778 

160.719 

313.000 

18 

267.795 

521.944 

229.575 

447.381 

200.917 

391.458 

178.630 

347.963 

160.808 

313.167 

19 

267.943 

522.222 

229.702 

447.619 

201.028 

391.667 

178.729 

348.148 

160.897 

313.333 

20 

268.091 

522.500 

229.829 

447.857 

201.139 

391.875 

178.827 

348.333 

160.986 

313.500 

21 

268.239 

522.77'8 

229.956 

448.095 

201.250 

392.083 

178.926 

348.519 

161.075 

313.667 

22 

268.392 

523.056 

230.087 

448.333 

201.365 

392.292 

179.028 

348.704 

161.167 

313.833 

23 

268.545 

523.333 

2:30.218 

448.571 

201  .480 

392.500 

179.130 

348.889 

161.258 

314.000 

24 

268.693 

523.611 

230.345 

448.810 

201.591 

392.708 

179.229 

349.074 

161.347 

314.167 

25 

268.841 

523.889 

230.472 

449.048 

201.702 

392.917 

179.328 

349.259 

161.436 

314.333 

26 

268.994 

524.167 

230.603 

449.286 

201.817 

393.125 

179.430 

349.444 

161.528 

314.500 

27 

269.147 

524.444 

•J30.734 

449  524 

201.931 

393.333 

179.532 

349.630 

161.620 

314.667 

28 

269.295 

524  722 

230.861 

449.762 

202.042 

393.542 

179.630 

349.815 

161.709 

314.833 

29 

269.443 

525.000 

230.988 

450.  OCO 

202.153 

393.750 

179.729 

350.000 

161.798 

315.000 

30 

269.591 

525.278 

231.115 

450.238 

202.265 

393.958 

179.828 

350.185 

161.887 

315.167 

31 

269.739 

525.556 

231.242 

450.476 

202.376 

394.167 

179.927 

350.370 

161.976 

315.333 

32 

269.892 

525.833 

231.373 

450.714 

202.490 

394.375 

180.029 

350.556 

162.067 

315.500 

33 

270.045 

526.111 

231.504 

450.952 

202.605 

394.583 

180.131 

350.741 

162.159 

315.667 

34 

270.193 

526.389 

881.681 

451.190 

202.716 

394.792 

180.229 

350.926 

162.248 

315.833 

35 

270.341 

526.667 

231.758 

451.429 

202.827 

395.000 

180.328 

351.111 

162.337 

316.000 

36 

270.494 

526.944 

231.889 

451.667 

202.942 

395.208 

180.430 

351.296 

162.429 

316.167 

37 

270.647 

527.222 

232.020 

451.905 

203.057 

395.417 

180.532 

351.481 

162.521 

316.333 

38 

270.795 

527.500 

232.147 

452.143 

203.168 

395.625 

180.631 

351.667 

162.610 

316.500 

39 

270.943 

527.778 

232.274 

452.381 

203.279 

395.833 

180.730 

351.852 

162.698 

316.667 

40 

271.091 

528.056 

332.401 

452.619 

203.390 

396.042 

180.828 

352.037 

162.787 

316.833 

41 

271.239 

528.333 

232.5-<8 

452.857 

203.501 

396.250 

180.927 

352.222 

162.876 

317.000 

42 

271.392 

528.611 

232.659 

453.095 

203.616 

396.458 

181.029 

352.407 

162.968 

317.167 

43 

271.545 

528.889 

.232.790 

453.333 

203.730 

396.667 

181.131 

352.593 

163  060 

317.333 

44 

271.693 

529.167 

232.917 

453.571 

203.841 

396.875 

181.230 

352.778 

163.149 

317.500 

45 

271.841 

529.444 

233.044 

453.810 

203.953 

397.083 

181.329 

352.963 

163.238 

317.667 

40 

271.994 

529.722 

233.175 

454.048 

204.067 

397.292 

181.431 

353.148 

163.329 

317.833 

47 

272.147 

530.000 

<233.306 

454.286 

204.182 

397.500 

181.533 

353.333 

163.421 

318.000 

48 

272.295 

530.278 

233.433 

454.524 

204  293 

397.708 

181.631 

353.519 

163.510 

318.167 

49 

272  443 

^30.556 

233.560 

454.762 

204.404 

397.917 

181.730 

353.704 

163.599 

318.333 

5O 

272  !  696 

530.833 

233.691 

455.000 

204.519 

398.125 

181.832 

353  889 

163.691 

318.500 

51 

272.749 

531.111 

233.822 

455.238 

204.633 

398.333 

181.934 

354.074 

163.783 

318.667 

52 

272.897531.389 

233.949 

455.476 

204.745 

398.542 

182.033 

354,259 

163.872 

318.833 

53 

273.045531.667 

234.076 

455.714 

204.856 

398.750 

182.132 

354.444 

163.9(1 

319.000 

54 

273.1981531.944 

234.207455.952 

204.970 

398.958 

182  234 

354  630 

164.052 

'319.167 

55 

273.  350  1532.222 

234.338450.190 

205.085 

399.167 

182.336 

354.815 

164.144 

319.333 

5C> 

273.498532.500 

234.  465'456.  429 

205.196 

399.375 

182.434 

355.000 

164.233 

319.500 

57 

273.6471532.778 

234.592456.667 

205.307 

399.583 

182.533 

355.  1R5 

164.322 

319.667 

58 

273.  7  99  1533.056 

234.723456.905 

205.422 

399.792 

182.635 

355.370 

164.414 

319.833 

59 

109 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


32° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 
~~O" 

Tun. 
T642.98 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

3200.  00 

821.519 

1600.00 

547.715 

1066.67 

410.824 

800.000 

328.696 

640.000 

1 

1643.87 

3.  '01.  67 

821.963 

1600.83 

548.012 

1067.22 

411.046 

800.417 

328.873 

640.333 

3 

1644.75 

3203.33 

822.407 

1601.67 

548.308 

1067.78411.208 

800.833 

329.051 

640.667 

3 

1645.67 

3205.00 

822.865 

1602.50 

548.613 

1068.33 

411.497 

801.250 

329.235 

641.000 

4 

1646.59 

3206.67 

823.324 

1603.  33 

548.919 

1068.89 

411.726 

801.667 

329.418 

641.333 

5 

1647  47 

3208.33 

823.768 

1604.17 

549.215 

1069.44 

411.919 

802.083 

329.590 

641.667 

6 

1648.315 

3210.00 

824.212 

1605.00 

549.511 

1070.00 

412.171 

802.500 

329.773 

642.000 

7 

1649.25 

3211.67 

824.656 

1605.83 

549.807 

1070.56 

412.393 

802.917 

329.951 

642.333 

8 

1650.1-1 

3213.33 

825.100 

1606.67 

550.103 

1071.11 

412.615 

803.333 

330.129 

642.667 

9 

1651.06 

3215.00 

825.558 

1607.50 

550.409 

1071.67 

412.844 

803.750 

330.312 

643.000 

10 

1651.97 

3216.67 

826.017 

1608.33 

550.714 

1072.22 

413.073 

804.167 

330.495 

643.333 

11 

1652.89 

3218.33 

826.475 

1609.17 

551.020 

1072.78 

413.302 

804.583 

330.679 

643.607 

13 

1653.81 

3220.00 

820.933 

1610.00 

551.325 

1073.33 

413.532 

805.000 

330.862 

644.000 

13 

1654.69 

3221.67 

827.377 

1610.83 

551.622 

1073.89 

413.754 

805.417 

331.040 

644.333 

14 

1655.58 

3223.33 

827.822 

1611.67 

551.918 

1074.44 

413.976 

805.833 

331.218 

644.667 

15 

1656.50 

3225.00 

828.280 

1612.50 

552.223 

1075.00 

414.205 

806.250 

331.401 

645.000 

10 

1657.42 

3226.67 

828.738 

1613.33 

552.529 

1075.56 

414.434 

806.667 

331.584 

645.333 

17 

1658.30 

3228.33 

829.182 

1614.17 

552.825 

1076.11 

414.656 

807.083 

331.762 

645.667 

18 

1659.19 

3230.00 

829.626 

1615.00 

553.121 

1076.67 

414.878 

807.500 

331.940 

646.000 

19 

1660.11 

3231.67 

830.085 

1615.83 

553.427 

1077.22 

415.108 

807.917 

332.123 

646.333 

30 

1661.03 

3233.33 

830.543 

1616.67 

553.732 

1077.78 

415.337 

808.333 

332.307 

646.667 

21 

1661.91 

3235.00 

830.987 

1617.50 

554.028 

1078.33 

415.559 

808.750 

332.484 

647.000 

22 

1662.80 

3236.67 

881.481 

1618.  as 

554.324 

1078.89 

415.781 

809.167 

332.662 

647.333 

23 

1663.72 

3238.33 

831.890 

1619.17 

554.630 

1079.44 

416.010 

809.583 

332.845 

647.667 

24 

1664.64 

3240.00 

832.348 

1620.00 

554.936 

1080.00 

416.239 

810.000 

333.029 

648.000 

25 

1665.52 

3241.67 

832.792 

1620.83 

555.232 

1080.56 

416.461 

810.417 

333.206 

648.333 

26 

1666.41 

3243.33 

833.236 

1621.67 

555.528 

1081.11 

416.081 

810.833 

333.881 

648.667 

37 

1667.33 

3245.00 

833.695 

1622.50 

555.833 

1081.67 

416.913 

811.250 

388.667 

649.000 

28 

1668.24 

3246.67 

834.153 

1623.33 

556.139 

1082.22 

417.142 

811.667 

333.751 

649.333 

29 

1669.13 

3248.33 

834.597 

1624.17 

556.435 

1082.78 

417.364 

812.083 

333.929 

649.667 

30 

1670.02 

3250.00 

835.041 

1625.00 

556.731 

1083.33 

417.586 

812.500 

334.106 

650.000 

31 

1670.94 

3251.67 

835.500 

1625.83 

557.037 

1083.89 

417.815 

812.917 

334.290 

650.333 

32 

1671.85 

3253.33 

835.958 

1626.67 

557.342 

1084.44 

418.045 

813.333 

334.473 

650.667 

33 

1672.74 

3255.00 

836.402 

1627.50 

557.638 

1085.00 

418.267 

813.750 

334.651 

651.000 

34 

1673.63 

3256.67 

836.846 

1628.33 

557.934 

1085.56 

418.489 

814.167 

334.828 

651.333 

35 

1674.55 

3258.33 

837.304 

1629.17 

558.240 

1086.11 

418.718 

814.583 

135.012 

651.667 

36 

1675.46 

3260.00 

837.763 

1630.00 

558.546 

1086.67 

418.947 

815.000 

335.195 

652.000 

37 

1676.38 

3261.67 

838.221 

1630.83 

558.851 

1087.22 

419.176 

815.417 

335.379 

652.333 

38 

1677.30 

3263.33 

838.680 

1631.67 

559.157 

1087.78 

419.406 

815.833 

835.563 

652.667 

39 

1678.19 

3265.00 

839.124 

1632.50 

559.453 

1088.  33 

419.628 

816.250 

335.740 

653.000 

4O 

1679.07 

3266.67 

839.568 

1633.33 

559.749 

1088.89 

419.850 

816.667 

335.917 

653.333 

41 

1679.99 

3268.33 

840.026 

1634.17 

560.055 

1089.44 

420.079 

817.083 

336.101 

653.667 

43 

1680.91 

3270.00 

840.485 

1635.00 

560.360 

1090.00 

420.308 

817.500 

336.284 

054.000 

43 

1681.80 

3271.67 

840.929 

1635.83 

560.656 

1090.50 

420.530 

817.917 

336.462 

654.  333 

44 

1682.68 

3273.33 

841.373 

1636.67 

560.952 

1091.11 

420.752 

818.333 

336.640 

654.667 

45 

1683.60 

3275.00 

841.  as  i 

1637.50 

561.258 

1091.67 

420.982 

818.750 

336.823 

655.000 

46 

1684.52 

3276.67 

842.289 

1638.33 

561.564 

1092.22 

421.211 

819.167 

337.006 

655.833 

47 

1685.43 

3278.33 

842.748 

1639.17 

561.869 

1092.78421.440 

'819.583 

337.190 

655.667 

48 

1686.35 

3280.00 

843.206 

1610.00 

562.175 

1093.33421.669 

820.000 

337.373 

656.000 

49 

1687.24 

3281.67 

843.650 

1640.83 

562.471 

1093.89 

421.891 

820.417 

337.551 

656.333 

5O 

1688.13 

3283.33 

844.094 

1641.67 

562.767 

1094.44 

422.113 

820.833 

337.728 

656.607 

51 

1689  04 

3285.00 

844.553 

1642.50 

563.072 

1095.00422.343 

821.250 

337.912 

657.000 

53 

1689.96 

3286.67 

845.011 

1643.33  563.378 

1095.56422.572 

821.667 

338.095 

657.333 

53 

1690.85 

3288.33 

845.455 

1644.17563.674 

1096.lli422.794 

822.083 

338.273 

657.667 

54 

1691.74 

3290.00 

845.899 

1645.00  563.970  1096.67:423.016 

822.500 

338.451 

658.000 

55 

1692  65 

3291.67 

846.358 

1645.83  564.276  1097.22  423.245 

822.917 

338.634 

658.333 

56 

1693.57 

3293.33 

846.816 

1  646  .  67  564  .  58  1  1  1  097  .  78  423  .  475 

823.333 

338.817 

658.667 

57 

1694.49 

3295.00 

847.274 

1647.50  564.887  1098.33  423.704 

823.750 

339.001 

659.000 

58 

1695.40 

3296.67 

847.733 

1648.33  565.  193  1  1098.  89  423.933 

824.167 

339.184 

659.333 

59 

1696.29 

3298.33 

848.177 

1649.17  565.48911099.44  424.155 

824  583 

339.362 

659.667 

110 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

32° 
M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |    Arc. 

273.952 

533.333 

234.854 

457.143 

205.537 

400.000 

182.737 

355.556 

10  4.  506  320.0i() 

~o~ 

274.100 

533.611 

234.981 

457.381 

205.648 

400.208 

182.836 

355.741 

164.594320.167 

1 

274.218 

533.889 

235.108 

457.619 

205.759 

400.417 

182.935 

355.926 

164.683320.333 

2 

274.401 

534.167 

235.239 

457.857 

205.874 

400.625 

183.037 

356.111 

164.775320.500 

3 

274.554 

534.444 

235.3701458.095 

205.988 

400.833 

183.139 

356.296 

164.867 

320.067 

4 

274.702 

534.722 

235.497 

458.333 

206.099 

401.042 

183.237 

356.481 

164.956 

320.833 

5 

274.850 

535.001) 

235.624 

458.571 

206.210 

401.250 

183.336 

356.667 

165.045 

321.000 

6 

274.998 

535.278 

235.751 

458.810 

206.321 

401.458 

183.435 

356.852 

165.134 

321  .  107 

7 

275.147 

535.55(5 

235.878 

459.048 

206.433 

401.667 

183.534 

357.037 

105.223 

321.333 

8 

275.299 

535.833 

236.009 

459.286 

206.547 

401.875 

183.636 

357.222 

165.314 

321.500 

9 

275.452 

536.111 

236.140 

459.524 

206.662 

402.  083 

183.738 

357.407 

165.406 

321.667 

10 

275.605 

536.389 

236.271 

459.762 

206.777 

402.292 

183.840 

357.593 

165.498 

321.833 

11 

275.758 

536.667 

236  402 

460.000 

206.891 

402.500 

183.942 

357.778 

165.590 

322.000 

12 

275.906 

536.944 

236.529 

460.238 

207.002 

402.708 

184.040 

357.963 

165.679 

322.167 

13 

276.054 

5*7.222 

236.656 

460.476 

207.114 

402.917 

184.139 

358.148 

165.768 

322.333 

14 

276.207 

537.500 

236.787 

460.714 

207.228 

403.125 

184.241 

358.333 

165.859 

322.500 

15 

276.360 

537.778 

236.918 

460.952 

207.343 

403.333 

184.343 

358.519 

165.951 

322.667 

16 

276.508 

538.056 

237.045 

461.190 

207.454 

403.542 

184.442 

358.704 

166.040 

322.833 

17 

276.656 

538.333 

237.172 

461.429 

207.565 

403.750 

184.541 

358.889 

166.129 

323.000 

18 

276.809 

538.611 

237.303 

461.667 

207.680 

403.958 

184.643 

359.074 

166.221 

323.167 

19 

276.962 

538.889 

237.434 

461.905 

207.794 

404.167 

184.745 

359.259 

166.313 

323.333 

2O 

277.110 

539.167 

237.561 

462.143 

207.906 

404.375 

184.843 

359.444 

166.402 

323.500 

21 

277  258 

539.444 

237.688 

462.381 

208.017 

404.583 

184.942 

359.630 

166.491 

323.667 

22 

277.411 

539.722 

237.819 

41)2.01!) 

208.131 

404.792 

185.044 

359.815 

166.582 

323.833 

23 

277.564 

540.000 

237.950 

462.857 

208.246 

405  .DOO 

185.146 

360.000 

166.674 

324.000 

24 

277.712 

540.278 

238.077 

463.095 

208.357 

405.208 

185.245 

360.185 

166.763 

321.167 

25 

277.860 

540.556 

238.204 

463.333 

208.468 

405.417 

185.344 

300.370 

166.852 

324.333 

26 

27'8.013 

540.  833 

238.335 

463.571 

208.583 

405.625 

185.446 

360.556 

166.944 

324.500 

27 

278.165 

541.111 

238.466 

463.810 

208.698 

405.833 

185.547 

360.741 

167.036 

324.667 

28 

278.314 

541.389 

238.593 

464.048 

208.809 

406.042 

185.646 

360.926 

167.124 

324.833 

29 

278.462 

541.667 

238  720 

464.286 

208.920 

406.250 

185.745 

361.111 

167.213 

325.000 

30 

278.615 

541.944 

238.851 

464.524 

209.025 

406.458 

185.847 

361.296 

167.305 

325.167 

31 

278.767 

542.222 

238.98^ 

464.762 

209.149 

406.667 

185  949 

361.481 

167.397 

325.333 

32 

278.915 

542.500 

239.109 

465.000 

209.260 

406.875 

186.048 

361.667 

167.486 

325.500 

33 

279.064 

542.778 

239.236 

465.238 

209.371 

407.083 

186.147 

361.852 

167.575 

325.667 

34 

279.216 

543.056 

239.367 

465.476 

209.486 

407.292 

186.248 

362.037 

167.667 

325.833 

35 

279.369 

543.333 

239.498 

465.714 

209.601 

407.500 

186.350 

362.222 

167.758 

326.000 

36 

279.522 

543.611 

239  629 

465.952 

209.715 

407.708 

186.  4521362.  407 

167.850 

326.167 

37 

27'9.675 

543.889 

239.760 

466.190 

209.830 

407.917 

186.554 

362.593 

167.942 

326.333 

38 

279.823 

544.167 

239.887 

466.429 

209.941 

408.125 

186.653 

362.778 

168.031 

326.500 

39 

279.971 

544.444 

240.014 

466.667 

210.052 

408.333 

186.752 

362.963 

168.120 

326.667 

4O 

2H0.124 

544.722 

240.145 

466.905 

210.167 

408.542 

186.854 

363.148 

168.212 

326.833 

41 

280,277 

545.000 

240.276 

467.143 

210.282 

408.750 

186.956 

363.333 

168.303 

327.000 

42 

280.  425  '545.  278 

240.403 

467.381 

210.39:J, 

408.958 

187.055 

363.519 

168.392 

327.167 

43 

280.  57  3  '545.  550 

240.530 

467.619 

210.504 

409.167 

187.153 

363.704 

168.481 

327.333 

44 

280.726515.8*3 

240.661 

467.857 

210.619 

409.375 

187.255 

363.889 

168.573 

327.500 

45 

280.879 

546.111 

240.792 

468.095 

210.733 

409.583 

187.&57 

364.074 

168.665 

327.667 

46 

281.032 

546.389 

240.923 

468.333 

210.848 

409.792 

187.459 

364.259 

168.757 

327.833 

47 

281.184 

546.66; 

241.054 

4(58.571 

210  063 

410.000 

187.561 

364.444 

168.848 

328.000 

48 

281.333 

546.944 

241.181 

468.810 

211  074 

410.20,^ 

187.660 

364.630 

168.937 

328.167 

49 

281.481 

547.222 

241.308 

469  048 

211.185 

410.417 

187.759 

364.815 

169.026 

328.333 

5O 

281.633 

547.500 

241.430 

4U9.286 

211.300 

410.625 

187.861 

365.000 

169.118 

328.500 

51 

281.786 

547.778 

241.570 

469.524 

211.414 

410.833 

187.963 

365.185 

169.210 

328.667 

52 

281.934 

548.056 

241.697 

469.762 

211.525 

411.042 

188.062365.370 

169.299 

328.833 

53 

282.082 

548.333 

241.824 

470.000 

211.636 

411.250 

188.160 

365.556 

169.388 

329.000 

54 

282.235 

548.611 

241.955 

47'0.238 

211.751 

411.458 

188.262 

365.741 

169.479 

329.167 

55 

£82.388 

548.889 

242.086470.476 

211.806 

411.667 

188.364 

365.926 

169.571 

329.333 

56 

282.541 

549.167 

242.217470.714 

211.980 

411.875 

188.466 

366.111 

169.663 

329.500 

57 

282.694 

549.444 

242.348470.952 

212.095 

412.083 

188.568 

366.296 

169.755 

329.667 

58 

282.842 

549.722 

242.475471.190 

212.206 

412.292 

188.667 

366.481 

169.844 

329.833 

59 

111 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


33 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~O~ 

1697.16 

3300.00 

848.62 

1650.  OC 

565.785 

1100.00 

424.377 

825.00< 

339.540 

660.000 

1 

1698.10 

3301.67 

849.079 

1650.82 

566.090 

1100.56 

424.606 

825.417 

339.723 

660.333 

2 

1699.01 

3303.33 

849.538 

1651.6? 

566.396 

1101.11 

424.836 

825.833 

339.906 

660.667 

3 

1699.93 

3305.00 

849.996 

1652.50 

566.702 

1101.67 

425.065 

826.250 

340.090 

661.00D 

4 

1700.85 

3306.67 

850.454 

1653.33 

567.007 

1102.22 

425.294 

826.667 

340.273 

661.333 

5 

1701.73 

3308.33 

850.899 

1654.17 

567.303 

1102.78 

425.516 

827.08? 

340.451 

661.667 

6 

1702.62 

3310.00 

851.343 

1655.00 

567.599 

1103.33 

425.738 

827.500 

340.629 

662.000 

7 

1703.54 

3311.67 

851.801 

1655.83 

567.905 

1103.89 

425.967 

827.917 

340.812 

662.333 

8 

1704.46 

3313.33 

852.259 

1656.67 

568.211 

1104.44 

426.197 

828.333 

340.995 

662.067 

9 

1705.37 

3315.00 

852.718 

1657.50 

568.516 

1105.00 

426.426 

828.750 

341.179 

663.000 

10 

1706.29 

3316.67 

853.176 

1658.33 

568.822 

1105.56 

426.655 

829.167 

341.362 

663.333 

11 

1707.18 

3318.33 

853  620 

1659.17 

569.118 

1106.11 

426.877 

829.583 

341.540 

663.667 

12 

1708.0? 

3320.00 

854.064 

1660.00 

569.414 

1106.67 

427.099 

830.000 

341.718664.000 

13 

1708.98 

3321.67 

854.523 

1660.83 

569.720 

1107.22 

427.328 

830.417 

341.901  664.333 

14 

1709.90 

3323.33 

854.981 

1661.67 

570  025 

1107.78 

427.558 

830.833 

342.084664.667 

15 

1710.82 

3325.00 

855.439 

1662.50 

570.331 

1108.33 

427  787 

831.250 

342.268  665.000 

1(> 

1711.73 

3326.67 

855.898 

1663.33 

570.636 

1108.89 

428.'  01  6 

831.667 

342.  451  '665.  333 

17 

1712.62 

3328.33 

856.342 

1664.17 

570.932 

1109.44 

428.238 

832.083 

342.629'665.667 

18 
19 

1713.51 
1714.43 

3330.00 
3331.67 

856.786 
857.244 

1665.00 
1665.83 

571.229 
571.534 

1110.00 
1110.56 

428.460 
428.690 

832.500 
832.917 

342.806 
342.990 

666.000 
666.333 

30 

1715.34 

3333.33 

857.703 

1666.67 

571.840 

1111.11 

428.919 

833.333 

343.173 

666.667 

31 

1716.26 

3335.00 

858.161 

1667.50 

572.145 

1111.67 

429.148 

833.750 

343  357667.000 

22 

1717.18 

3336.67 

858.620 

1668.33 

572.451 

1112.22 

429.377 

834.167 

343.540667.333 

23 

24 

1718.06 
1718.95 

3338.33 
3340.00 

859.064 
859.508 

1669.17 
1670.00 

572.747 
573.043 

1112.78 
1113.33 

429.599 
429.821 

834.583 
835.000 

343.718607.667 
343.895668.000 

25 

1719.87 

3341.67 

859.966 

1670.83 

573.349 

1113.89 

430.051 

835.417 

344.079668.333 

3(> 

1720.79 

3343.  33 

860.424 

1671.67 

573.654 

1114.44 

430.280 

835.833 

344.262 

668.667 

27 

721.70 

3345.00 

860.883 

1672.50 

573.960 

1115.00 

430.509 

836.250 

344.446 

669.000 

38 

722.62 

3346.67 

861.341 

1673.33 

574.266 

1115.56 

430.788 

836  667 

314.629 

669.333 

29 

723.54 

3348.33 

861.800 

1674.17 

574.571 

1116.11 

430.967 

837.083 

344.812 

669.667 

30 

724.45 

3350.00 

862.258 

1675.00 

574.877 

1116.67 

431.197 

837.500 

344.996 

670.000 

31 

725.34 

3351.67 

862.702 

1675.83 

575.173 

1117.22 

431.419 

837.917 

345.174 

670.333 

32 

726.23 

3353.33 

863.146 

1676.67 

575.469 

1117.78 

431.641 

838.333 

345.351 

67'0.667 

33 

7*7.15 

3355.00 

863.604 

1677.50 

575.775 

1118.33 

431.870 

838.750 

345.535 

671.000 

34 

728.06 

3356.67 

364.063 

678.33 

576.080 

1118.89 

432.099 

839.167 

345.718 

671.333 

35 

728.98 

3358.33 

864.521 

679.17 

576.386 

1119.44 

432.329 

839.583 

345.901 

671.667 

36 

729.90 

3360.00 

864.980 

1680.00 

576.691 

1120.00 

432.558 

840.000 

346.085 

672.000 

37 

730.81 

3331.67 

865.438 

680.83 

576.997 

1120.56 

432.787 

840.417 

346.268 

672.333 

38 

731.73 

3i)3.33 

865.896 

1681.67 

577.303 

.121.11 

433.016 

810.833 

34(5.452 

072.667 

39 

732.62 

365.00 

866.341 

1682.50 

577.599 

1121.67 

433.238 

841.250 

346.629 

673.000 

4O 

733.51 

366.67 

66.785 

683.33 

577.895 

1122.22 

433.460 

841.667 

340.807 

673.333 

41 

731.42 

368.331867.243 

1684.17 

578.200 

1122.78 

33.090 

S42.083 

346.990 

673.667 

43 

735.34 

370.00867.701 

1685.00 

578.506 

1123.33 

433.919 

842.500 

347.174 

674.000 

43 

736.  26 

371  67868.160 

685.83578.812 

1123.89 

34.148 

812.917 

347.357 

074.333 

44 

737.17 

3373.33 

363.618 

686.67 

579.117 

1124.44 

34.377 

843.333 

347.541 

674.667 

45 

733.09 

3375.00 

869.077 

687.50 

579.423 

1125.00 

434.607 

843.750 

347.724 

075.000 

4  a 

739.01 

3376.67 

809.535 

688.33 

579.728 

1125.56 

34.83(5 

844.167 

347.907 

675.333 

47 

739.89 

3378.33 

869.979 

689.17 

580.024 

126.11 

435.058 

844.583 

348.085 

075.607 

48 

740.78 

3380.00 

870.423 

690.00 

580.321 

1126.67 

35.280 

845.000 

348.2(53 

676.000 

49 

741.70 

3331.67 

870.881 

690.83 

580.626 

1127.22 

435.509 

845.417 

343.446 

676.333 

50 

7'42.62 

33S3.33 

871.340 

691.67 

580.932 

1127.78 

35.738 

845.833 

348.630 

676.667 

51 

743.53 

3385  00 

87  1.798 

692.50581.2371128.33 

35.968 

846.250 

348.813 

677.000 

53 

7'4  4.  45  3386.  67 

872.257 

693.33581.543  1128.89 

36.197 

846.667 

348.996 

677.333 

53 

745.  37|  3388.  33 

872.715 

694.17 

581.8491129.44 

36.426 

847.083 

349.180 

677.607 

54 

740.23  3390.00  873.173  1695.00 

582.1541130.00 

36.655 

847  500 

349.3(53 

078.000 

55 

747  .  1  7  3301  .  67  :  873  .617  1695  .  83  582  .  450  1  130  .  56 

36.877 

847.917 

349.541 

678.333 

5(J 

748  .  06  3393  .  33  874  .  06  1  1  696  .  67  582  .  746  11  31  .  1  1 

37.099 

818.333 

349.719 

678.607 

57 

748  .  98  3395  .  00  874  .  520  1  697  .  50  583  .  052  1  1  3  1  .  67 

37  329 

848.750 

319.902 

679.000 

58 

749.8!)  3390.67  874.978  1698.33  583.358  1132.22 

37.55S 

849.167 

350.085  679.333 

59 

750.81  3398.33  875.437  1699.17  583.663  1132.78 

37.787 

849.583 

350.269679.667 

112 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

looo 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

282.990 

550.000 

242.602 

471.429 

212.317 

412.500 

188.766 

366.667 

169.933 

330.000 

o 

283.143 

550.278 

242.733 

471.667 

212.432 

412.708 

188.868 

366.852 

170.024 

330.167 

1 

283.296 

550.556 

242.861 

471.905 

212.547 

412.917 

188.970 

367.037 

170.116 

330.333 

2 

283.449 

550.833 

242.995 

472.143 

212.661 

413.125 

189.072 

367.222 

170.208 

330.500 

3 

283.602 

551.111 

243.126 

472.381 

212.776 

413.333 

189.174 

367.407 

170.300 

330.667 

4 

283.750 

551.389 

243.253 

472.619 

212.887 

413.542 

189.272 

367.593 

170.389 

330.833 

5 

283.898 

551.667 

243.380 

472.857 

212.998 

413.750 

189.371 

367.778 

170.478 

331.000 

6 

284.051 

551.944 

243.511 

473.095 

213.113 

413.958 

189.473 

367.963 

170.569 

331.167 

7 

284.203 

552.222 

243.642 

473.333 

213.228 

414.167 

189.575 

368.148 

170.  661  1331.333 

8 

284.356 

553  r  500 

243.773 

473.571 

213.342 

414.375 

189.677 

368.333 

170.753 

331.500 

9 

284.509 

552.778 

243.904 

473.810 

213.457 

414.583 

189.779 

368.519 

170.845 

331.667 

10 

284.657 

553.056 

244.031 

474.048 

213.568 

414.792 

189.878 

368.704 

170.934 

331.833 

11 

284.805 

553.333 

244.158 

474.286 

213.679 

415.000 

189.977 

368.889 

171.023 

332.000  12 

284.958 

553.611 

244.289 

474.524 

213.794 

415.208 

190.078 

369.074 

171.114 

332.167 

13 

285.111 

553.889 

244.420 

474.762 

213.909 

415.417 

190.180 

369.259 

171.206 

332.333 

14 

285.264 

554.167 

244.551 

475.000 

214.023 

415.625 

190.282 

369.444 

171.298 

332.500 

15 

285.417 

554.444 

244.682 

475.238 

214.138 

415.833 

190.384 

369.630 

171.390 

332.667 

16 

285.565 

554.722 

244.809 

475.476 

214.249 

416.042 

190.483 

369.815 

171.479 

332.833 

17 

285.713 

555.000 

244.936 

475.714 

214.360 

416.250 

190.582 

370.000 

171.568 

333.000 

18 

285.866 

555.278 

245.067 

475.952 

214.475 

416.458 

190.684 

370.185 

171.659 

333.167 

19 

286.019 

555.556 

245.198 

476.190 

214.590 

416.667 

190.786 

370.370 

171.751 

333.333 

2O 

286.171 

555.833 

245.329 

476.429 

214.704 

416.875 

190.888 

370.556 

171.843 

333.500 

21 

286.324 

556.111 

245.460 

476.667 

214.819 

417.083 

190.990 

370.741 

171.935 

333.667 

22 

286.472556.389 

245.587 

476.905 

214.930 

417.292 

191.089 

370.926 

172.024 

333.833 

23 

286.621  556.667 

245.714 

477.143 

215.041 

417.500 

191.187 

371.111 

172.113 

334.000 

24 

286.773556.944 

245.845 

477.381 

215.156 

417.708 

191.289 

371.296 

172.204 

334.167 

25 

286.  92(5  i  557.  222 

245.976 

477.  61  !) 

215.270 

417.917 

191.391 

371.481 

172.296 

334.333 

26 

287.079 

557.500 

246.107 

477.857 

215.385 

418.125 

191.493 

371.667 

172.388 

334.500 

27 

287.232 

557.778 

246.238 

478.095 

215.500 

418.333 

191.595 

371.852 

172.480 

334.667 

28 

287.385 

558.056 

246.369 

478.333 

215.615 

418.542 

191.  C97 

372.037 

172.572 

334.833 

29 

287.538 

558.333 

246.500 

478.571 

215.729 

418.750 

91.799 

372.222 

172.663 

335.000 

30 

287.686 

558.611 

246.627 

478.810 

215.840 

418.958 

191.898 

372.407 

172.752 

335.167 

31 

287.834 

558.889 

246.754 

479.048 

215.951 

419.167 

191.997 

372.593 

172.841 

335.333 

32 

287.987 

559.167 

246.885 

479.286 

216.066 

419.375 

192.099 

372.778 

172.933 

335.500 

33 

288.140 

559.444 

247.016 

479  524 

216.181 

419.583 

192.201 

372.963 

173.025 

335  667 

34 

288.292 

559.722 

247.147 

479.762 

216.295 

419.792 

192.303 

373.148 

173.117 

335  833 

35 

288.445 

560.000 

247.278 

480.000 

216.410 

420.000 

192.405 

373-.  333 

173.208 

836.000 

36 

288.598 

560.278 

247.410 

480.238 

216.525 

420.208 

192.506 

373  51!) 

173.300 

336.167 

37 

288.751 

560  556 

247.541 

480.476 

216.640 

420.417 

192.608 

373.704 

173.392 

336.333 

38 

288.899 

560.833 

247.668 

480.714 

216.751 

420.625 

192.707 

373.889 

173.481 

336.500 

39 

289.047 

561.111 

247.794 

480.952 

216.862 

420.833 

192.806 

374.074 

173.570 

336.667 

4O 

289.200 

561.389 

247.925 

481.190 

216.976 

421.042 

192.908 

374.259 

173.662 

336  .  833 

41 

289.353 

561.667 

248.057 

481.429 

217.  C91 

421.250 

193.010 

374.444 

173.753 

337.000 

42 

289.506 

561.944 

248.188 

481.667 

217.206 

421.458 

193.112 

374.630 

173.845 

337.167 

43 

289.659 

562.222 

248.319 

481.905 

217.320 

421.667 

193.214 

374.815 

173.937 

337.333 

44 

289.811 

562.500 

248.450 

482.143 

217.435 

421.875 

193.316 

375.000 

174.029 

337.500 

45 

289.964 

562.778 

248.581 

482.381 

217.550 

422.083 

193.418 

375.185 

174.121 

337.667 

46 

290.1121563.056 

248.708 

482.619 

217.661 

422.292 

193.517 

375.370 

174.210 

337.833 

47 

290.260563.333 

248.835 

482.857 

217.772 

422.500 

193.615 

375.556 

174.298 

338.000 

48 

290.413 

563.611 

248.966 

483.095 

217.887 

422.708 

193.717 

375.741 

174.390 

338.167 

49 

290.566 

563.889 

249.097 

4a^.333 

218.001 

422.917 

193.819 

375.926 

174.482 

338.333 

5O 

290.719 

564.167 

249.228 

483.571 

218.116 

423.125 

193.921 

376.111 

174.574 

338.500 

51 

290.872 

564.444 

249.359 

483.810 

218.231 

423.  3a3 

194.023 

376.296 

174.666 

338.667 

52 

291.025 

564.722 

249.490 

484.048 

218.345 

423.542 

194.125 

376.481 

:  74  .  757 

338.833 

53 

291.178 

565.000 

249.621 

484.286 

218.460 

423.750 

194.227 

376.667 

174.849 

339  000  54 

291.326 

565.278 

249.748 

484.524 

218.571 

423.958 

194.326 

376.852 

174.938 

339.167  55 

291.474 

565.556 

249.875 

484.762 

218.682 

424.167 

194.425 

377.037 

175.027 

339.333  50 

291.627 

565.833 

250.006 

485.000 

218.797 

424.375 

194.527377.222 

175.119 

339.500 

57 

291.780 

566.111 

250.137 

485.238 

218.  P12 

424.583 

194.629377.407 

175.211 

339.667 

58 

291.932 

566.389250.268 

485.476 

219.026424.792 

194.7311377.593 

175.302 

339.  B33   59 

113 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


34° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

1751.73 

3400.00 

875.895 

1700.00 

583.909 

1133.33 

488.016 

850.000 

350.452 

080.000 

1 

1752.64 

3401.67 

876  353 

1700.83 

584.274 

1138.80 

43S.246 

850.417 

350.636 

680.333 

2 

1753.56 

3403  33 

876.812 

1701.67 

584.58d 

1134.44 

438.475 

850.833 

350.819 

080.607 

3 

1754.48 

3405.00 

877.270 

1702.50 

584.886 

1135.00 

438.704 

851.250 

351.002 

681.000 

4 

1755.39 

3406.67 

877.729 

1703.33 

585.191 

1135.56 

438.933 

851.667 

351.186 

681.333 

5 

1756.31 

3408.33 

878.187 

1704.17 

585.497 

1136.11 

439.102 

852.083 

351.369 

081.007 

6 

1757.23 

3410.00 

878.645 

1705.00 

585.802 

1136.67 

439.392 

852.500 

351.553 

682.000 

7 

1758.11 

3411.67 

879.089 

1705.83 

586.093 

1137.22 

439.014 

852.917 

351.730 

682.333 

8 

1759.00 

3413.33 

879.534 

1706.67 

5SO  .  805 

1137.78 

489.830 

853.333 

351.908 

082  007 

9 

1759.92 

3415.00 

879.992 

1707  50 

586.700 

1138.33 

440.005 

853.750 

352.091 

683.000 

10 

1760.84 

3416  67 

880.450 

1708.33 

587.006 

1138.89 

440.294 

854.167 

352.275 

683.333 

11 

1761.75 

3418.33 

880.909 

1709.17 

587.311 

1139.44 

440.524 

854.583 

352.458 

683.667 

12 

1762.67 

3420.00 

881.367 

1710.00 

587.617 

1140.00 

440.753855.000 

352.642 

684.000 

13 

1763.59 

3421.67 

881.825 

1710.83 

587.923 

1140.56 

440  982 

855.417 

352.825 

684.  333 

14 

1764.50 

3423.33 

882.284 

1711.67 

588.228 

1141.11 

441.211 

855.833 

353.008 

684.667 

15 

1765.42 

3425.00 

882.742 

1712.50 

588.534 

1141.67 

441.440 

856.250 

353.192 

685.000 

16 

1766.34 

3426.67 

883.  20l!  1713.  33 

588.839 

1142.22 

441.670856.667 

353.375 

685.  333 

17 

1767.25 

3428.33 

883.659J1714.17 

589.145 

1142.78 

441.899857.086 

353  559 

685.667 

18 

1768.17 

3430.00 

884.117  1715  00 

589.451 

1143.33 

442.1-8 

857.500 

353.742 

686.000 

19 

1769.06 

3431.67 

884.561 

1715.83 

589.747 

1143.89 

442.350 

857.917 

353.920 

686.333 

30 

1769.95 

3433.33 

885.006 

1716.67 

590.043 

1144.44 

442.572 

858.333 

354.097 

686.667 

31 

1770.86 

3435.00 

885.464 

1717.50 

590.348 

1145.00 

442.801 

858.750 

854.281 

687.000 

22 

1771.78 

3436.67 

885.922 

1718.33 

590.654 

1145.56 

443.03! 

859.167 

354.464 

687.333 

23 

1772.70 

3438.33 

886.381 

1719.17 

590.960 

1146.11 

443.260 

859.583 

354.648 

687.667 

34 

1773.61 

3440.00 

886.839 

1720.00 

591.265 

1146.67 

443.489860.000 

354.831 

688.000 

35 

1774.53 

3441.67 

887.297 

1720.88 

591  571 

1147.22 

443.718 

860.417 

355.014 

688.333 

36 

1775.45 

3443.33 

887.756 

1721.67 

591.870 

1147.78 

443.948860.833 

355.198 

688.667 

37 

1776.36 

3445.00 

888.214 

1722.50 

592.182 

1148.33 

444.177 

861  250 

355.381 

689.000 

38 

1777.28 

3446.67 

888.673 

1723.83 

592.488 

1148.89 

444.406 

861.607 

355.  565  1689.383 

39 

1778.20 

3448.33 

889.131 

1724.17 

592.793 

1149.44 

444.635 

862.083 

355.748 

689.667 

30 

1779.11 

3450.00 

889.589 

1725.00 

593.099 

1150.00 

444.865 

862.500 

355.931  690.000 

31 

1780.03 

3451.67 

890.048 

1725.83 

593.405 

1150.56 

445.094  862.917 

350.115690.333 

33 

1780.95 

3453.33 

890  500 

1726.67 

593.710 

1151.11 

445.323 

803.333 

356.298  690.667 

33 

1781.86 

3455.00 

890.965 

1727.50 

594.016 

1151.67 

445.552 

803.750 

356.482691.000 

34 

1782.78 

3456.67 

891.423 

1728.33 

594.321 

1152.22 

445.781 

804.167 

356.605091.333 

35 

1783.70 

3458.33 

891.881 

1729.17 

594.627 

1152.78 

446.011 

864.583 

356.848601.667 

36 

1784.61 

3460.00 

892.340 

1730.00 

594.933 

1153.33 

446.240865.000 

357.032692.000 

37 

1785.50 

3461.67 

892.784 

1730.83 

595.220 

1153.89 

416.462 

865.417 

357.210092.333 

38 

1786.39 

3463.33 

893.228 

1731.67 

595.525 

1154.44 

446.684  865.833 

357.387692.667 

39 

1787.31 

3465.00 

893.686 

1732.50 

595.830 

1155.00 

446.913866.250 

357.571  693.000 

40 

1788.22 

3466.67 

894.145 

1733.33 

596.136 

1155.56 

447.143866.667 

357.754003.333 

41 

1789.14 

3468.33 

894.603 

1734.17 

596.442 

1156.11 

447.372867.083 

357.937693.667 

43 

1790.06 

3470.00 

895.061 

1735.00 

596.747 

1156.67 

447.601 

867.500 

35S.121  694.000 

43 

1790.97 

3471.67 

895.520 

1735.83 

597.053 

1157.22 

447.830807.917 

358  304  004.333 

44 

1791.89 

3473.33 

895.978 

1736.67 

597.358 

1157.78 

448.059 

80S.  333 

358.488694.607 

45 

1792.81 

3475.00 

896.437 

1737.50 

597.664 

1158.33 

448.289 

808.750 

358.071  095.000 

46 

1793.72 

3476.67 

896.895 

1738.33 

597.970 

1158.89 

448.518809.167 

358.854095.333 

47 

1794.64 

3478.33 

897.353 

1739.17 

598.275 

1159.44 

448.747 

809.583 

350.038  695.607 

48 

1795.56 

3480.00 

897.812 

1740.00 

598.581 

1160.00 

448.976870.000 

350.2211696.000 

49 

1796.47 

3481.67 

898.270 

1740.83 

598.880 

1160.56 

449.206870.417 

359.405696.333 

5O 

1797.39 

3483.33 

898.729 

1741  67 

599.192 

1161.11 

449.435  870.833 

359.  5F8  696.  667 

51 

1798.31 

3485.00 

899.187 

1742.50 

599.498 

1101.07 

449.664 

871.250 

359.771  697  000 

53 

1799.22 

3486  67 

899.645 

1743.33 

599.803 

1102.22 

449.893871.667 

359.955 

097.383 

53 

1800.14 

3488.33 

900.104 

1744.17 

600.109 

1102.78 

450.123 

872.083 

360.138697.067 

54 

1801.06 

3490.00 

900.562 

1745.00 

600.415 

1103.33 

450.352 

872.500 

360.322698.000 

55 

1801.97 

3491.67 

901.0201745.83 

000.720 

1163.89 

450.581 

872.917 

360.  505  1  698.  333 

56 

1802.89 

3493.  33  1901.  479  1746.67 

601.026 

1164.44 

450.810 

873.333 

360.688698.667 

57 

1803.81 

3495.00  901  .937  1747.50  601  .331 

1165.00 

451.039873.750 

360.  872|  009  000 

58 

1804.73 

3496.67 

902.  396  1748.  33!  00  1.637 

1165.56 

451.269 

874.167 

361.055609.333 

59 

1805.61 

3498.33 

902.  854;  1749.  17  1601.943 

1166.11 

451  .  498  874  .  583  36  1  .  239  \  699  .  607 

114 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

34° 

Tan. 

Arc. 
566^667 

Tan. 

250.399 

Arc. 

485.714 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

~7T 

292.085 

219.141425.000 

194.833 

377.778 

175.394 

340.000 

292.238 

566.944 

250.530 

485.952 

219.256425.208 

194.934 

377.963 

175.486 

340.167 

i 

292.391 

567.222 

250.661 

486  190 

219.370 

425.417 

195.036 

378.148 

175.578 

340.333 

2 

292.544 

567.500 

250.792 

486.429 

219.485 

425.625 

195.138 

378.333 

175.670 

340.500 

3 

292.697 

567.778 

250.923 

486.667 

219.600 

425.833 

195.240 

378.519 

175.761 

340.667 

4 

292.850 

568.056 

251.054 

486.905 

219.715 

426.042 

195.342 

378.704 

175.853 

340  833 

5 

293.002 

568.333 

251.185 

487.143 

2  19.  829  1426.250 

195.444 

378.889 

175.945 

341.000 

6 

293.150 

568.611 

251.312 

487.381 

219.940 

426.458 

195.543 

379.074 

176.034 

341.167 

7 

293.299 

568.889 

251.439 

487.619 

•>20.051 

426.667 

195.642 

379.259 

176.123 

341.333 

8 

293.451 

569.167 

251.570 

487.857 

220.166 

426.875 

195.744 

379.444 

176.215 

341.500 

9 

293.604 

569.444 

251.701 

488.095 

220.281 

427.083 

195.846 

379  630 

176.306 

341.667 

10 

293  .  757 

569.722 

251.832488.333 

220.395 

427.292 

195.948 

379.815 

176  398 

341.833 

11 

293  910!  570.  000 

251.9(53488.571 

220  510 

427.500 

196.050 

380.000 

176.490 

342.000 

12 

294.063570.278 

252.094488.810 

220.625 

427.708 

196.152 

380  185 

176.582 

342.167 

13 

294.216 

570.556 

252.225489.048 

220.740 

427.917 

196.254 

380  370 

176.674 

342.333 

14 

294.369 

570.833 

252.356489.286 

220.854 

428  125 

196  356 

380.556 

17'6.765 

342.500 

15 

294.521 

571.111 

252.487489.524 

220  969 

428.333 

196.458 

380.741 

176  857 

34-.'.  667 

16 

294.674 

571.3*9 

252.618:489.762 

221.084 

428.542 

196.560 

380.926 

176.949 

342.833 

17 

294.827 

571.667 

252.7501490.000 

221.198 

428.750 

196.661 

381.111 

177.041 

343.000 

18 

294.975 

571.944 

252.876 

490.238 

221.309 

428  958 

196.760 

381.296 

177.130 

343.167 

19 

295.123 

572.222 

253.003 

490.476 

221.4-20 

429.167 

196.859 

381.481 

177.219 

343.333 

2O 

295.276 

572.500 

253.134 

490.714 

221.535 

429  375 

196.961 

3S1  667 

177.310 

343.500 

21 

295.429 

572.778 

253  268 

490.952 

221.650 

429.583 

197.063 

381.852 

177.402 

343.667 

22 

295.582 

573.056 

253.397 

491.190 

221.765 

429.792 

197.165 

382.037 

177.494 

343.833 

23 

295.735 

573  333 

253.528 

491  .429 

221.879 

430.000 

197  267 

382.222 

177.586 

344.000 

24: 

295  888 

573.611 

253.659 

491.667 

221.994 

430.208 

197.369 

382.407 

177.677 

344.167 

25 

296.040 

573.889 

253.790 

491.905 

222.109 

430.417 

197.471 

382.593 

177.769 

344.333 

26 

296.193 

574.167 

253.921 

492.143 

222.223 

430.625 

197.573 

382.778 

177.861 

344.500 

21 

296.346 

574.444 

254.052 

492.381 

222.338 

430.833 

197.675 

382.963 

177.953 

344.667 

28 

296.499 

574.722 

254.183 

492.619 

222.453 

431.042 

197.777 

383.148 

178  045 

344.833 

29 

296.652 

575.000 

254.314 

492.857 

222.567 

431.250 

197.879 

383.333 

178.136 

345  000 

30 

296.805 

575.278 

254.445 

493.095 

2-22.682 

431.458 

197.981 

383.519 

178.228 

345.167 

31 

296.958 

575.556 

254.576 

493.333 

222.797 

431.667 

198  083 

383.704 

178.320 

345.333 

32 

297.110 

575.833 

254.707 

493.571 

222.911 

431.875 

198.185 

383.889 

178.412 

345.500 

33 

297.263 

576.111 

254.838 

493.810 

223.026 

432  083 

198.287 

384.074 

178.504 

345.667 

34 

297.416 

576.389 

254.969 

494.048 

223.141 

432.292 

198.388 

3S4.259 

178.595 

345.833 

35 

297.569 

576.667 

255.100 

494.280 

223.255 

432.500 

198.490 

384  .  444 

178.687 

346.000 

36 

297.717 

576.944 

255.227 

494.524 

223.367 

432.7'08 

198.589 

384.630 

178.776 

346.167 

37 

297.865 

577.22v 

255.354 

494.762 

223.478 

432.917 

198.688 

384.815 

178.865 

346.333 

38 

298.018 

577.500 

255.485 

495.000 

223.592 

433.125 

198.790 

385.000 

178.957 

346.500 

39 

298.171 

577.778 

255.616 

495.238 

223.707 

433.333 

198.892 

385.185 

179.049 

346.667 

40 

298.324 

578.0.56 

255.747 

495.476 

223.822 

433.542 

198.994 

385.370 

179.140 

346.833 

41 

298.477 

578.333 

255.878 

495.714 

223  936 

433.750 

199.096 

385.556 

179.232 

347.000 

4:2 

298.630 

578.611 

256.009 

495.952 

224.051 

433  958 

199.198 

385.741 

179.324 

347.167 

43 

2U8.  7S2 

578.889 

256.140 

496.190 

224.166 

434.167 

199.300 

385.926 

179.416 

347.333 

44 

298.935 

579.167 

256.271 

496.429 

224.280434.375 

199.402 

386.111 

179.508 

347.500 

45 

299  088 

579.444 

256.402 

496  667 

224.395434.583 

199.504 

386.296 

179.599 

347.667 

46 

299  241 

579.722 

256.533 

496.905 

224.510434.792 

199.606 

386.481 

179.691 

347.833 

47 

299  394  580.000 

256.664 

497.143 

224.624:435.000 

199.7'08 

386.667 

179.783 

348.000 

48 

299.547 

580.278 

256  .  795 

497.381 

224.739435.208 

199.810 

386.852 

179.875 

348.167 

49 

299.700 

580.556 

256.927 

497.619 

224.854 

435.417 

199.912 

387.037 

179.967 

348.333 

5O 

299.852580.833 

257.058 

497.857 

'224.969 

435.625 

200.014 

387.222 

180.058  348  500 

51 

300  005 

581.111 

257.189 

498.095 

225.083 

435.833 

200.115 

387.407 

180.150348.667 

52 

300.158 

581.389 

257.320 

498.333 

225.  198  1436.  042 

200.217 

387.593 

180.242348.833 

53 

300.311 

581.667 

257.451 

498.571 

225  313436.250 

200.319 

387.778 

180.334349.000 

54 

300.  464  1581.944 

257.582 

498.810 

225.427436.458 

200.421 

387.963 

180.425  349  167 

55 

300.617 

582.222 

257.713 

499.048 

225.542436.667 

200.523 

388.148 

180.517349.333 

56 

300.770 

582.500 

257.844 

499.286 

225.657436.875 

200.625 

388.333 

180.609349.500 

57 

300.922582.778 

257.975 

499.524 

225.771437.083 

200.727 

388.519 

180.701  349.667 

58 

301.  075  1583.056 

258.106 

499.762 

225.886437.292 

200.829 

388.704 

180.793349.833 

59 

115 


TABLE   XIV. — ACTUAL    TANGENTS,    ETC. 


35° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

3500.00 

Tan. 
903.312 

Arc. 

1750.00 

Tan. 

602  248 

Arc. 

1166.  67 

Tan. 

Arc. 

Tan. 

Arc. 

0 

1806.56 

451.727 

875.000 

861.422 

700.000 

1 

1807.48 

3501.67 

903.771 

1750.83 

602.554 

1167.22 

451.956 

875.417 

361.605 

700.333 

2 

1808.3'.) 

3503.33 

904.229 

1751.67 

602.859 

1167.78 

452.186 

875.833 

361.789 

700.607 

3 

1809.31 

3505.00 

904.688 

1752.50 

603.165 

1108.3:3 

452  415 

876.250 

361.972 

701.000 

4 

1810.23 

3506.67 

905.146 

1753.33 

003.471 

1168.89 

452.644 

876.667 

362.156 

701.333 

5 

1811.14 

3508.33 

905.604 

1754.17 

603.776 

1169  44 

452.873 

877.083 

362.339 

701.007 

6 

1812.06 

'3510.00 

906.063 

1755.00 

604.082 

1170.00 

453.103 

877.500 

362.523 

702.000 

7 

1810.98 

•3511.67 

906.521 

1755.83 

604.388 

1170.56 

453.332 

877.917 

302.700 

702.333 

8 

1813.89 

8513.88 

906.980 

1756.67 

604.693 

1171.11 

453.561 

878.333 

302.889  702.  G07 

9 

1814.81 

3515.00 

907.438 

1757.50 

604.999 

1171.67 

453.790 

8?'8.750 

363.073 

703.000 

1O 

1815.7:5 

3516.67 

907.896 

1758.33 

605  304 

1172.22 

454  019 

879.167 

363  250 

703  333 

11 

1816.64 

3518  33 

908.355 

1759.17 

605.610 

1172  78 

454  249 

879.  583  1363.  440 

703  667 

13 

1817.56 

3520.00 

908.813 

1760.00 

605.916 

1173.33 

454.478 

880.  000i363.  623 

704.000 

13 

1818.48 

3521.67 

909.271 

1760.83 

606.221 

1173.81) 

454.707 

880.417363.806 

704.333 

14 

1819.39 

:3523.33 

909.730 

1761.67 

606  527 

1174.44 

454  936 

880.  833  i  363.  990 

704.667 

15 

1820.31 

3525.00 

910.188 

1762.50 

606.832 

1175.00 

455.100 

881.250364.173 

705.000 

16 

1821.23 

3526.67 

910.647 

1763.33 

607.138 

1175.56455.395 

881.667 

364.357 

705.333 

17 

1822.14 

3528.33 

911.105 

1764.17 

607.444 

1176.11 

455.624 

882  083 

364.540 

705.667 

18 
19 

1823.06 
1823.98 

3530.00 
3531.6? 

911.563 
912  022 

1765.00 
1765.83 

607.749 
608.055 

1176  67 
1177.22 

455.853 
456.083 

H82.500 
882.917 

364.723 
364.907 

706.000 
706.333 

20 

1821.89 

3533  33 

912.480 

1766.67 

608.360 

1177.78 

456.312 

883.333 

365  090 

706.667 

21 

1825.81 

3535.00 

912.939 

1767.50 

008.  606 

1178.33 

456.541 

883.750 

365.274 

707.000 

22 

1826.73 

3536.6? 

913.397 

1768.33 

608.972 

1178.89 

456.7?'0 

884.167 

365.457 

707.333 

23 

1827.64 

3538.33 

913.855 

1769.17 

609.277 

1179.44 

456.999 

884.583 

305.640 

707.667 

34 

1828.56 

3540.00 

914.314 

1770.00 

609.583 

1180.00 

457.229 

885.000365.824 

708.000 

25 

1829.48 

3541.67 

914.772 

1770.83 

009.889 

1180.56 

457.458 

885.417366.007 

708.333 

26 

1830.39 

3543.33 

915.231 

1771.67 

610.194 

1181.11 

457.687 

885.833300.191 

708.007 

21 

1831.31 

3545.00 

915.689 

1772.50 

610.500 

1181.67 

457.916 

886.250306.374 

709.000 

28 

1832.23 

3546.67 

916.147 

1773.33 

610.805 

1182.22 

458.146 

886.00?  306.557 

709.333 

39 

1833.14 

3548.33 

916.606 

1774.17 

611.111 

1182.78 

458.375 

887.083300.741 

709.667 

30 

1834.06 

3550.00 

917.064 

1775.00 

611.417 

1183.33 

458.604 

887.500366.924 

710.000 

31 

183  L  98 

3551.67 

917.522 

1775.83 

611.722 

1183.89 

458.833 

887.917307.108 

710.333 

32 

1835.89 

3553.33 

917.981 

1776.67 

612.028 

1184.44 

459.063 

888.333367.291 

710.667 

33 

1836.81 

3555.00 

918.439 

1777.50 

612.333 

1185.00 

459.292 

888.750367.4?'4 

711.000 

34 

1837.73 

.'5556.67 

918  898 

1778.33 

012.639 

1185.56 

459.521 

889.  167  1367.658 

711.333 

35 

1838.64 

3558.33 

919.356 

1779.17 

612.945 

1186.11 

459.750 

889.583  367.841 

711.667 

36 

1839.56 

3560.00 

919.814 

1780.00 

613.250 

1186  67 

459.979 

890.  000  '308.  025 

712.000 

37 

18-10.51 

3561.67 

920.287 

1780.83 

613.565 

1187.22 

460.216 

890.417308.214 

712.333 

38 

1841.45 

3563.33 

920.760 

1781.67 

013.881 

1187.78 

460.452 

890.833  308.403 

712.667 

39 

1842.37 

3565.00 

921.218 

1782.50 

014.180 

1188.33 

400.681 

891.250368.586 

713.000 

4O 

1843.29 

3566.67 

921.677 

1783.33 

614.492 

1188.89 

460.911 

891.667308.770 

713.333 

41 

1844.20 

3568  33 

1)22.135 

1784.17 

614.797 

1189.44 

401.140 

892.083308.953 

713.607 

43 

1845.12 

3570.00 

922.593 

1785.00 

615.103 

1190.00 

461.369 

892.500369.137 

714.000 

43 

1846.04 

3571.67 

1)23.052 

1785.83 

015.409 

1190.56 

461.598 

892.917309.320 

714.333 

44 

1846.95 

3573.33 

9-23.510 

i?'86.67 

615.711 

1191.11 

401.828 

893.333309.503 

714.607 

45 

1847.8?' 

3575.00 

923  969 

1787.50 

616.020 

1191.67 

462.057 

893.750309.087 

715.000 

46 

1848.79 

3576.67 

924.427 

1788  33 

616.326 

1193.22 

462.280 

894.107309.870 

7l5.3:-;3 

47 

1849.70 

3578.33 

924.885 

1789.17 

610.631 

1192.78 

402.515 

894.583370.054 

715.607. 

48 

1850.62 

3580.00 

925.344 

1790.00 

016.93? 

1193.33 

402.745 

895.000370.237 

716.000 

49 

1851.54 

3581  .  07 

925.802 

1?90.S3 

617.242 

1193.89 

462.974 

895.417370.420 

716.333 

50 

1852.45 

3583.33 

926.261 

1701.67 

017  548 

1194.44 

463.203 

895.833370.604 

716  607 

51 

1853.37 

3585.00 

926.719 

1792.50 

617.854 

1195.00 

403.432 

896.250370.787 

717.000 

53 

1854.29 

3586.67 

927  1?  7 

1793.3:3 

018.159 

1195.56 

463.601 

896.667370.971 

717.333 

53 

1855.23 

3588.33 

927.650 

1?94  17 

618.474 

1196.11 

463.898 

897.  083  3?  1.1  60 

717.607 

54 

1856.18 

3590.00 

928.123 

1795.00618.790 

1196  67464.134 

897  500371.349 

718.000 

55 

1857.09 

3591.67 

928.581 

1795.83619.095 

1197.22464.303 

897.917371.532 

718.333 

56 

1858.01 

3593.33 

9J  !9.  040 

1796  67 

019.401 

1197.78464.593 

80S.  333  371.  71  6  718.007 

57 

1858.93 

3595.00929.498 

1797  50  619  706 

1198.334(54.822 

898.750371.899:719.000 

58 

1859.84 

3596.67929.956 

1798.33620.012 

1198.89405.051 

899.167372.082:719.333 

59 

1860.76 

3598.  33!  930.  415  1799.17  620.318  1199.44  465.280  899.583  372.266  ?19.6G7 

11(3 


TABLE   XTV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

35° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

301.228 

583.333258.237 

500.000 

226.001 

437.500 

200.931 

388.889 

180.884 

350.000 

o 

301.381 

583.6111258.368 

500.238 

226.115437.708 

201.033 

389.074 

180.976 

350.167 

1 

301.534 

583.880258.499 

500.476 

226.2301437.917 

201.135 

389.259 

181.068 

350.333 

2 

301.687 

584.1671258.630 

500.714 

226.345438.125 

201.237 

389.444 

181.160 

350.500 

3 

301.840 

584.444!  258  761 

500.952 

226.459438.333 

201.339 

389.630 

181.252 

350.667 

4 

301.992 

584.722258.892 

501.190 

226.574  438.542 

201.441 

389.815 

181.343 

350.833 

5 

802.145 

585.000259.023 

501.429 

226.689438.750 

201.543 

390.000 

181.435 

351.000 

6 

302.298 

585.278259.154 

501.667 

226.  803  '438.  958 

201.645 

390.185 

181.527 

351.167 

7 

302.451 

585.556259.285 

501.905 

226.918439.167 

201.747 

390.370 

181.619 

351  .  333 

8 

302.604 

585.  833-259.416 

502.143 

227.  033  439.375 

201.849 

390.556 

181,711 

351.500 

9 

302.757 

586.111  259.547 

502.381 

227.148 

439.583 

201.951 

390.741 

181.802 

351.667 

1O 

302.910 

586.389259.678 

502.619 

227.262 

439.792 

202.053 

390.926 

181.894 

351.833 

11 

303.062 

586.667 

259.809 

502.857 

227.377 

440.000 

202.155 

391.111 

181.986 

352.000 

303.215 

586.944 

259.941 

503.095 

227.492 

440.208 

202.257 

391.296 

182.078 

352.167 

13 

303.368 

587.222260.072 

503.333 

227.606 

440.417 

202.359 

391.481 

182.169 

352.333 

14 

303.521 

587.  500  1260.  203 

503.571 

227.721 

440.625 

202.461 

391.667 

182.261 

352.500 

15 

303.674 

587.778260.334 

503.810 

227.836 

440.833 

202.563 

391.852 

182.353 

352.667 

16 

303.827 

588.056:260.465 

504.048 

227.950 

441.042 

202.665 

392.037 

182.445 

352.833 

17 

303.980 

588.333260.596 

504.286 

228.065 

441.250 

202.767 

392.222 

182.537 

353.000 

18 

304.132 

588.611  260.727 

504.524 

228.180 

441.458 

202.868 

392.407 

182.628 

353.167 

19 

304.285 

588.889260.858 

504.762 

228.294 

441.667 

202.970 

392.593 

182.720 

353.333 

20 

304  .  438 

589.167260.989 

505.000 

228.409 

441.875 

203.072 

392.778 

182.812 

353.500 

21 

304.591  589.444 

261.120 

505.238 

228.524 

442.083 

203.174 

392.963 

182.904 

353.667 

22 

304.744 

589.722261.251 

505.476 

228.638 

442.292 

203.276 

393.148 

182.996 

353.833 

23 

304.897 

590.000261.382 

505.714 

228.753 

442.500 

203.378 

393.333 

183.087 

354.000 

24 

305.050 

590.278261.513 

505.952 

228  868 

442.708 

203.480 

393.519 

183.179 

354.167 

25 

305.202 

590.  556  [261.644 

506.190 

228.982 

442.917 

203.582 

393.704 

183.271 

354.3133 

26 

305.355 

590.  833;  261.  775 

506.429 

229.097 

443.125 

203.684 

393.889 

183.363 

354.500 

27 

305.508 

591.111 

261.906 

506.667 

229.212 

443.333 

203.786 

394.074 

183.455 

354.667 

28 

305.661 

591.389 

262.037 

506.905 

229.327 

443.542 

203.888 

394.259 

183.546 

354.833 

29 

305.814 

591.667 

262.168 

507.143 

229.441 

443.750 

203.990 

394.444 

183.638 

355.000 

30 

305.967 

591.944 

262.299 

507.381 

229.556 

443.958 

204.092 

394.630 

i  as.  730 

355.167 

31 

306.120 

592.222 

262.430 

507.619 

229.671 

444.167 

204.194 

394.815 

183.822 

355.333 

32 

306.272 

592.500 

262.561 

507.857 

229.785 

444.375 

204.296 

395.000 

183.913 

355.500 

33 

306.425 

592.778 

262.692 

508.095 

229.900 

444.583 

204.398 

395.185 

184.005 

355.667 

34 

306.578 

593.056 

262.823 

508.333 

230.015 

444.792 

204.500 

395.370 

184.097 

355.  a33 

35 

306.731 

593.333 

262.955 

508.571 

230.129445.000 

204.602 

395.556 

184.189 

356.000 

36 

306.889 

593.611 

263.090 

508.810 

230.  248  !  445.  208 

204.707 

395.741 

184.284 

356.167 

37 

307.046 

593.889 

263.225 

509.048 

230.366445.417 

204.812 

395.926 

184.378 

356.333 

38 

307.199 

594.167 

263.356 

509.286 

230.481  445.625 

204.914 

396.111 

184.470 

356.500 

39 

307.352 

594.444 

263  487 

509.524 

230.595 

445.833 

205.016 

396.296 

184.562 

356.667 

4O 

307.505 

594.722263.618 

509.762 

230.710446.042 

205.118 

396.481 

184.654 

356.833 

41 

307.658 

595.000263.749 

510.000 

230.825446.250 

205.220 

396.667 

184.745 

357.000 

42 

307.811 

595.278263.880 

510.238 

230.939446.458 

205.322 

396.852 

184.837 

357.167 

43 

307.963 

595.556264.011 

510.476 

231.054446.667 

205.424 

397.037 

184.929 

357.3^33 

44 

308.116 

595.833264.142 

514,714 

231.169446.875 

205.526 

397.222 

185.021 

357.500 

45 

308.269 

596.111 

264.273 

510.952 

231.283447.083 

205.628 

397.407 

185.113 

357.667 

46 

308.422 

596.389 

264.404 

511.190 

231.398447.292 

205.730 

397.593 

185.204 

357.833 

47 

308.575 

596  667264.535 

511.429 

231.513447.500 

205.832397.778 

185.296 

358.000 

48 

308.728 

596.944 

264.666 

511.667 

231.627447.708 

205.934 

^397.963 

185.388 

358.167 

49 

308.881 

597.222264.797 

511.905 

231.742447.917 

206.036 

308.148 

185.480 

358.333 

50 

309.033 

597.500264.928 

512.143 

231.857448.125 

206.138 

398.333 

185.571 

358.500 

51 

309.186 

597.778265.059 

512.381231.971  448.333 

206.240 

398.519 

185.663 

358.667 

52 

309.344 

598  056  265.195  512.619  232.090  448.542 

206.345 

398.704 

ia5  758 

358.8:33 

53 

309.502 

598.333265.330512.857 

232.208448.750 

206.450 

398.889 

185.853 

359.000 

54 

309.654 

598.611  265.461 

513.095 

232.323  448.  958 

206  552 

399.074 

185.944 

359.167 

55 

309.807 

598.889265.59i 

513.  .333  232  .  437  449  .  1  67 

206  654 

399.259 

186.036 

359.333 

56 

309.960 

599.167265.723513.571 

232.552449.375 

206.756 

399.444 

186.128 

359.500 

57 

310.113 
310.266 

599.444  265.854  513.810  232.667  449  583 
599.722  265.985  5  14.  048  1232.  781  449.792 

206.858399.630 
206.960l399.815 

186.220 
186.312 

•359.667 
359.833 

58 
59 

117 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


36° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

1861.68 

3600.00 

930.873 

1800.00 

620.623 

1200.00 

465.510900.000 

372  449 

720.000 

1 

1862.59 

3601.67 

931.331 

1800.83 

620.929 

1200.56 

465  739  900.417 

372.633 

720.333 

2 

1863.51 

3603.33 

931.790 

1801.67 

621.234 

1201.11 

465.  968!  900.  833 

372.810 

720.667 

3 

1864.43 

3605.00 

932.248 

1802.50 

621.540 

1201.67 

466.  197  1901.  250 

373.000 

721.000 

4 

1865.34 

3606.67 

9:32.707 

1803.33 

621.846 

1202.22 

466.427,901.667 

373.183 

721.333 

5 

1866.26 

3608.33 

933.165 

1804.17 

622.151 

1202.78 

466.656902.083 

373.366 

721.067 

6 

1867.18 

3610.00 

933.623 

1805.00 

622.457 

1203.33 

466.885902.500 

373  550 

722.000 

7 

1868.12 

3611.67 

934.096 

1805.83 

622.772 

1203.89 

467.121  902.917 

373.739 

722.  333 

8 

1869.07 

3613.33 

934.569 

1806.67 

623.087 

K'04.44 

467.358|'J03.333 

373.  928  1722.  607 

9 

1869.99 

3615.00 

935.027 

1807.50 

623.393 

1205.00 

467.587 

903.750 

374.111 

723.000 

10 

1870.90 

3616.67 

935.486 

1808.33 

623.698 

1205.56 

467.816 

904.167 

374.295 

723.333 

11 

1871.82 

3618.33 

935.944 

1809.17 

624.004 

1206.11 

468.045 

904.583 

374.478 

723.667 

12 

1872.74 

3620.00 

936.402 

1810.00 

624.310 

1206.67 

408.275 

905.000 

374  662 

724.000 

13 

1873.65 

3621.67 

936.861 

1810.83 

624.615 

1207.22 

468.504 

905.417 

374.845 

724.3:33 

14 

1874.57 

3623.33 

937.319 

1811.67 

624.921 

1207.78 

468.733 

905.833 

375.028 

724.667 

15 

1875  49 

3625.00 

937.778 

1812.50 

625.226 

1208.33 

408.962 

906.250 

375.212 

725  000 

16 

1876.40 

3626.67 

938.236 

1813.33 

625.532 

1208.89 

469  192 

906.667 

375.395 

725.383 

17 

1877.35 

3628.33 

938.709 

1814.17 

625.847 

1209.44 

469.428 

907.083 

875.584 

725.667 

18 

1878.29 

3630.00 

939.181 

1815.00 

626.162 

1210.00 

469.604 

907.500 

375.774 

726.000 

19 

1879.21 

3631.67 

939.640 

1815.83 

626.468 

1210.56 

469.894 

907.917 

375.957 

726.333 

20 

1880.13 

3633.33 

940.098 

1816.67 

626.774 

1211.11 

470.123 

908.333 

376.140 

726.667 

21 

1881.04 

3635.00 

940.557 

1817.50 

627.079 

1211.67 

470.352 

908.750 

376.324 

727.000 

22 

1881.96 

3636  67 

941.015 

1818,33 

627.385 

1212.22 

470.581 

909.167 

376.507 

727.333 

23 

1882.88 

3638.33 

941.473 

1819.17 

027.690 

1212.78 

470  811 

909  583 

376.691 

727.667 

24: 

1883.79 

3640.00 

941.932 

1820.00 

627.996 

1213.33 

471.040 

910.000 

376.874 

728.000 

25 

1884.74 

3(541  .  67 

942.404 

1820.83 

028.311 

1213.89 

471.270 

910.41? 

377.063 

728.333 

2G 

1885.69 

3643.33 

942.877 

1821.67 

628.626 

1214.44 

471.513 

910.833 

377.252 

728.607 

21 

1886  60 

3645.00 

943.336 

1822.50 

628.932 

1215.00 

471.742 

911.250 

877.486 

729.000 

28 

1887.52 

3646.67 

943.794 

1823.33 

629.238 

1215.56 

471.971 

911.667 

377.619 

729.333 

29 

1888.44 

3648.33 

944.252 

1824.17 

629.543 

1216.11 

472.200 

912.083 

377.802 

729.007 

30 

1889.35 

3650.00 

944.711 

1825.00 

629.849 

1216.67 

472.430 

912.500 

377.986 

730.000 

31 

1890.27 

3651.67 

945.169 

1825.83 

630.154 

1217.22 

472.659 

912.917 

378.169 

730.333 

32 

1891.19 

3653.33 

945.627 

1826.67 

630.460 

1217.78 

472.888 

913.333 

378  353 

730.607 

33 

1892.13 

3655.00 

946.100 

1827.50 

630.775 

1218.33 

473.124 

913.750 

•378.542 

731.000 

34 

1893.08 

3656.67 

946.573 

1828.33 

631.090 

1218.89 

473.361 

914.16? 

378.731 

731.333 

35 

1893.99 

3658.33 

947.031 

18<59.17 

531.396 

1219.44 

473.590 

914.583 

378.  914 

731.667 

36 

1894.91 

3660.00 

947.490 

1830.00 

631.702 

1220.00 

473.819 

915.000 

379.098 

732  000 

37 

1895.83 

3661.67 

947.948 

1830.83 

632.007 

1220.56 

474.048 

915.417 

379.281 

732.333 

38 

1896.74 

3663.33 

948.406 

1831.67 

632.313 

1221.11 

474.278 

915.833 

379.465 

732.607 

39 

1897.66 

3665.00 

948.865 

1832.50 

632.618 

1221.67 

474.507 

916.250 

:379.648 

733.000 

4O 

1898.58 

3666.67 

949.323 

1833.33 

632.924 

1222.22 

474.736 

916.667 

•379.831 

733.333 

41 

1899.52 

3668.33 

949.796 

1834.17 

633.239 

1222.78 

474.973 

917.083 

'380.020 

733.667 

42 

1900.47 

3670.00 

950.269 

1835.00 

C33.554 

1223.33 

475.209 

917.500 

380.210 

734.000 

43 

1901.38 

3671.67 

950.727 

1835.83 

633.860 

1223.89 

475.438 

917.917 

380.393 

734.333 

44 

1902.30 

3673.33 

951.185 

1836.67 

634.166 

1224.44 

475.667 

918.333 

380.576 

7:34.667 

45 

1903.22 

3675.00 

951.644 

1837.50 

634.471 

1225.00 

475.897 

918.750 

380.760 

735.000 

46 

1904.13 

3676.67 

952.102 

1838.33 

634.777 

1225.56 

476.126 

919.167 

380.943 

735.333 

47 

1905.08 

3678.33 

952.575 

1839.17 

635.092 

1226.11 

476.362 

919.583 

381.132 

735.667 

48 

1906.03 

3680.00 

953.048 

1840.00 

635.407 

1226.67 

476.599 

920.000 

481.888 

736.000 

49 

1906.94 

3681.67 

953.506 

1840.83 

635.713 

1227.22 

476.828 

920.41? 

381.505 

736.333 

50 

1907.86 

3683.33 

953.964 

1841.67 

636.018 

1227.78 

477.057 

920.833 

381.688 

736.667 

51 

1908.78 

3685.00 

954.423 

1842.50 

636.324 

1228.33 

477.286 

921.250 

381.872 

?  37.  000 

52 

1909.69 

3686.67 

954.881 

1843.33 

636.630 

1228.89 

477.516 

921.667 

382.055 

737.333 

53 

1910.64 

3688.33 

955.354 

1844.17 

636.945 

1229.44 

477.752 

922.083 

382.2441737.607 

54 

1911.58 

3690.00 

955.827 

1845.00 

637.260 

1230.00 

477.988 

922.500 

382.433:738.000 

55 

1912.50 

3691.67 

956.285 

1845.83 

637.566 

1230.56 

478.218 

922.91? 

$82.  61  7  788.  3*3 

56 

1913.42 

3693  3:3 

956.743 

1846.67 

637.871 

1231.11 

478.447 

923.333 

382.  800  :  7*8.  667 

57 

1914.83 

3695.00 

957.202 

1847.  5( 

038.177 

1231.67 

478.676 

<L>:3  ?:>( 

382.  984  i  739.0(0 

58 

1915.25 

3096.67 

957.660 

1848.33 

638.482 

1232.22 

478.905924.16? 

383.107 

739.3:;:) 

59 

1916.20 

3698.33 

958.133 

1849.1? 

638.798 

1232.78 

479.  142  1924.  583 

383.356 

739.007 

118 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

36° 

Tan. 
310.419 

Arc. 

eooTooo 

Tan. 
2667lil> 

Arc. 
5147286 

Tan. 

2327896 

Arc. 

450TOOO 

Tan. 

2077062 

Arc. 
4007000 

Tan.  I  Arc. 
18^740313607000 

M. 
~O~ 

310.  572  GOO.  278 

266.247 

514.524 

233.011 

450.208 

207.164 

400.185 

186.495 

360.167 

1 

310.724  600.556 

266.378 

514.762 

233.125 

450.417 

207.266 

400.370 

186.587 

360.3:33 

2 

310.8771600.833 

266.509 

515.000 

2:33.240 

450.625 

207.368 

400.556 

186.679 

360.500 

3 

811.080601.111 

266.640 

515.238 

233.355 

450.833 

207.470 

400.741 

186.770 

360.667 

4 

311.183 

601.389 

266.771 

515.476 

233.470 

451.042 

207.572 

400.926 

186.862 

360.833 

5 

311.336 

601.667 

266.902 

515.714 

233.584 

451.250 

207.673 

401.111 

186.954 

361.000 

6 

311.494 

601.944 

267.037 

515.952 

233.702 

451.458 

207.779 

401.296 

187.049 

361.167 

7 

311.651 

602.222 

267.172 

516.190 

233.821 

451.667 

207.884 

401.481 

187.143 

361.333 

8 

311.804 

602.500 

267.304 

516.429 

233.935 

451.875 

207.986 

401.667 

187.235 

361.500 

9 

311.957 

602.778 

267.435 

M6.667 

234.050 

452.083 

208.088 

401.852 

187.327 

361.667 

1O 

312.110 

603.056 

267.566 

:>16.905 

234.165 

452.292 

208.190 

402.037 

187.419 

361.833 

11 

312.263 

603.3:33 

267.697 

517.143 

234.279 

452.500 

208.292 

402.222 

187.511 

362.000 

12 

312.415 

603.611 

267.828 

517.381 

234.394 

452.708 

208.394 

402.407 

187.602 

362.167 

13 

312.568 

603.889 

267.959 

517.619 

234.509 

452.917 

208.496 

402.593 

187.694 

362.333 

14 

312.721 

604.167 

268.090 

517.857 

234.624 

453.125 

208.598 

402.778 

187.786 

362.500 

15 

312.874 

604.444 

268.221 

518.095 

234.738 

453333 

208.700 

402.963 

187.878 

362.667 

16 

313.032 

604.722 

268.356 

518.333 

234.857 

453.542 

208.805 

403.148 

187.972 

362.833 

17 

313.189 

605.000 

268.491 

518.571 

234.975 

453.750 

208.910 

403.333 

188.067 

363.000 

18 

313.342 

605.278 

268.622 

518.810 

235.089 

453.958 

209.012 

403.519 

188.159 

363.167 

19 

313.495 

605.556 

268  753 

519.048 

235.204 

454.167 

209.114 

403.704 

188.251 

363.333 

2O 

313.648 

605.833 

268.884 

519.286 

235.319 

454.375 

209.216 

403.889 

188.342 

363.500 

21 

313.801 

606.111 

269.015 

519.524 

235.434 

454.583 

209.318 

404.074 

188.434 

363.667 

22 

313.954 

606.389 

269.146 

519.762 

235.548 

454.792 

209.420 

404.259 

188.526 

363.833 

23 

314.106 

606.667 

269.277 

520.000 

235.663 

455.000 

209.522 

404.444 

188.618 

364.000 

24 

314.264 

606.944 

269.412 

520  238 

235.781 

455.208 

209.627 

404.630 

188.712 

364.167 

25 

314.422 

607.222 

269.548 

520.476 

235.899 

455.417 

209.732 

404.815 

188.807 

364.333 

26 

314.575 

007.500 

269.679 

520.714 

236.014 

455.625 

209.834 

405.000 

188.899 

364.500 

27 

314.727 

607.778 

269.810 

520.952 

-'36.129 

455.833 

209.930 

405.185 

188  991 

364.667 

28 

314.880 

608.056 

269.941 

521.190 

236.243 

456.042 

210.038 

405.370 

189.082 

364.833 

29 

315.033 

608.333 

270.072 

521.429 

236.358 

456.250 

210.140 

405.556 

189.174 

365.000 

30 

315.186 

608.611 

270.203 

521.667 

236.473 

456.458 

210.242 

405.741 

189.266 

365.167 

31 

315.339 

608.889 

270.334 

521.905 

236.588 

456.667 

210.344 

405.926 

189.358 

365.333 

32 

315.497 

609.167 

270.469 

522.143 

236.706 

456  875 

210.441) 

406.111 

189.452 

365.500 

33 

315.654 

609.444 

270.601 

522.381 

236.824 

457.083 

210.554 

406.296 

189.547 

365.667 

34 

315.807 

609.722 

270.735 

522.619 

236.939 

457.292 

210.656 

406.481 

189.639 

365.833 

35 

315.960 

610.000 

270.866 

522.857 

237.053 

457.500 

210.758 

406.667 

189.731 

366.000 

36 

316.113 

610.278 

270.997 

523.095 

237.168 

457.708 

210.860 

406.852 

189.822 

366.167 

37 

316.266 

610.556 

271.128 

523.333 

237.283 

457.917 

210.962 

407.037 

189.914 

366.333 

38 

316.418 

610.833 

271.259 

523.571 

237.397 

458.125 

211.064 

407.222 

190.006 

366.500 

39 

316.571 

611.111 

271.390 

523.810 

237.512 

458.333 

211.166 

407.407 

190.098 

366.667 

4O 

316.729 

611.389 

271.526 

524.048 

237.630 

458.542 

211.271 

407.593 

190.193 

366.833 

41 

316.887 

611.667 

271  661 

524.286 

237.749 

458.750 

211.376 

407.778 

190.287 

367.000 

42 

317.039 

611.944 

271.792 

524.524 

237.863 

458.958 

211.478 

407.963 

190.379 

367.167 

43 

317.192 

612.222 

271.923 

524.762 

237.978 

459.167 

211.580 

40S.148 

190.471 

367.33-3 

44 

317.345 

612.500 

272.054 

525.000 

238.093 

459.375 

211.682 

408.333 

190.563 

367.500 

45 

317.498 

612.778 

272.185 

525.238 

238.207 

459.583 

211.784 

408.519 

190.654 

367.667 

46 

317.656 

613.056 

272.320 

525.476 

238.326 

459.792 

211.889 

408.704 

190.749 

367.833 

47 

317.813 

613.333 

272.455 

525.714 

238.444 

460.000 

211.994 

408.889 

190.844 

368.000 

48 

317.966 

613.611 

272.586 

525.952 

238.559 

460.208 

212.096 

409.074 

190.935 

368.167 

49 

318.119 

613.889 

272.717 

526.190 

238.673 

460.417 

212.198 

409.259 

191.027 

368.333 

5O 

318.272 

614.167 

272.848 

526.429 

238.788 

460.625 

212.300 

409.444 

191.119 

368.500 

51 

318.425 

614.444 

272.979 

526.667 

238.903 

460.833 

212.402 

409.630 

191.211 

368.667 

52 

318.582 

614.722 

273.114 

526.905 

239.021 

461.042 

212.507 

409.815 

191.305 

368  833 

53 

318.740 

615.000 

273.250 

527.143 

239.139 

461.250 

212  612 

410.000 

191.400 

369.000 

54 

318.893615.278 

273.  3*1  1527.  381 

239.254461.458 

212.714 

410.  185 

191  .492 

369.167 

55 

319.046  615.556 

273.512527.619 

239.369461.C-67 

212.816 

410  370 

191.584 

369.333 

56 

319.1!)9615.833 

273.643527.857 

239.483461.875 

212.918 

410  556 

191.676 

369.500 

57 

319.35li6l6.ni 

273.774528.095 

239.598462.083 

213.020 

410.741 

191.767 

369.667 

58 

319.509616.389 

273.909528.333 

239.716'462.292213.125 

410.926 

191.862 

369.833 

59 

119 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


37° 

Ivi7 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan.      Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

1917.14  3700.00 

95H.OOO 

1KW.OO 

639.113 

1233.33 

479.378 

925.000 

383.545 

740.000 

1 

1918.008701.07959  0(54 

1850.83 

639.418 

1233.89 

479.607 

925.417 

383.729 

740  333 

2 

1918.973703.33 

959.522 

1851.67 

639.724 

1234.44 

479.837 

925.833 

383.912 

740.607 

3 

1919.893705.00 

959.981 

1852.50 

640.030 

1235.00 

480.000 

926.250 

384.090 

741.000 

4 

1920.81:3706  67 

960.439 

1853.33 

640.335 

1235.56 

480.295 

920.607 

384.279 

741.:J33 

5 

1921.758708.38 

960.912 

1854.17 

640.650 

1236.11 

480.531 

1(27.083 

384.408 

741.607 

6 

19*22.703710.00 

961.385 

1855.00 

640.966 

1236.67 

480.768 

927.500 

384.657 

742.000 

7 

1923.62 

3711.67 

961.843 

1855.83 

641.271 

1237.22 

480.997 

927.917 

384.841 

742.333 

8 

1924.53 

3713.33 

962.301 

1856.67 

041.577 

1237.78 

481.226 

928.333 

385.024 

742.007 

9 

1925.45  3715.00 

962.760 

1857.50 

041.882 

1238.33 

481.455 

928.750 

385.207 

743.000 

10 

1926.373716.67 

963.218 

1858.33 

642.188 

1238.S9 

481.685 

929.167 

385.391 

743.333 

11 

1927.31  3718.33 

963.691 

1859.17 

642.503 

1239.44 

481.921 

929.583 

385.580 

743.007 

13 

1928.263720.00 

964.164 

1860.00 

642.818 

1240.00 

482.157 

930.000 

385.769 

744.000 

13 

1929.  17  13721.  67 

964.622 

1860.83 

643.124 

1240.56 

482.387 

930.417 

385.952 

744.333 

14 

1930.093723.33 

965.080 

1861.67 

643.430 

1241.11 

482.616 

930.833 

386.136 

744.607 

15 

1931.013725.00 

965.539 

1862.50 

643.735 

1241.67 

482.845 

931.250 

386.319 

745.000 

16 

1931.  92  1  3726.  67 

965.997 

1863.33 

644.041 

1242.22 

483.  074 

931.667 

386.503 

745.333 

17 

1932.873728.33 

966.470 

1864.17 

044.356 

1242.78 

483.311 

932.083 

386.692 

745.607 

18 

1933.81  3730.00 

966.943 

1865.00 

044.671 

1243.33 

483.547 

932.500 

386.881 

746.000 

19 

1934.73 

3731.67 

967.401 

1865.83 

644.977 

1243.89 

483.776 

932.917 

387.064 

746.333 

20 

1935.65 

3733.33 

967.859 

1866.67 

645.282 

1244.44 

484.006 

933.333 

387.248 

746  .  667 

21 

1936.59 

3735.00 

908.332 

1867.50 

645.597 

1245.00 

484.242 

933.750 

387.437 

747.000 

22 

1937.54 

3736.67 

968.805 

1868.33 

645.913 

1245.50 

484.478 

934.107 

387.020 

747.333 

23 

1938.46  3738.33 

969.263 

1869.17 

646.218 

1240.11 

484.708 

934.583 

387.809 

747.607 

34 

1939.37 

8740.00 

909.722 

1870.00 

646.524 

1246.67 

484.937 

935.000 

387.993 

748.000 

25 

1940.32 

3741.67 

970.194 

1870.83 

646.839 

1247.22 

485.173 

935.417 

388.182 

748.333 

2G 

1941.26 

3743.33 

970.667 

1871.67 

647.154 

1247.78 

485.410 

935.833 

388.371 

748.667 

27 

1942.18 

3745.00 

971.125 

1872  .'50 

647.460 

1248.33 

485.639 

936.250 

388.555 

749.000 

28 

1943  10 

3746.67 

971.584 

1873.33 

647.765 

1248.89 

485.868 

936.607 

388.738 

749.333 

29 

1944.01 

3748.33 

972.042 

1874.17 

648.071 

1249.44 

486.097 

937.083 

388.921 

749.667 

30 

1944.93 

3750.00 

972.500 

1875.00 

648.377 

1250.00 

486.327 

937.500 

389.105 

750.000 

31 

1945.88 

3751.67 

972.973 

1875.83 

648.692 

1250.56 

486.503 

937.917 

389.294 

750.333 

32 

1946.82 

3753.  33 

973.446 

1876.67 

649.007 

1251.11 

486.799 

938.333 

389.483 

750.607 

33 

1947.74 

3755.00 

973.904 

1877.50 

649.313 

1251.07 

487.029 

938.750 

389.006 

751.000 

34 

1948.65 

3756.67 

974.363 

1878.33 

049.618 

1252.22 

487.258 

939.167 

389.850 

751.333 

35 

1949.60 

3758.33 

974.835 

1879.17 

649.933 

1252.78 

487.494 

939.583 

390.039 

751.667 

36 

1950.54 

3760.00 

975.308 

1880.00 

650.249 

1253.33 

487.731 

940.000 

390.228 

752.000 

37 

1951.46 

3761.67 

975.767 

1880.83 

650.554 

1253.89 

487.960 

940.417 

390.412 

752.333 

38 

1952  38 

3763.33 

976.225 

1881.07 

050.860 

1254.44 

488.189 

940.833 

390.595 

752.667 

39 

1953.32 

3705.00 

976.698 

1882.50 

651.175 

1255.00 

488.426 

941.250 

390.784 

753.000 

40 

1954.27 

3766.67 

977.170 

1883.33 

651.490 

1255.56 

488.662 

941.667 

390.973 

753.333 

41 

1955.19 

3768.33 

977.629 

1884.17 

651.796 

1256.11 

488.891 

942.083 

391.157 

753.667 

42 

1956.10 

3770.00 

978.087 

1885.00 

652.101 

1256.67 

489.120 

942.500 

391.340 

754.000 

43 

1957.05 

3771.67 

978.560 

1885.83 

052.416 

1257.22 

489.357 

942.917 

391.529 

754.333 

44 

1957.99 

3773.33 

979.033 

1886.67 

652.732 

1257.78 

489.593 

943.333 

391.718 

754.607 

45 

1958.91 

3775.00 

979.491 

1887.50 

653.037 

1258.33 

489.822 

943.750 

391.902 

755.000 

46 

1959.83 

3776.67 

979.949 

1888.33 

653.343 

1258.89 

490.052 

944.167 

392.085 

755.333 

47 

1960  77 

3778.33 

980.422 

1889.17 

653.658 

1259.44 

490.288 

944.583 

392.274 

755.607 

48 

1961.72 

3780.00 

980.895 

1890.00 

653.973 

1260.00 

490.524 

945  000 

392.463 

756.000 

49 

1962.63 

3781.67 

981.353 

1890.83 

G54.279 

1260.56 

490.754 

945.417 

392.647 

756.333 

5O 

1963.55 

3783.33 

981.812 

1891.67 

654.584 

1261.11 

490.983  945.833 

392.830 

756.667 

51 

1964.50 

3785.00 

982.284 

1892.50 

654.900 

1261.67 

491.219946.250 

393  019 

757.000 

53 

1965.44 

3786.67 

982.757 

1893.33 

655.215 

1262.22 

491.456,946.667 

393.208 

757.333 

53 

1966.30 

3788.33 

983.215 

1S94.17 

655  5:20 

1262.78 

491.685947.083 

393.392 

757.607 

54 

1967.28 

3790.00 

983.674 

1895.00 

655.826 

1263.33 

491.914:947.500 

393.575 

758.000 

55 

1968.22 

3791.67 

984.14611895.83 

656.141 

1263.89 

492.15l'947.917 

393.764 

758.333 

56 

1969.17 

3793.33 

984.6191896.67 

656.456 

1264.44 

492.387  948.333 

393.954 

758.607 

57 

1970.08 

3795.00 

985.0781897.50 

656.762 

1265.00 

49.2.616948.750 

394.  137  1759.000 

58 

1971.00 

3796.67 

985.5361898.33 

657.008 

1205.56 

492.845949.167 

394.320759.333 

59 

1971.94 

3798.33 

9^6.009  1899.17 

657.383 

1266.11 

493.082949.583 

394.  509  1759.007 

120 


'TABLE  XIV. — ACTUAL  TANGENTS,  ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

37" 

Tan. 

319.667 

Arc. 

616.667 

Tan. 

274.044 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 
411.111 

Tan. 

191.957 

Arc. 

370.000 

M. 

528.571 

239.835 

462  500 

213.230 

O 

3  19.8:20 

616.944 

274.175528.810239.949 

462.708 

213.332 

411.296 

192.048 

370.167 

1 

319.972 

617.222 

274.306  529.048 

240  064 

462.917 

213.434 

411.481 

192.140 

370.333 

2 

320.125 

617.500 

274.437 

529.286 

240.179 

463.125 

213.536 

411.667 

192.232 

370.500 

3 

320.278 

617.778 

274.568 

529.524 

240.293 

463.333 

213.638 

411.852 

192.324 

370.667 

4 

320.436 

618.056 

274.703 

529.762 

240.412 

463.542 

213.743 

412.037 

192.418 

370.833 

5 

320.593 

618.333 

274.838 

530.000 

240.530 

463.750 

213.849 

412.222 

192.513 

371.000 

6 

320.746 

618.611 

274.970 

530.238 

240.644 

463.958 

213.951 

412.407 

192.605 

371.167 

7 

320.899 

618.889 

275.101 

530.476 

240.759 

464.167 

214.053 

412.593 

192.697 

371.333 

8 

321.052 

619.167 

275.232 

530.714 

240.874 

464.375 

214.155 

412.778 

192.788 

371.500 

9 

321.205 

619.444 

275.363 

530.952 

240.989 

464.583 

214.256 

412.963 

192.880 

371.667 

10 

321.363 

619.722 

275.498 

531  .  190 

241.107 

464.792 

214.362 

413.148 

192.975 

371.833 

11 

321.520 

620.000 

275.633 

531.429 

241.225 

465.000 

214.467 

413.333 

193.070 

372.000 

12 

321.673 

620.278 

275.764 

531.667 

241.340465.208 

214.569 

413.519 

193.161 

372.167 

13 

321.826 

620.556 

275.895 

531.905 

241.454 

465.417 

214.671 

413.704 

193.253 

372.333 

14 

321.979 

620.833 

276.026 

532.143 

241.569 

465  625 

214.773 

413.889 

193.345 

372.500 

15 

322.132 

621.111 

276.157 

532.381 

241.684 

465.833 

214.875 

414.074 

193.437 

372.667 

16 

322.289 

621.389 

276.292 

532.619 

241.802 

466.042 

214.980 

414.259 

193.531 

372.8.33 

17 

322.447 

621.667 

276.42, 

532.857 

241.920 

466.250 

215.085 

414.444 

193.626 

373.000 

18 

322.600 

621.944 

276.558 

533.095 

242.035 

466.458 

215.187 

414.630 

193.718 

373.167 

19 

322.753 

622.222 

276.689 

533.333 

242.150 

466.667 

215.289 

414.815 

193.810 

373.333 

20 

322.910 

622.500 

276.825 

•333.571 

242.268 

466.875 

215.394 

415.000 

193.904 

373.500 

21 

323.068 

622.778 

276.960 

533.810 

242.386 

467.083 

215.499 

415.185 

193.999 

373.667 

22 

323.221 

623.056 

277.091 

534.048 

242.501 

467.292 

215.601 

415.370 

194.091 

373.833 

23 

323.374 

623.333 

277.222 

534.286 

242.616 

467.500 

215.703 

415.556 

194.183 

37'4.000 

24 

323.531 

623.611 

277.357 

534.524 

242.734 

467.708 

215.808 

415.741 

194.277 

374.167 

25 

323.689 

623.889 

277.492 

534.762 

242.852 

467  917 

215.913 

415.926 

194.372 

374.333 

26 

323.842 

624.167 

277.623 

535.000 

242.967 

468.125 

216.015 

416.111 

194.464 

374.500 

27 

323.995 

624.444 

277.754 

535.238 

243.082 

468.333 

216.117 

416.296 

194.555 

374.667 

28 

324.147 

624.722 

277.885 

535.476 

243.196 

468.542 

216.219 

416.481 

194.647 

374.833 

29 

324.300 

625.000 

278.016 

535.714 

243.311 

468.750 

216.321 

416.667 

194.739 

375.000 

30 

324.458 

625.278 

278.151 

535.952 

243.429 

468.958 

216.426 

416.852 

194.834 

375.167 

31 

324.616 

625.556 

278.287 

536.190 

243.547 

469.167 

216.532 

417.037 

194.928 

375.3133 

32 

324.768 

625.833 

278.418 

586.429 

243.662 

469.375 

216.634 

417.222 

195.020 

375.500 

33 

324.921 

626.111 

278.549 

536.667 

243.777 

469.583 

216.735 

417.407 

195.112 

375.667 

34 

325.079 

626.389 

278.684 

536.905 

243.895 

469.792 

216.841 

417.593 

195.207 

375.833 

35 

325.237 

626.667 

278.819 

537.143 

244.013 

470.000 

216.946 

417.778 

195.301 

376.000 

36 

325.389 

626.944 

278.950 

537.381 

244.128 

470.208 

217.048 

417.963 

195.393 

376.167 

37 

325.542 

627.222 

279.081 

537.619 

244.243 

470.417 

217.150 

418.148 

195.485 

376.333 

38 

325.700 

627.500 

279.216 

537.857 

244.361 

470.625 

217.255 

418.333 

195.579 

376.500 

39 

325.858 

627.778 

279.351 

538.095 

244.479 

470.  833 

217.360 

418.519 

195.674 

376.667 

40 

326.010 

628.056 

279.482 

538.333 

244.594 

471.042 

217.462 

418.704 

195.766 

376.833 

41 

326.163 

628.333 

279.613 

538  571 

244.709 

471.250 

217.564 

418.889 

195.858 

377.000 

42 

326.321 

628.611 

279.749 

538.810 

244.827 

471.458 

217.669 

419.074 

195.952 

377.167 

43 

326.479 

628.889 

279.884 

539.048 

244.945 

471.667 

217.774 

419.259 

196.047 

377.333 

44 

326.631 

629.167 

280.015 

539.286 

245.060 

471.875 

217.876 

419.444 

196.139 

377.500 

45 

326.781 

629.444 

280.146 

539.524 

245.175 

472.083 

217.978 

419.630 

196.231 

377.667 

46 

326.942 

629.722 

280.281 

539.762 

245.293 

472.292 

218.083 

419.815 

196.325 

377.833 

47 

327.100 

630.000 

280.416 

540.000 

245.411 

472.500 

218.188 

420.000 

196.420 

378.000 

48 

327.252 

630.278 

280.547 

540.238 

245.526 

472.708 

218.290 

420.185 

196.512 

378.167 

49 

327.405 

630.556 

280.678 

540.476 

245.640 

472.917 

218.392 

420.370 

196.604 

378.333 

50 

327.563 

630.833 

280.813 

540.714 

245.759 

473.125 

218.498 

420.556 

196.698 

378.500 

51 

327.721 

631.111 

280.348 

540.952 

245.877 

473.333 

218.603 

420.741 

196.793 

378.667 

52 

327.873 

631.389 

281.079 

541.190 

245.992 

473.542 

218.705 

420.926 

196.885 

378.833 

53 

328.026 

631.667 

281.210 

541.429 

246.106 

473.750 

218.807 

421.111 

196.976 

379.000 

54 

328.184 

631.944 

281.346 

541.667 

246.225 

473.958 

218.912 

421.296 

197.071 

379.167 

55 

328.342 

632.  22  -2 

281.481 

541.905 

246.343 

474.167 

219.017 

421.481 

197.166 

379.333 

56 

328.494 

632.500 

281.612 

542.143 

246.458 

474.375 

219.119 

421.667 

197.258 

379.500 

57 

328.647 

632.778 

281.743 

542.381 

246.572 

474.583 

219.221 

421.852 

197.349 

379.667 

58 

328.805 

633.056 

281.878 

542.619 

246.691 

474.792 

219.326 

422.037 

197.444 

379.833 

59 

131 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


38° 
M7 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  I   Arc. 

~0~ 

1972.89 

3800.00 

9S6.481  1900.00 

657.698 

1266.67 

493.318 

950.000394.699760.000 

1 

1973.81 

3801.67 

986.9401900.83 

658.003 

1267.22 

493.547 

950.417394  882 

760.333 

2 

1974.72 

3803.33 

987.  398  1  1901.  67 

658.309 

1267.78 

493.777 

950.833395.065 

760.667 

3 

1975.67 

3805.00 

987.871  1902.50 

658.624 

1268.33 

494.013 

951.250395.255 

761.000 

4 

1976.61 

3806.67 

988.344  1903.33 

658.939 

1268.89 

494.249 

951.667395.444 

761.333 

5 

1977.  53  1  3808.  33 

988.802:1904.17 

659.245 

1269.44 

494.479 

952.083395.627 

761.667 

6 

1978.45 

3810.00 

989.  260  !  1905.  00 

659.551 

1270.00 

494.708 

952.500395.810 

762.000 

7 

1979.3!) 

3811.67 

989.733  1905.83 

659.866 

1270.56 

494.944 

952.9J7i396.000 

762.333 

8 

1980.34 

3813.33 

990.206 

1906.67 

660.181 

1271.11 

495.181 

953.333396.189 

762.667 

9 

1981.28 

3815.00 

990.678 

1907.50 

660.496 

1271.67 

495.417 

953.750 

396.378 

763.000 

10 

1982.23 

3816.67 

991.151 

1908.33 

660.811 

1272.22 

495.653 

954.167 

396.567 

763.333 

11 

1983.15 

3818.33 

991.610 

1909.17 

661.117 

1272.78 

495.883 

954.583:396.750 

763  667 

12 
13 

1934.06 
1985.01 

3820.00 
3821.67 

992.068 
992.541 

1910.00 
1910.83 

661.423 

661.738 

1273.33 

1273.89 

496.112 
496.348 

955.000J  396.  934 
955.417397.123 

764.000 
764.333 

14 

1985.95 

3823  33 

993.  013  [191  1.67 

662.053 

1274.44 

496.585 

955.833:397.312 

764.667 

15 

1986.87 

3825.00 

993.  472  !  191  2.  50 

662.358 

1275.00 

496.814 

956.  250;  397.495 

765.000 

16 

1987.79 

3826.67 

993.930il913.33 

662.664 

1275.56 

497.043 

956.  667  j  397.  679 

765.333 

17 

1988.73 

3828.33 

994.403 

1914.17 

662.979 

1276.11 

497.280 

957.083397.868 

765  .  667 

18 

1989.68 

3830.00 

994.876 

1915.00 

663.294 

1276.6? 

497.516 

957.500 

398.057 

766.000 

19 

1990.60 

3831.67 

995.334 

1915.83 

663.600 

1277.22 

497.745 

957.917 

398.241 

766.333 

20 

1991.51 

3833.33 

995.792 

1916.67 

663  906 

1277.78 

497.974 

958.333 

398.424 

766.667 

21 

1992.46 

3835.00 

996.265 

1917.50 

664.221 

1278.33 

498.211 

958.750398.613 

767.000 

22 

1993.40 

3836.67 

996.738 

1918.33 

664.536 

1278.89 

498.447 

959.167 

398.802 

767.333 

23 

1994.35 

3838.33 

997.211 

1919.17 

664.851 

1279.44 

498.684 

959.583 

398.991 

767.667 

24 

1995.29 

3840.00 

997.683 

1920.00 

665.166 

1280.00 

498.920 

960.000 

399.181 

768.000 

25 

1996.21 

3841  67 

998.142 

1920  83 

665.472 

1280.56 

499.149 

960.417 

399.364 

768.333 

26 

1997.13 

3843  33 

998.600 

1921.67 

665.777 

1281.11 

499.378 

960.833 

399.547 

768.667 

27 

1998.07 

3845.00 

999.073 

1922.50 

666.093 

1281.67 

499.615 

961  250 

399.730 

769.000 

28 

1999.02 

3846.67 

999.545 

1923.33 

666.408 

1282.22 

499.851 

961  .  667 

399.926 

769.333 

29 

1999.96 

3848.33 

1000.02 

1924.17 

666.723 

1282.78 

500.088 

962.083 

400.115 

769.667 

30 

2000.91 

3850.00 

1000.49 

1925.00 

667.038 

1283.33 

500.324 

962.500 

400.304 

770.000 

31 

2001.83 

3&51.67 

1000.95 

1925.83 

667.344 

1283.89 

500.553 

962.917 

400.48? 

770.333 

32 

2002.74 

3853.33 

1001.41 

1926.67 

667.649 

1284.44 

500.782 

963.333 

400.671 

770.667 

33 

2003.69 

3855.00 

1001.88 

1927.50 

667.965 

1285.00 

501.019 

963.750 

400.  86( 

771.000 

34 

2004.63 

3856.67 

1002.35 

1928.33 

668.280 

1285.56 

501.255 

964.167 

401.049 

771.333 

35 

2005.58 

3858.33 

1002.83 

1929.17 

668.595 

1286.11 

501.492 

964.583 

401.238 

771.667 

36 

2006.52 

3860.00 

1003.30 

1930.00 

668.910 

1286.67 

501.728 

965.000 

401.427 

772.000 

37 

2007.44 

3861.67 

1003.76 

1930.83 

669.216 

1287.22 

501.957 

965.417 

401.611 

772.333 

38 

2008.36 

3863.33 

1004.22 

1931.67 

669.521 

1287.78 

502.186965.833 

401.794 

772.667 

39 

2009.30 

3865.00 

1004.79 

1932.50 

669.836 

1288.33 

502.423 

966.250 

401.983 

773.000 

4O 

2010.25 

3866.67 

1005.16 

1933.  as 

670.152 

1288.89 

502.659 

966.667 

402.172 

773.333 

41 

2011.19 

3868.33 

1005.73 

1934.17 

670.467 

1289.44 

502.896967.083 

402.361 

773.667 

42 

2012.14 

3870.00 

1006.11 

1935.00 

670.782 

1290.00 

503  132  967.500 

402.551 

774.000 

43 

2013.06 

3871.67 

1006.56 

1935.83 

671.088 

1290.56 

503.361  967.917 

402.734 

774.333 

44 

2013.97 

3873.33 

1007.02 

1936.67 

671.393  1291.11 

503.591  968.333 

402.917 

774.667 

45 

2014.92 

3875.00 

1007.50 

1937.50 

671.  708  J1291.  67 

503.827l96S.750 

403.107 

775.000 

46 

2015.86 

3876.67 

1007.97 

1938.33 

672.  023  '1292.  22 

504.063969.167 

403.296 

775.333 

47 

2016.81 

3878.33 

1008.44 

1939.17 

672.339!  1292.  78 

504.300969.583 

403.485 

775.667 

48 

2017.75 

3880.00 

1008.91 

1940.00 

672.65411293.33 

504.536:970.000 

403.674 

776.000 

49 

2018.67 

3881.67 

1009.37 

1940.83 

672.959 

1293.89 

504.765,970.417 

403.857 

776.333 

50 

2019.59 

3883.33 

1009.83 

1941.67 

673.265 

1294.44 

504.995970.833 

404.041 

776.667 

51 

2020.53 

3885.00 

1010.30 

1942.50 

673.580 

1295.00 

505  231  971.2501404.230 

777.000 

52 

2021.48 

3886.67 

1010.78 

1943.33 

673.895 

1295.56 

505.467971*667404.419 

777.333 

53 

2022.42 

3888.33 

1011.25 

1944.17 

674.210 

1296.11 

505.704  972.083404.608 

777.667 

54 

2023.37 

3890.00 

1011.72 

1945.00 

674.526 

1296.67 

505.940972.500:404.797 

778.000 

55 

2024.293891.67 

1012.18 

1945.83 

674.831 

1297.22 

506.169972.917404.981 

778.333 

56 

2025.  20  3893.  33!  101  2.  64 

19-16.67 

673.187 

1297.78 

506  .  399  973  .  333  405  .  1  64 

778.667 

57 

2026.153895.00 

1013.11 

1947.50 

575.452 

1298.33 

506  .  635  973  .  750  '4  05  .  353 

779.000 

58 

2027.  09  13896.67 

1013.58 

1948.33 

675.767 

1298.88 

506.871  974.167405.542 

779.333 

59 

2028.  0413898.  33  1014.  06 

1949.1? 

676.082 

1299.44 

507.108974.583i405.732 

779.667 

TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

38° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

328.963 

633.333 

282.013542.857 

246.809 

475.000 

219.431 

422.222 

197.539 

380.000 

O 

329.115633.611 

282.144543.095 

246.923 

475.208 

219.533 

422.407 

197.630 

380.167 

'   1 

329.  268  1633.889 
329.426634.167 

282.2751543  333 
282.410543.571 

247.038 
247.156 

475.417 
475.625 

219.  635 
219.740 

422.593 

422.778 

197.722 
197.817 

380.333 
380.500 

2 
3 

329.583 

634.444 

282.545:543.810 

247.275 

475.833 

219.845 

422.963 

197.912 

380.667 

4 

329.736 

634.722 

282.677 

544.048 

247.389 

476.042 

219.947 

423.148 

198.003 

380.833 

5 

329.881) 

635.000 

282.808 

544.286 

247.504 

476.250 

220.049 

423.333 

198.095 

381.000 

6 

330.047 

635.278 

282.943 

544.524 

247.622 

476.458 

220.154 

423.519 

198.190 

381.167 

7 

330.204 

635.556 

283.078 

544.762 

247.741 

476.667 

220.260 

423.704 

198.284 

381  .333 

8 

330.362 

635.833 

283.213 

545.000 

247.859 

476.875 

220.365 

423.889 

198.379 

381.500 

9 

330.520 

636.111 

283.348 

545.238 

247.977 

47".  083 

220.470 

424.074 

198.474 

381  667 

10 

330.673 

636.389 

283.479 

545.476 

248.092 

47".  292 

220.572 

424.259 

198.566 

381.833 

11 

330  825 

636.667 

283.610 

545.714 

248.207 

47".  500 

220.674 

424.444 

198.657 

382.000 

12 

330.983 

636.944 

883,746 

545.952 

248.325 

47".  708 

220.779 

424.630 

198.752 

382  167 

13 

331.141 

637.222 

283.880 

546.190 

24».443 

47".  917 

220.884 

424.815 

198.847 

382.333 

14 

331.294 

637.500 

284.012 

546.429 

248.558 

478.125 

220.986 

425.000 

198.938 

382.:.00 

15 

881.446 

637.778 

284.143 

546.667 

248.672 

478.333 

221.088 

425.185 

199.030 

382  667 

16 

331.604 

638.056 

284.278 

546.905 

248.791 

478.542 

221.193 

425.370 

199.125 

382.833 

17 

331.762 

638.333 

284.413 

547.143 

248.909 

478.750 

221.298 

425.556 

199.220 

383.000 

18 

331.915 

638.611 

284.544 

547.381 

249.024 

478.958 

221.400 

425.741 

199.311 

383.167 

19 

332.067 

638.889 

284.675 

547.619 

249.138 

479.167 

221.502 

425.926 

199.403 

383.333 

2O 

332.225 

639.167 

284.810 

547.857 

249.257 

479.375 

221.607 

426.111 

199.498 

383.500 

21 

332.383 

6:39.444 

284.945 

548.095 

249.375 

479.583 

221.713 

426.296 

199.592 

383.  C67 

2  2 

332.540 

639.722 

285.080 

548.333 

249.493 

479.792 

221.818 

426.481 

199.687 

383.833 

23 

332.  60S 

640.000 

285.215 

548.571 

249.611 

480.000 

221.923 

426.667 

199.782 

384.000 

24 

332.851 

640.278 

285.347 

548.810 

249.726 

480.208 

222.025 

426.852 

199.874 

384  107 

25 

383.004 

640.556 

285.478 

549.048 

249.841 

480.417 

222.127 

427.037 

199.965 

384.333 

26 

333.161 

640.833 

285.613 

549.286 

249.959 

480.625 

222.232 

427.222 

209.060 

384.500 

27 

333.319 

641.111 

285.748 

549.524 

250.077 

480.833 

222.337 

427.407 

200.155 

384.667 

28 

333.477 

641.389 

285.883 

549.762 

250.196 

481.042 

222.442 

427.593 

200.249 

384.833 

29 

333.634 

641.667 

286.018 

550.000 

250.314 

481.250 

222.547 

427.778 

200.344 

385.000 

30 

3:33.787 

641.944 

289  149 

550.238 

250.429 

481  458 

222.649 

427.963 

200.436 

385.167 

31 

333.940 

642.  22* 

286.280 

550.476 

250  543 

481.667 

222.751 

428.148 

200.528 

385.333 

32 

834.098 

642.500 

286.415 

550.714 

250.661 

481.875 

222.856 

428.333 

200.622 

385.500 

33 

334.255 

642.778 

286.550 

550.952 

250.780 

482.083 

222.962 

428.519 

200.717 

385.667 

34 

334.413 

643.056 

286.686 

551.190 

250.898 

482.292 

223.067 

428.704 

200.812 

385.833 

35 

334.571 

643.333 

286.821 

551.429 

251.016 

482.500 

223.172 

428.889 

200.906 

386.000 

36 

334.723 

643.611 

286.952 

551.667 

251.131 

482.708 

223.274 

429.074 

200.998 

386.167 

37 

3:34.876 

643.889 

287.083 

551.905 

251.246 

482.917 

223.376 

429.259 

201.090 

386.333 

38 

335.034 

644.167 

287.218 

552.143 

251.364 

483.125 

223.481 

429.444 

201.184 

386.500 

39 

335.192 

644.444 

287.353 

552.381 

251.482 

483.333 

223.586 

429.630 

201.279 

386.667 

4O 

335.349 

644.722 

287.488 

552.619 

251.600 

483.542 

223.691 

429.815 

201.374 

386.833 

41 

335.507 

645.000 

287.623 

552.857 

251.719 

483.750 

223.796 

430.000 

201.468 

387.000 

42 

335.660 

645.278 

287.754 

553.095 

251.833 

483  958 

223.898 

430.185 

201.560 

387.167 

43 

3:35.813 

645.556 

287.885 

553.333 

251.948 

484.167 

224.000 

430.370 

.201.652 

387.3:33 

44 

335.970 

645.833 

288.021 

553.571 

252.066 

484.375 

224.106 

430.556 

201.747 

387.500 

45 

336.128 

646.111 

288.156 

553.810 

252.185 

484.583 

224.211 

430.741 

201.841 

387.607 

46 

336.285 

646.389 

288.291 

554.048252.303 

484.792 

224.316 

430.926 

201.936 

387.833 

47 

336  443 

646.667 

288.426 

554.286 

252.421 

485.000 

224.421 

431.111 

208.031 

388.000 

48 

336.596 

646.944 

288.557554.524 

252.536 

485.208 

224  523 

431.296 

202.122 

388.167 

49 

336.749 

647.222 

288.688554.762 

252.651 

485.417 

224.625 

431.481 

202.214 

388.333 

5O 

336  906 

647.500 

288.823555.000252  769 

485.625 

224.730 

431.667 

202.309 

388.  £00 

51 

3:37.064 

647  .  77'8  288  .  958  555  .  23S  252  .  887 

485.833 

224.835 

431.852 

202.404 

388.  007 

52 

337.222 

648.056  280.094  555.476  253.005 

486.042 

224.940 

432.037 

202.498 

388.  K33 

53 

337.370 

64S  3331289  .  220  555  .  714  253  .124 

486.250 

225.045 

432.222 

202.59.3 

389.000 

54 

337.532 

648.611  289.30D  555.952  2ft3  238 

48(5.458 

225.147 

432.407 

202.685 

389.167 

55 

337  .  OH5  64H  .  889  289  .  491  556  .  1  90  253  .  353 

486.667 

225.249 

432.593 

202.776 

389.333 

56 

337.843  6-19.  107  289.  (26  556.429  253.471 

486.875 

225.355 

432.778 

202.871 

389.500 

57 

338.000  649.444  289  761  556.667  253.590 

487.083 

225.460 

432.963 

202.966 

389.607 

58 

338  .  158^  649  .  702  289  .  896  556  .  905  253  .  708 

487.292 

225.565 

433.148 

203.060 

389.833 

59 

TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


39° 

1°  Curve. 

3°  Curve. 

3°  Curve, 

4°  Curve. 

5°  Curve. 

M. 

Tan. 
2028798 

Arc. 

Tan. 

A  re. 

Tan. 

Arc. 

Tan. 

Arc. 

975.000 

Tan. 

Arc. 

780.  UOO 

O 

3900.00 

1014.53 

1950.00 

676.398 

1300.00 

507.344 

405.921 

1 

2029.93 

3901.67 

1015.00 

1950.83 

676.713 

1300.56 

507.581 

975.417 

406.110 

780.  333 

2 

2030.87 

3903.33 

1015.47 

1951.67 

677.028 

1301.11 

507.817 

975.833 

406.299 

780.607 

3 

2031.79 

3905.00 

1015.93 

1952.50 

077.333 

1301.67 

508.046 

976.250 

406.482 

781.000 

4 

2032.71 

3906.67 

1016.39 

1953.33 

077  .  G3(J 

1302.22 

508.275 

976.667 

406.660 

781.333 

5 

2033  65 

3908.33 

1016.86 

1954.17 

077.  95^ 

1302.78 

508.512 

977.083 

406.855 

781.667 

6 

203  t.  GO 

3910.00 

1017.34 

1955.00 

078.269 

1303.33 

508.748 

977.500 

407.044 

182.000 

7 

2035.54 

3911.67 

1017.81 

1955.83 

078.585 

1303.89 

508.985 

977.917 

407.233 

782.333 

8 

2033.49 

3913.33 

1018.28 

1956.67 

678.900 

1304.44 

509.221 

978.333 

407.422 

782.607 

9 

2037.43 

3915.00 

1018.75 

1957.50 

679.215 

1305.00 

509.457 

978.750 

407.611 

783.000 

1O 

2038.38 

3916.67 

1019.23 

1958.33 

679.530 

1305.56 

509.694 

979.167 

407.801 

;  83.  333 

11 

2039.30 

3918.33 

1019.69 

1959.17 

679.836 

1306.11 

509.923 

979.583 

407.984 

783.  G07 

12 

2040.21 

3920.00 

1020.14 

1960.00 

680.141 

1306.07 

510.152 

980.000 

408.107 

784.000 

13 

2041.16 

3921.67 

1020.62 

1960.83 

680.456 

1307.22 

510.389 

9S0.417 

408.357 

784.333 

14 

2042.10 

3923.33 

1021.09 

1961.67 

680.772 

1307.78 

510.625 

980.833 

408.546 

784.067 

15 

2043.05 

3925.00 

1021.56 

1962.50 

681.087 

1308.33 

510.861 

981.250 

408.735 

785.000 

16 

2044.00 

3926.67 

1022.04 

1963.33 

681.402 

1308.89 

511.098 

981.667 

408.924 

785.333 

17 

2044.94 

3928.33 

1022.51 

1904.17 

681.717 

1309.44 

511.334 

982.083 

409.113 

785.607 

18 

2045.89 

3930.00 

1022.98 

1965.01 

68.2.03.' 

1310.00 

511.571 

982.500 

409.302 

786.000 

19 

2046.83 

3931.67 

1023.45 

1965.83 

682.347 

1310.56 

511.807 

982.917 

409.491 

786.333 

20 

2047.78 

3933.33 

1023.93 

1966.67 

682.663 

1311.11 

512.043 

983.333 

409.680 

786.667 

21 

2048.69 

3935.00 

1024.38 

1967.50 

682.968 

1311.67 

512.273 

983.750 

409.804 

787.000 

22 

2049.61 

3936.67 

1024.84 

1968.33 

683.274 

1312.22 

512.502 

984.167 

410.047 

787.333 

23 

2050.56 

3938.33 

1025.32 

1909.17 

683.589 

1312.78 

512.738 

984.583 

410.236 

787.007 

34 

2051.50 

39  JO.  00 

1025.79 

1970.00 

683.904 

1313.33 

512.975 

985.000 

410.426 

788.000 

35 

2052.45 

3941.67 

1026.26 

1970.83 

684.219 

1313.89 

513.211 

985.417 

410.615 

788.333 

36 

2053  39 

3913.33 

1026.73 

1971.67 

084.534 

1314.44 

513.447 

985.833 

410.804 

788.607 

37 

2054.34 

3945.00 

1027.21 

1972.50 

684.850 

1315.  CO 

513.084 

986.250 

410.993 

789.000 

38 

2055.28 

3946.67 

1027.68 

HI73.33 

685.165 

1315.50 

513.920 

986.667 

411.182 

789.333 

39 

2056.23 

3948.33 

1028.  15 

1974.17 

085.480 

1316.11 

514.157 

987.083 

411.371 

789.007 

30 

2057.17 

3950.00 

1028  62 

1975.00 

685.795 

1316.67 

514.393 

987.500 

411.560 

790.000 

31 

2058.12 

3951.67 

1029.10 

1975.83 

086.110 

1317.22 

514.629 

987.917 

411.750 

790.333 

33 

2059.06 

3953.33 

1029.57 

1976.67 

086.425 

1317.78 

514.800 

988.333 

411.939 

790.067 

33 

2059.98 

3955.00 

1030  03 

1977.50 

686.731 

1318.33 

515.095 

888.750 

412.122 

791.000 

34 

2060.90 

3956.67 

1030.49 

1978.33 

087.037 

1318.89 

515.324 

989.167 

412.305 

791.333 

35 

2061.84 

3958.33 

1030.96 

1979.17 

687.352 

1319.44 

515.561 

989.583 

412.495 

791.  G07 

36 

2062.79 

3960.00 

1031.43 

1980.00 

687.667 

1320.00 

515.797 

990.000 

412.684 

792.000 

37 

^063.73 

3961.67 

1'  :31.90 

1980.83 

687.982 

1320.56 

516.033 

990.417 

412.873 

792.333 

38 

2064.68 

3963.33 

1032.38 

1981.67 

688.297 

1321.11 

516.270 

990.833 

413.062 

792.007 

39 

2065.62 

3965.00 

1032.85 

1982.50 

688.612 

1321.67 

516.506 

991.250 

413.251 

793  000 

40 

2066.57 

3966.67 

1033.32 

1983.33 

688.928 

1322.22 

516.743 

991.667 

413.440 

793.333 

41 

2067.52 

3968.33 

1033.80 

1984.17 

689.243 

1322.78 

516.979 

992.083 

413.629 

793.667 

43 

2068.46 

3970.00 

1031.27 

19a5.00 

089.558 

1323.33 

517.215 

992.500 

413.819 

794.000 

43 

2069.41 

3971.67 

1034.74 

1985.83 

689.873 

1323.89 

517.452 

992.917 

414  008 

794.333 

44 

2070.35 

3973.33 

1035.21 

1986.67 

690.188 

1324.44 

517.088 

993.3,'33 

414.197 

794.607 

45 

2071.30 

3975.00 

1035.69 

1987.50 

690.503 

1325.00 

517.925 

993.750 

414.386 

795.000 

46 

.W2.243976.67 

1036.16 

1988.33 

690.819 

1325.56 

•518.161 

994.167 

414.575 

795.333 

47 

2073.163978.33 

1036.62 

1989.17 

691.124 

1320.11 

518.390 

994.583 

414.758 

795.  G67 

48 

2074.083980.00 

1037.08 

1990.00 

691.430 

1&6.67 

5l8.€19i995.000 

414.942 

796.000 

49 

2075.023981.67 

1037.55 

1990.83 

091.745 

1327.22 

518.856  995.417 

415.131 

796.333 

50 

2075.973983.33 

1038.02 

1991.67 

692.060 

1327.78 

519.C9.; 

995.833 

415.320 

796.667 

51 

2076.91  3985.00 

1038.49 

1992.50 

692.375 

1328.33 

519.3-29 

996.250 

41  5.  509  j  797.  000 

53 

2077.  80  3986.  67 

1038.97 

1993.33 

692.691 

1328.89:519.505 

996.667 

415  G98 

797.333 

53 

2078.  80  13988.  33 

1039.44 

1994.17 

093.006 

1329.  44!519.  801 

997.083 

415.888 

797.007 

54 

2079.  75  13990.  00  11039.  91 

1995.00 

693.321 

1330.00520.038 

997.500 

416.077 

798.000 

55 

2080.603991.671040.39 

1995.83 

693  636 

1330.50520.274 

997.917 

416.260 

798.333 

56 

2081.643993.831048.86 

1996.67 

093.951 

1331.11  520.511 

998.833 

416.455 

798.667 

57 

2082.583995.001041.33 

1997.50 

694.266 

1331.67520.747 

998.750 

416.644 

799.000 

58 

J083.  53  3996.  07  104  1.80 

1998.33 

694.581 

1332.22520.983 

999.167 

416.833 

799.333 

59  12081.  4813998.  33;  1045.  28 

1999.17694.897 

1332.78521.220 

999.583 

417.022 

799.667 

124 


TABLE   XIV. — ACTUAL   TANGENTS, ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

30° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

253.826 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 
390".000 

M. 
O 

338.310 

650.  OUO 

290.031 

557.143 

487.500 

225.670 

433.333 

203.155 

838.473 

050.278 

2<J0.166 

557.381 

253.944 

487.708 

225.775 

433.519 

203.250 

390.167 

1 

338.63! 

050  .  550 

290.302 

557.619 

254.003 

487.917 

225.880 

433.704 

203  344 

390.333 

2 

338.  78-1 

050.833 

290.433 

557.857 

254.177 

488.125 

225.982 

433.889 

203.436 

390.500 

3 

338.937 

051.111 

290.564 

558.095 

254.292 

488.333 

226.084 

434  074 

203.528 

390.607 

4 

339.094 

051.389 

290.699 

558.333 

254.410 

488.542 

226.189 

434.259 

203.623 

390.833 

5 

339.25'J 

051.667 

290.834 

558.571 

254.529 

488.750 

220.295 

434.444 

203.717 

391.000 

6 

339.409 

051.944 

290.969 

558.810 

254.64? 

488.958 

226.400 

434.630 

203.812 

391.167 

7 

339.507 

652.222 

291.104 

559.048 

254.705 

489.107 

226.505 

434.815 

203.907 

391.333 

8 

339.725 

652.500 

291.239 

559.286 

254.883 

489.375 

226.610 

435.000 

204.001 

391.500 

9 

339.882 

652.778 

291.375 

559.524 

255.002 

489.583 

226.715 

435.185 

204.096 

391.667 

10 

340.035 

653.056 

291.500 

559.762 

255.110 

489.792 

226.817 

435.370 

204.188 

391.833 

11 

340.188 

653.333 

291.637 

560.000 

255.231 

4'JO.OOO 

220.919 

435.556 

204.279 

392.000 

13 

340.346 

053.611 

291.772 

560.238 

255.349 

490.208 

227.024 

435.741 

^04.374 

392.167 

13 

340.503 

653.889 

291.907 

560.476 

255.408 

490.417 

227.129 

435.926 

204.469 

392.333 

14 

340.661 

054.167 

292.042 

560.714 

255.580 

490.625 

227.235 

436.111 

204.563 

392.500 

15 

3-10.819 

654.444 

292.177 

560.952 

255.704 

490.833 

227.340 

436.296 

204.658 

392.66? 

16 

310.976 

654.722 

292/312 

501.190 

255.822 

491.042 

227.445 

436.481 

204.753 

392.833 

17 

341.134 

655.000 

292.447 

561  .429 

255.941 

491.250 

227.550 

436.607 

204.847 

393.000 

18 

341.292 

655.278 

292.583 

561.667 

256.059 

491.458 

227.655 

436.852 

204.942 

393.16? 

19 

341.449 

655.556 

292.718 

561.905 

256.177 

491.667 

227.760 

437.037 

205.037 

393.333 

20 

341.602 

655.833 

292.849 

562.143 

256.292 

491.875 

227.862 

437.222 

^05.129 

393.500 

21 

341.755 

650.111 

292.980 

562.381 

256.406 

492.083 

227.964 

437.407 

205.220 

393.66? 

22 

341.913 

050  .  389 

293.115 

562.619 

256.525 

492.292 

228.009 

437.593 

205.315 

393.833 

23 

342.070 

056.607 

293.250 

562  857 

256.043 

492.500 

228.174 

437.778 

205.410 

394.000 

24 

342.228 

056.944 

293.385 

563.095 

256.761 

492.708 

228.280 

437.903 

205.504 

394.167 

25 

342.385 

657.222 

293.520 

503.333 

256.880  492.917 

228.385 

438.148 

205.599 

394.333 

26 

342.543 

657.500 

293.655 

563.571 

256.998 

493.125 

228.490 

438.333 

205.694 

394.500 

27 

342.701 

657.778 

293.791 

563.810 

257.116 

45)3.333 

228.595 

438.519 

-^05.788 

394.667 

28 

342.858 

658.050 

293.926 

564.048 

257.234 

493.542 

228.700 

438.704 

205.883 

394.833 

29 

343.016 

658.333 

294.061 

564.286 

257.353 

493.750 

228.805 

438.889 

205.978 

395.000 

3O 

343.174 

058.011 

294.196 

564.524 

257.471 

493.958 

228.911 

439.074 

206.072 

395.167 

31 

343.331 

658.889 

294.331 

564.762 

257.589 

494.167 

229.016 

439.251) 

206.167 

395.333 

32 

343.484 

659.167 

294.462 

565.000 

257.704 

494.375 

229.118 

439.444 

200.259 

395.500 

33 

343.637 

659.444 

294.593 

565.238 

257.819 

494.583 

229.220 

439.630 

206.351 

395.607 

34 

343.795 

059.722 

294.728 

565.47'6 

257.937 

494.792 

229.325 

439.815 

206.445 

395.  £83 

35 

343.952 

660.000 

294.864 

565.714 

258.055 

495.000 

229.430 

440.000 

206.540 

396.000 

36 

344.110 

660.278 

294.999 

565.952 

258.173 

495.208 

229.535 

4-'0.l85 

206.634 

396.167 

31* 

344.268 

660.556 

295.134 

566.190 

258.292 

495.417 

229.640 

•140.370 

206.729 

396.333 

38 

344.425 

660.833 

295.269 

566.429 

258.410 

495.625 

229.745 

440.556 

206.824 

396.500 

39 

314.583 

661.111 

295.404 

566.667 

258.528 

495.833 

229.850 

440.741 

206.918 

396.667 

40 

344.740 

661.389 

295.539 

560.905 

258.  646  |496.  042 

229.956 

440.926 

207.013 

396.833 

41 

344.898 

661.667 

295.674 

507.143 

258.  765  1  496.  250 

230.061 

441.111 

207.108 

397.000 

42 

345.056 

661.944 

295.809 

567.381 

258.883496.458 

230.166 

441.290 

207.202 

397.167 

43 

345.213 

662.222 

295.945 

567.619 

259.001  496.667 

230.271 

441.481 

-,'07.297 

397.338 

44 

345.371 

662.500 

296.080 

567.857 

259.  120  :  496.  875 

230.376 

441.667 

207.392 

397.500 

45 

345.529 

062.778 

296.215 

568.095 

259.238 

497.083 

230.481 

441  852 

207.486 

397.667 

40 

345.681 

603.056 

296.346 

568.333 

•,'59.352 

497.292 

230.583 

442.03? 

207.578 

397.83* 

47 

345.834 

063.333 

296.477 

568.571  259.467 

497.500 

230.685 

442  222 

207.670 

398.000 

48 

345.992 

063.611 

296.612 

568.810 

259.585 

497.708 

230.790 

442.407 

207.765 

398.167 

49 

346.150 

063.889 

296.747 

569.048 

259.704 

497.917 

230.896 

442.593 

207.859 

398.333 

50 

340.307 

004.167 

296.882 

569.  286  '•  259.  822 

498.125 

231.001 

442.778 

207.954 

398.500 

51 

340.40'* 

064.444 

297.018 

569.524 

259.940 

498.333 

231.100 

442.963 

208.049 

398.667 

52 

846.033 

•M4.7-32 

297.153 

569.762 

260.058 

498.542 

231.211 

443.148 

208.143 

398.833 

53 

340.780 

0(55.000 

297.288 

570.000260.177 

498.750 

231.316 

443.333 

208.238 

399.000 

54 

340.938 

005.  2T8 

297.423 

570.238260.295 

498.958 

231.421 

443.519 

208.333 

399.167 

55 

347.  095 

005.550 

297.558 

570.476  260.413499.167 

231.527 

443.704 

208.427 

399.333 

56 

347.263 

C05.  833 

297.693 

570.714260.532499.375 

231.632 

443.889 

208.522 

399.500 

57 

347.411  IGOG.  in 

297.828 

570.  952!  260.  650  499.  583 

231.737 

444.074 

208.617 

399.607 

58 

347.5081660.389 

297.964 

571.190i28Q.768  499.792 

231.842 

444.259 

208.711 

399.833 

59 

135 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


40° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 
~~O~ 

Tan. 

Arc. 

Tan.  j    Arc. 

Tan.       Arc. 
6957212  1333.33 

Tan. 
521.456 

Arc. 

TbooToo 

Tan.  |   Arc. 
417.212800.000 

.3085.424000.00 

1042.75:2000.00 

1 

J086.874001.67 

043.222000.83 

695.527  1333.89 

521.693 

1000.42 

417.401  800.333 

2 

2087.31  4003.33 

1043.692001.67 

695.8421334.44 

521.929 

1000.83 

417.590800.007 

3 

2088.264005.00 

1044.17 

2002.50 

696.157  1335.00 

522.165 

1001.25 

417.779801.000 

4 

3089.204006.67 

1044.64 

2003.33 

690.472  1335.56 

522.402 

1001.67 

417.908801.333 

5 

20U0.154008.33 

1045.11 

2004.17 

696.788  1336.11 

522.038 

1002.08 

418.157801.607 

6 

2091.094010.00 

1045.58 

2005.00 

697.103  1336.67 

523.875 

1002.50 

418.346  802.000 

7 

2092.0414011.67 

1046.06 

2005.83 

697  418  1337.22 

523.111 

1002.92 

418.535802.333 

8 

2092.984013.33 

1046  53 

2006.67 

697.733  1337.78 

523.347 

1003.33 

418.725802.067 

9 

3093.93 

4015.00 

1047.00 

2007.50 

098.048 

1338.33 

523.584 

1003.75 

418.914803.000 

1O 

2094.87 

4016.67 

1047.48 

2008.33 

698.363 

1338.89 

523.820 

1004.17 

419.103803.333 

11 

3095.82 

4018.33 

W47.95 

2009.17 

698.679 

1339.44 

524.057 

1004.58 

419.292803.067 

12 

3096.77 

4020.00 

1048.42 

2010.00 

698.994 

1340.00 

524.293 

1005.00 

419.481  804.000 

13 

3097.71 

4031.67 

1048.89 

3010.83 

699.309 

1340.56 

524.529 

1005.42 

419.670804.333 

14 

30!)8.66 

4023.33 

1049.37 

3011.67 

699.624 

1341.11 

524.766 

1005.83 

419.859804.667 

15 

3099.60 

4025.00 

1049.84 

2012.50 

699.939 

1341.67 

525.002 

1006.25 

420.049805.000 

16 

'100.55 

4026.67 

1050.31 

2013.33 

700.254 

1342.22 

525.  23S 

1006.67 

420.238805.333 

17 

3101.49 

4028.33 

1050.78 

2014.17 

700.570 

1348.78 

525.475 

1007.08 

420.427805.667 

IS 

310-3.44 

4030.00 

1051.26 

2015.00 

700.885 

1343.33 

525.711 

1007.50 

420.616806.000 

19 

3103.3S 

4031.67 

1051.73 

3015.83 

701.200 

1343.89 

525.948 

1007.92 

490.806  806.888 

2O 

3104.33 

4033.33 

1052.20 

2016.67 

701.515 

1344.44 

526.184 

1008.33 

420.994806.667 

21 

2105.27 

4035.00 

1052.68 

2017.50 

701.830 

1345.00 

526.420 

1008.75 

421.183807.000 

22 

3106.22 

403(3.6; 

1053.15 

2018.33 

702.145 

1345.56 

526.657 

1009.17 

421.373 

807.333 

23 

3107.16 

4038.33 

1053.62 

3019.17 

702.401 

1346.11 

526.893 

1009.58 

421.562 

807.607 

24 

3108.11 

4040.00 

1054.09 

2020.00 

703.776 

1346.67 

527.130 

1010.00 

421.751 

808.000 

25 

3109.06 

4041.67 

1054.57 

3030.83 

703.091 

1347.22 

527.866 

1010.42 

421.940 

808.333 

26 

3110  00 

4043.33 

1055.04 

2021.67 

703.406 

1347.78 

527.602 

1010.83 

422.129 

808  667 

27 

3110.95 

4045.00 

I0».5l 

2022.50 

703.721 

1348.33 

527.839 

1011.25 

422.318 

809.000 

28 

2111.89 

4046.67 

1055.98 

2023.33 

704.036 

1348.89 

528.075 

1011.67 

422.507 

809.333 

29 

3112.84 

4048.33 

1056.46 

2024.17 

704.352 

1349.44 

528.312 

1012.08 

422.690 

809.667 

30 

2113.78 

4050.00 

1056.93 

2025.00 

704.667 

1350.00 

528.548 

1012.50 

422.886 

810.000 

31 

2114.73 

4051.67 

1057.40 

2025.83 

704.982 

1350.56 

528.784 

101  2.  9-, 

423.075 

810.333 

32 

2115.67 

4053.  3  3 

1057.88 

2026.67 

705.297 

1351.11 

529  021 

1013.3° 

423.264 

810.667 

33 

2116.62 

4055.00 

1058.35 

2037.50 

705.612 

13)1.87 

529.257 

1013.75 

423.453 

811:000 

34 

2117.56 

4056.6; 

1058.82 

2028.33 

705.927 

1352.22 

529.494 

1014.17 

423.642 

811.333 

35 

2118.51 

4058.33 

1059.29 

2029.17 

706.243 

1352.78 

529.730 

1014.58 

423.831 

811.667 

36 

2119.45 

4060.00 

1059.77 

203).  00 

706.558 

1353.33 

529.960 

1015.00 

424  020 

812.000 

37 

2120.40 

4061.6; 

1060.24 

2030.83 

706.873 

1353.89 

530.203 

1015.42 

424.210 

P.  12.  333 

38 

2121.35 

4063.33 

1060.71 

2031.67 

707.188 

1354.44 

530.439 

1015.83 

424.399 

812.667 

39 

2122.29 

4065.00 

1061.18 

2032.50 

707.503 

1355.00 

530.676 

1016.25 

424.588 

813.000 

4O 

2123.24 

4066.67 

1061.66 

2033.33 

707.818 

1355.56 

530.912 

1016.67 

424.777 

813.333 

41 

2124.18 

4068.33 

1062.13 

2034.17 

708.134 

1356.11 

531.148 

1017.08 

424.966 

813.667 

42 

2125.13 

4070.00 

10*32.60 

2035.00 

708.449 

1356.67 

531.385 

1017.50 

425.155 

814.000 

43 

3126.07 

4071.6; 

1063.08 

20,35.83 

708.764 

1357.2-3 

531.621 

1017.92 

425.344 

814.333 

44 

2127.02 

4073.3 

tO"3.55 

2036.67 

709.079 

1357.78 

531.858 

1018.33 

425.534 

814.607 

45 

2127.99 

4075.  0( 

1064.04 

2037.50 

709.404 

1358.33 

532.101 

1018.75 

425.728815.000 

46 

2128.97 

4076.67 

1064.52 

2038.33 

709.728 

1358.89 

532.345 

1019.17 

425.923815.333 

47 

2129.91 

4078.3-1 

1064.99 

2039.17 

710.  044(1359.  44 

532.581 

1019.58 

426.112815.667 

48 

3130.86 

4080.01 

1065.47 

2040.00 

71  0.359;  1360.  0( 

532.817 

1020.00 

426.  302!  81  6.  000 

49 

2131.80 

4081.67 

1065.94 

2040.83 

710.674  1360.56 

533.054 

1020.42 

426.491 

816.333 

50 

2132.75 

4083..  33 

1066.41 

2011.67 

710.989  1361.11 

533.290 

1020.83 

426.680 

816  667 

51 

2133.69 

4085.  0( 

1066.89 

2012.50 

711.304 

13(31.67 

533  527 

1021.25 

426.809817.000 

52 

2134.64 

4086.67 

1067.36 

2043.33 

711  619 

1862.22 

533.763 

1021.67 

427.  058  SI  7.  333 

53 

2135.58 

4088.33 

1067.83 

2044.17 

711.935 

1363.78 

533.999 

1023.08 

427.247 

817.007 

54 

2136.53 

4090.  0( 

1068.302045.00 

712.250 

1363.33 

534.236 

1022.50 

427.430 

818.000 

55 

3137  47 

4091.67 

1068.782045.83 

712.565 

1303.89 

534.472(1022  9-3 

427.625 

818.333 

5(> 

2138.42 

4093.33 

1069.252040.67 

712.880 

1304.44 

534.709 

1023.33427.815 

818.607 

57 

2139.37 

4095.00 

1069.722047.50 

713  195 

1305.00 

534.945 

1023.754-38.004 

819.000 

58 

2140.31 

4096.67 

1070.19,2048.33 

713.510 

1305.56 

535.181 

1024.174-38.193 

819.333 

59 

2141.26 

4098.33 

1070.  67  j  2049.  17 

713.8261366.11 

535.418  1024.58.428.382 

819.667 

126 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

4O° 
3l7 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |   Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

347.726 

666.667298.099 

571.429 

260  .  886  500  .  000  '231  .  947 

444  .  444  208  -  806  400  .  000 

o 

347.884 

666.  944  298.  234s  57  1.667 

261.005  500.  208  '232.  052 

444.630120*   901|400.167 

1 

348.041 

667.222  298.869  571.  905 

261.123500.417232.157 

444.  815!  20^  995400.333 

2 

348.199 

667.  500  298.  504  1  572.  143 

261.241  500.625232.263 

445.000  20£  .090  400.500 

3 

348.357 

667.778298.639 

572.381 

261.359500  833:232.368 

445.185j20lM85400.667 

4 

348.514 

668.056298.774 

572.619 

261.478  501.042 

232.473 

445  .  370  20S  .  279  400  .  833 

5 

348.672 

668.333298.909 

572.857 

261.596501.250 

232.578 

445.556 

209.374401.000 

6 

348.829 

668.611:299.045 

573.095 

261.714501.458 

232.683 

445.741 

209.  4691401.  167 

7 

348.987 

668.889299.180573.333 

261.833501.667 

232.788 

445.926 

209.563 

401.333 

8 

349.145 

669.167 

299.315 

573.571 

261.951 

501.875 

232.893 

446.111 

209.658 

401.500 

9 

349.302 

669.444 

299.450 

573.810 

262.069 

502.083 

232.999 

446.296 

209.752 

401.667 

10 

349.460 

669.  722  299.  5&5 

574.048 

262.187502.292 

233.104 

446.  481  1209.  847 

401.833 

11 

349.618 

670.000299.720 

574  286 

262.306  502.500 

233.209 

446.667 

209.942 

402.000 

13 

349.775 

670.  278  i  299.  855 

574.524 

262.424  502.708 

233.  31  4  1446.852 

210.036 

402.167 

13 

349.933 

670.556299.991 

574.762 

262  542  502.917 

233.419 

447.037 

210.131 

402.333 

14 

350.091 

670.  833  1  300.  126 

575.000 

262.660503.125 

233.524 

447.222 

210.226 

402.500 

15 

350.248 

671.1  Hi  300.  261 

575.238 

262.779:503.333 

233.630 

447.407 

210.320 

402.667 

16 

350.406 

671.389300.396 

575.476 

262.  897  |503.542 

233.735 

447.593 

210.415 

402.833 

17 

350.563 

671.667300.531 

575.714 

263.015  503.750 

233.840 

447.778 

210.510 

403.000 

18 

350.721 

671.944 

300.666 

575.952 

263.133 

503.958 

233.945 

447.963 

210.604 

403.167 

19 

350.879 

672.222 

300.801 

576.190 

263.252 

504.167 

234.050 

448.148 

210.699 

403.333 

2O 

351.036 

672.500 

300.937 

576.429 

263.3;OJ504.375 

234.155 

448.333 

210.794 

403.500 

31 

351.194 

672.778 

301.072 

576.667 

263.488 

504.583 

234.260 

448.519 

210.888 

403.667 

22 

351..  352 

673.056 

301.207 

576.905 

263.607 

504.792 

234.366 

448.704 

210.983 

403.833 

23 

351.  509 

673.333 

301.342 

577.143 

263.725 

505.000 

234.471 

448.889 

211.078 

404.000 

24 

351.667 

673.611 

301.477 

577.381 

263.843 

'505.208 

234.57'6 

449.074 

211.172 

404.167 

25 

351.825 

673.889 

301.612 

577.619 

263.961 

505.417 

234.681 

449.259 

211.267 

404.333 

26 

351.982 

674.167 

301.747 

577.857 

264.080 

505.625 

234.786 

449.444 

211.362 

404.500 

21 

352.140 

674.444 

301.883 

578.095 

264.198 

505.833 

234.891 

449.630 

211.456 

404.667 

28 

352.297 

674.722 

302.018 

578.333 

264.316 

506.042 

234.996 

449.815 

211.551 

404.833 

29 

352.455 

675.000 

302.153 

578.571 

264.434 

506.250 

235.102 

450.000 

211.646 

405.000 

3O 

862.613 

675.278 

302.288 

578.810 

264.553 

506.458 

2a5.207 

450.185 

211.740 

405.167 

31 

352.770 

675.556 

302.423 

579.048 

264.671 

506.667 

235.312 

450.370 

211.835 

405.333 

32 

852.928 

675.833 

302.558 

579.286 

264.789 

506.875 

235.417 

450.556 

211.930 

405.500 

33 

b53.086 

676.111 

302.693 

579.524 

264.908 

507.083 

235.522 

450.741 

212.024 

405.667 

34 

353.243 

676.389 

302.828 

579.762 

265.026 

507.292 

235.627 

450.926 

212.119 

405.833 

35 

353.401 

676.667 

302  964 

580.000 

265.144 

507.500 

235.732 

451.111 

212.214 

406.000 

36 

863.559 

676.944 

303.099 

580.238 

265.262 

507.708 

235.838 

451.296 

212.308 

406.167 

37 

353.716 

677.222 

303.234 

580.476 

265.381 

507.917 

235.943 

451.481 

212.403 

406.333 

38 

353.874 

677.500 

303.369 

580.714 

265.499 

508.125 

236.048 

451.667 

212.498 

406.500 

39 

354.031 

677.778 

303  504 

580.952 

265.617 

508.333 

236.153 

451.852 

212.592 

406.667 

40 

354.189(678.056 

303.639 

581.190 

265.735 

508.542 

236.258 

452.037 

212.687 

406.833 

41 

354.347 

678.333 

303.774 

581.429 

265.854 

508.750 

236.363 

452  222 

212.782 

407.000 

42 

354.504 

678.611 

303.910 

581.667 

265.972 

508.958 

236.469 

452.407 

212.876 

407.167 

43 

354.662678.889 

304  045 

581.905 

266.090 

509.167 

236.574 

452.593 

212.971 

407.333 

44 

354.824679.167304.184 

582.143 

266.212 

509.375 

236.682 

452.778 

213.068 

407.500 

45 

354.987679.444304  323 

582.381 

266.334 

509.  5&3 

236.790 

452.963 

213.168 

407.667 

46 

355.  144  !  679.  722  304.  458 

582  619 

266.452509.792 

236.896 

453.148 

213.261 

407.833 

47 

355  .  302  680  .  000  304  .  593 

582.857 

266.  570  !510.  000 

237.001 

453.333 

213.355 

408.000 

48 

355.460 

680.278 

304.729 

583.095 

266.689 

510.208 

237.106 

453.519 

213.450 

408.167 

49 

355.617 

680.556 

304.864 

583.333 

266.807 

510.417 

237.211 

453.704 

213.545 

408.333 

50 

355  .  775  680  .  833  304  .  909 

583.571 

266.925510.625 

237.316 

453.889 

213.639408.500 

51 

355.933681.111 

805.134:583.810 

267.044510.883 

237.421 

454.074 

21  3.  734  '408.  667 

52 

356.090681.389305.269 

584.048 

267.162 

511.042 

237.526 

454.259 

213.829408.833 

53 

356.  248  681.  6671305.  404 

584.286 

267.280 

511.250 

237.632 

454.444 

213  923409.000 

54 

356.406681.944305.53!) 

584.524 

267.398 

511.458 

•-'37.737 

454.630 

214.018  409.167 

55 

356  .  563  682  .  222  305  .  (>75 

584.762 

267.517 

511.667 

237.842 

454.815 

214.113409.333 

56 

356.721  682.  500  305.  H  10 

585.000 

267.635 

511.875 

237.947 

155.000 

214.207409.500 

57 

356  .  878  682  .  778  305  .  945 

5S5.238 

267.753 

512.083 

238.052 

455.185 

214.302409.667 

58 

357.036:683.056306.080 

585.476 

267.871 

512.292 

238.157 

455.370 

214.397409.833 

59 

127 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


41° 

1ST 

1°  Curve. 

2°  Carve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O  [2142.20 

4100.00 

10n.  14  2050.00;  714.  141 

1366.67 

535.654 

1025.00 

428.571 

820.000 

1  12143.18 

4101.671071.632050.83 

714.465 

1367.  22 

535  .  898  i  1  025  .  42  428  .  766 

820.333 

2  2144.15 

4103.331072.11 

2051.67 

714.790 

1367.78 

536.141 

1025.83 

428.961 

820.667 

3 

2145.10 

4105.00 

1072.59 

-,'052.50 

715.105 

1368.33 

536.378 

1026.25 

429.150 

821.000 

4 

2146.04 

4106.67 

1073.06 

2053.33 

715.420 

1368.89 

536.614 

1026.67 

429.339 

821.333 

5 

2146.99 

4108.33 

10?3.53 

2054.1? 

715.736 

1369.44 

536.850 

1027.08 

429.528 

821.6(57 

6 

2147.93 

4110.00 

1074.00 

2055.00 

716.051 

1370.00 

537.087 

1027.50 

429.71? 

8-J2.000 

7 

2148.88 

4111.6? 

1074.48 

2055.83 

716.366 

1370.56 

537.323 

1027.92 

429.907 

822.333 

8 

2149.82 

4113.33 

1074.95 

2056.67 

716.681 

1371.11 

537.560 

1028.33 

430.0% 

822.667 

9 

2150.7? 

4115.00 

1075.42 

2057.50 

716.996 

1371.6? 

537.796 

1028.  7'5 

430.285 

823.000 

10 

2151.71 

1116.6? 

1075.90 

2058.33 

717.311 

1372.22 

538.032 

1029.17 

430.474 

823.333 

11 

2152.69 

4118.33 

1076.38 

2059.17 

717.636 

1372.78 

538.276 

1029.58 

130.669 

823.667 

13 

2153  66 

4120.00 

1076.87 

•-'060.00 

717.961 

1373.33 

538.520 

1030.00 

4:10.864 

824  000 

13 

2154.61 

4121.67 

1077.34 

2060.83 

718.276 

1373.89 

538.756 

1030.4:3 

331.053 

824.333 

14 

2155.55 

4123.33 

1077.8-' 

2061.  6  r 

718.591 

1374.41 

538.992 

1030.83 

431.242 

824.667 

15 

2156.50 

4125.00 

1078.29 

2062.50 

718.906 

1375.00 

539.22!) 

1031.25 

431.431 

825.000 

16 

2157.44 

412(5.67 

1078.76 

2063.33 

719.222 

1375.56 

539.465 

1031.6? 

431.620 

825.333 

17 

2158.3',) 

4128.33 

1079.23 

2064.1? 

719.53? 

1376.11 

539.701 

1032.08 

431.809 

825.667 

18 

2159.33 

4130.00 

1079.71 

2065.00 

719.852 

1376.67 

539  938 

1032.50 

431.999 

826.000 

19 

2160.28 

1131.67 

1080.18 

^065.83 

720.167 

1377.22 

540.17'4 

1032.92 

432.188 

826.333 

20 

2161.22 

4133.33 

1080.65 

2066.67 

720.482 

1377.78 

540.411 

1033.33 

432.37? 

826.667 

81 

2162.20 

4135.00 

1081.14 

2067.50 

720.80? 

1378  33 

510.654 

1033.75 

432.572 

8-,'7.000 

22 

2163.17 

4136.6? 

1081.63 

2068.33 

721.132 

1378.89 

540.  80S 

1034.1? 

432.767 

827.  333 

23 

2164.12 

4138.33 

1082.10 

2069.1? 

721.44? 

1379.44 

541.134 

1031.58 

432.956 

827.667 

24 

2165.06 

4140.00 

1082.5? 

2070.00 

721.762 

1380.00 

541.371 

1035.00 

433.145 

828.000 

25 

2166.01 

4141.67 

1083.04 

2070.83 

722.077 

1380.56 

541.607 

1035.42 

433.334 

828.333 

26 

2166.95 

4143.33 

1083.52 

2071.67 

722.392 

1381.11 

541.843 

1035.83 

433.523 

828.667 

2V 

2167.90 

4145.00 

1083.99 

2072.50 

722.707 

1381.6? 

542.080 

1036.25 

433.712 

829.000 

28 

2168.84 

4146.6? 

1084.46 

2073.33 

723.0:>3 

1382.22 

542.316 

1036.6? 

433.901 

829.333 

29 

2169.82 

4148.33 

1084.95 

2074.17 

723.347 

1382.78 

542.560 

1037.08 

434.096 

829.667 

30 

2170.79 

4150.00 

1085.44 

2075.00 

723  672 

1383.33 

542.803 

1037.50 

434.291 

830.000 

31 

2171.74 

4151.67 

1085.91 

2075.83 

723.987 

1383.89 

543  010 

1037.92 

434.480 

830.333 

32  12172.68 

4153.33 

1086.38 

2076.67 

724.302 

1384.44 

543.276 

1038.33 

434.669 

830.667 

33   2173.63 

4155.00 

1086  85 

2077.50 

724.617 

1385.00 

543.512 

1038.75 

434.859 

831.000 

34 

2174.57 

4156.67 

IU87.33 

2078.33 

724.933 

1385.56 

543.749 

1039.17 

435.048 

831.333 

35 

2175.52 

4158.33 

1087.80 

2079.17 

725.248 

1386.11 

543.985 

1039.58 

435.237 

831  .  667 

36 

2176.46 

4160.00 

1088.27 

2080.00 

725.563 

1386.67 

544.222 

1040.00 

435.426 

832.000 

37 

2177.44 

4161.67 

1088.76 

2080.83 

725.888 

1387.22 

544.465 

1040.42 

435.621 

832.333 

38 

2178.41 

4163.33 

1089.25 

2081.6? 

726.212 

1387.78 

544.709 

1040.83 

435.816 

832.667 

39 

2179.36 

4165.00 

1089.72 

2082.50 

726.528 

1388.33 

544.945 

1041.25 

436.005 

833.000 

40 

2180.30 

4166.67 

1090.19 

2083.33 

726.843 

1388.89 

545.182 

104L67 

436.194 

833.333 

41 

2181.25 

4168.33 

1090.66 

2084.17 

727.158 

1389.44 

545.418 

1042.08 

436.383 

833.667 

43 

2182.19 

4170.00 

1091.14 

2085.00 

727.473 

1390.00 

545.654 

1042.50 

436.572 

834.000 

43 

2183.17 

4171.67 

1091.62 

2085.83 

727.798 

1390.56 

545.898 

1042.92 

436  767 

834.333 

44 

2184.14 

4173.33 

1092.11 

2086.67 

728.122 

1391.11 

546.141 

1043.33 

436.962 

834.667 

45 

2185.09 

4175.00 

1092.58 

2087.50 

728.438 

1391.6? 

546.378 

1043.75 

437.151 

835.000 

46 

2186.03 

4176.67 

1093.062088.33 

728.753 

1392.22 

546.614 

1044.17 

437.340 

835.333 

47 

2186.98 

4178.33 

1093.53 

2089.17 

729.068 

1392.78 

546.851 

1044.58 

437.529 

835.667 

48 

2187.92 

4180.00 

1094.00 

2090.00729.383 

1393.33 

547.08? 

1045.00 

437.718 

836.000 

49 

2188.90 

4181.67 

1094.49 

2090.83 

729.708 

1393.89 

547.331 

1045.42 

437.913 

836.333 

50 

2189.87 

4183.33 

1094.98 

2091.67 

730.033 

1394.44 

547.574 

1045.83 

438.108 

836.667 

51 

2190.82 

4185.00 

1095.45 

2092.50730.348 

1395.00 

547.811 

1046.25438.297 

837.000 

52 

2191.76 

4186.67 

1095.92 

2093.33730.663 

1395.56 

548.047 

1046.  6?!  438.  486 

837.333 

53 

2192.71 

4188.33 

1096.39 

2094.17730.978 

1396.11 

548  283 

1047.081438.676 

837.667 

54 

2193.65 

4190.00 

1096.87 

2095.00731.293 

1396.67 

548.520 

1047.50438.865 

838.000 

55 

2194.63 

4191.67 

1097.35 

2095.83731.618 

1397.22 

548.763 

1047.  921439.  060 

a38.333 

56 

2195.60 

4193.33 

1097.84 

2096.67731.943 

1397.78 

549  00711048.33  439.254 

838.667 

57 

2196.55 

4195.00 

1098.31 

2097.50732.258 

1398.33 

549  .  243  1  048  .  75  439  .  444 

839.000 

58 
59 

2197.49 
2198.44 

4196.67 
4198.33 

1098.79 
1099.26 

2098.33  732.573 
2099.17732.888 

1398.89 
1399.44 

549.  480  1049.  17|439.  633 
549.  71  6l  1049.  58!  439.  822 

839.  333 
839.667 

128 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

41° 

Tan. 

Arc. 

Tail. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

357.194 

6837338 

306.215 

585.714 

267.  990  1512.500 

238^262 

455.556 

214.491 

410.000 

0 

357.356 

683.611 

306.354 

585.952 

268.112 

512.708 

238.371 

455.741 

214.589 

410.167 

1 

357.519 

683.889 

306.494 

586.190 

268.233 

512.917 

238.479 

455.926 

214.686 

410.333 

2 

357.676 

684.167 

306.629 

586.429 

268.352 

513.125 

238.584 

456.111 

214.781 

410.500 

3 

357.834 

684.444 

306.764 

586.667 

268  470 

513.333 

238.689 

456.296 

214.876 

410.667 

4 

357.991 

684.722 

306.899 

586.905 

268.588 

513.542 

238.795 

456.481 

214.970 

410.833 

5 

358.149 

685.000 

307.034 

587.143 

268.706 

518:750 

238.900 

456.667 

215.065 

411.000 

6 

358.307 

685.278 

307.169 

587.381 

268.825 

513.958 

239.005 

456.852 

215.160 

411.167 

7 

358.464 

685.556 

307.304 

587.619 

268.943 

514.167 

239.110 

457.037 

215.254 

411.333 

8 

358.622 

685.833 

307.440 

587.857 

269.061 

514.375 

239.215 

457.222 

215.349 

411.500 

9 

358.780 

686.111 

307.575 

588.095 

269.180 

514.583 

239.320 

457.407 

215.443 

411.667 

10 

358.942 

686.389 

307.714 

588.338 

269.301 

514.7'J2 

239.429 

457.593 

215.541 

411.833 

11 

359.104 

686.667 

307.853 

588.571 

269.423 

515  000 

239.537 

457.778 

215.639 

412.000 

12 

359.262 

686.944 

307.988 

588.810 

269.541 

515.208 

239.642 

457.963 

215.733 

412.167 

13 

359.420 

687.222 

308.123 

589.048 

269.660 

515.417 

239.747 

458.148 

215.828 

412.333 

14 

359.577 

687.500 

308.259 

589.286 

269.778 

515.625 

239.852 

458.333 

215.923 

412.500 

15 

359.735 

687.778 

308.394 

589  524 

269.89(5 

515.833 

239.958 

458.519 

216.017 

412.667 

16 

359.893 

688.056 

308.529 

589.762 

270.015 

516.042 

240.063 

458.704 

216.112 

412.833 

17 

360.050 

688.333 

308.664 

590.000 

270.133 

516.250 

240.168 

45*.  889 

216.207 

413.000 

18 

360.208 

688.611 

308.799 

590.238 

270.251 

516.458 

240.273 

459.074 

216.301 

413.167 

19 

360.  36G 

688.889 

308.934 

590.476 

270.369 

516.667 

240.378 

459.259 

216.396 

413.338 

2O 

360.528 

689.167 

309.074 

590.714 

270.491 

516.875 

240.487 

459.444 

216.493 

413.500 

21 

360.690 

689.444 

309.213 

590.95* 

270.613 

517.083 

240.595 

459.630 

216.591 

413.667 

22 

360.848 

689.722 

309.348 

591.190 

270.731 

517.292 

240.700 

459.815 

216.686 

413.838 

23 

361.006 

690.000 

309.483 

591.429 

270.850 

517.5HO 

240.805 

460.000 

216.780 

414.000 

24 

361.163 

690.278 

309.618 

591.667 

270.968 

517.708 

240.910 

460.185 

216.875 

414.167 

25 

361.321 

690.556 

309.753 

591.905 

271.086 

517.917 

241.015 

460.370 

216.970 

414.333 

2G 

361.479 

690.833 

309-888 

592.143 

271.204 

518.125 

241.121 

460.556 

217.064 

414.500 

27 

361.636 

691.111 

310.024 

592.381 

271  323 

518.333 

241.226 

460.741 

217.159 

414.667 

28 

361.799 

691.389 

310.163 

592.619 

271.445 

518.542 

241.334 

460.926 

217.256 

414  833 

29 

361.961 

691.667 

310.302 

592.857 

271.566 

518.750 

241.442 

461.111 

217.354 

415.000 

3O 

362.119 

691.944 

310.437 

593.095 

271.685 

518.958 

241.548 

461.296 

217.449 

415.167 

31 

362.276 

692.222 

310.572 

593.338 

271.803 

519.167 

241.653 

461.481 

217.543 

415.333 

32 

362.434 

692.500 

310.707 

593..'.  71 

271.921 

519.375 

241.758 

461.667 

217.638 

415.500 

33 

362.592 

692.778 

310  843 

593.810 

•272.039 

519.583 

241.863 

461.852 

217.733 

415.667 

34 

362.749 

693.056 

310.978 

594.048 

272.158 

519.792 

241.968 

462.037 

217.827 

415.833 

35 

362.907 

693.333 

311.113 

594.286 

272.276 

520.000 

242.073 

402.222 

217.922 

416.000 

36 

363.069 

693.611 

311.252 

594.524 

272.398 

520.208 

242.182 

462.407 

218.019 

416.167 

37 

363.232 

693.889 

311.391 

594.762 

272.520 

520.417 

242.290 

462.593 

218.117 

416.383 

38 

363.389 

694.167 

311.526 

595.000 

272.638 

520.625 

242.395 

462.778 

218.212 

416.500 

39 

363.547 

694.444 

311.662 

595.238 

272.756 

520.833 

242.500 

462.963 

218.306 

416.667 

40 

363.705 

694.722 

311.797 

595.476 

272.876 

521.042 

242.605 

463.148 

218.401 

416.833 

41 

363.862 

695.000 

311.932 

595.714 

272.993 

521.250 

24-2.711 

463.333 

218.496 

417.000 

42 

364.025 

695.278 

312.071 

595.952 

273.115 

521.458 

242.819 

463.519 

218.593 

417.167 

43 

364.187 

695.556 

312.210 

596.190 

273.236 

5-21.667 

242  927 

463.704 

218.691 

417.338 

44 

364.345 

695.833 

312.346 

596.429 

273.355 

521.875 

243.032 

463  889 

218.785 

417.500 

45 

364.502 

696.111 

312.481 

596.667 

5*78.473 

522.083 

243.138 

464.074 

218  880 

417.667 

46 

364.660 

696.389 

312.616 

596.905 

273.591 

522.  V92 

243  243 

464.259 

218.975 

4  17.  880 

47 

364  818 

696.667 

312.751 

597.148 

273.710 

52-2.500 

243.348 

464.444 

219.069 

418.000 

48 

364.980 

696.944 

312.890 

597.381 

273.831 

522.708 

243.456 

464.630 

219.167 

418.167 

49 

365.142 

697.222 

313.029 

597.619 

273.953 

522.917 

243.565 

464.815 

219.264 

418.333 

50 

365.300 

(597.500 

813.165 

597.857 

274.072 

5-23.125 

243.670 

465.000 

•219.359 

418.500 

51 

365.458 

697.778 

313.300 

508.09? 

274.190 

523.333 

243.775 

4(55.185 

219.454 

418.667 

52 

365.615 

698.05(5 

313.435 

598.333 

274.308 

523.542 

243.880 

465.370 

219.548 

418.838 

53 

365.778 

698.333 

313.570 

598.571 

274.426 

523.750 

243.985 

465.556 

219.643 

419.000 

54 

365.935 

698.611 

813.709 

598.810 

374.548 

523.958 

244.093 

465.741 

219.740 

419.167 

55 

866.098 

698.889 

313.  84K 

599.048 

274.670 

524  .  1  67 

244.202 

465.926 

219.888 

419.338 

56 

366.255 

699.167 

318.984 

599.286 

274.788 

524.375 

244.307 

466.111 

219.933 

419.500 

57 

366.413 

699.444 

314.119 

599.524 

274.907 

524.583 

244  412 

466.296 

220.027 

419.667 

58 

366.571 

699.722 

314.254 

599.762 

275.025 

524  792244.517 

466.481 

220.122 

419.833 

59 

'139 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


43° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tail. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~0~ 

2199.38 

4200.1.0 

1099.73 

2100.00 

733.203 

1400.00 

549  952 

10:0.00 

440.011 

840.000 

1 

2200.36 

4-201.67 

1100.2-2 

2100.83 

733.528 

1400.50 

550.196 

1050.4-2 

440.200 

840.333 

3 

2201.33 

4203.33 

1100.71 

V101.67 

733.8f,3 

1401.11 

550.439 

1050.83 

440.401 

840.607 

3 

2-202.28 

4205.00 

1101.18 

2102.50 

734.108 

1401.07 

550.670 

1051.25 

440.590 

841.000 

4 

2203.22 

4206.67 

1101.65 

2103.33 

734.483 

1402.22 

550.912 

1051.67 

440.779 

841.333 

5 

2-204.20 

4208.33 

1102.14 

2104.1? 

734.808 

1402.  7b 

551.150 

1052.08 

440.974 

841.667 

6 

2205.1? 

4210.00 

1102.63 

2105.00 

735.132 

1403.33 

551.399 

1052.50 

441.169 

842.000 

7 

2206.12 

4211.67 

1103.10 

2105.83 

735.448 

1403.89 

551.630 

1052.92 

441.  3E8 

842.333 

8 

2207.06 

4213.33 

1103.57 

2106.67 

535.763 

14'»4.44 

551.872 

1053.33 

441.547 

842.667 

9 

2208.01 

4215.00 

1104.04 

2107.50 

736.078 

1405.00 

552.109 

1053.75 

441.736 

843.000 

1O 

2208.95 

4216.67 

1104.52 

2108.33 

736.393 

1405.56 

552.345 

1054.1? 

441.925 

843.333 

11 

2209.93 

4218.33 

1105.00 

2109.1? 

730.7181406.11 

552.589 

1054.58 

442.120 

843.667 

13 

2210.90 

4220.00 

1105.49 

2110.00 

737.0431406.67 

552.832 

1055.00 

442.315 

844.000 

13 

2211.85 

4221.6? 

1105.96 

2110.83 

i  37.3581407.  22 

553.068 

1055.42 

442.504 

844.333 

14 

2212.79 

4223.33 

1106.44 

2111.67 

737.6731407.78 

553.305 

1055.83 

442.693 

844.607 

15 

2213.76 

4225.00 

1106.92 

2112.50 

737.998  1408.33 

553.548 

1056.25 

142.888 

845.000 

16 

2214.74 

4226.67 

1107.41 

2113.33 

738.322:1408.89 

553.792 

1056.67 

4  43.  (.83 

845.333 

17 

2215.68 

4228.33 

1107.88 

2114.17 

738.03?  1409.44 

554.028 

1057.08 

443.272 

845.607 

18 

2216.63 

4230.00 

1108.36 

2115.00 

733  9531410.00 

554.205 

1057.50 

443.461 

846.000 

19 

2217.60 

4231.67 

1108.84 

2115.83 

739.277 

1410.50 

554.508 

1057.92 

443.656 

846.333 

20 

2218.58 

4233.33 

1109.33 

2116.6? 

739  602 

1411.11 

554.752 

1058.33 

443.851 

846.667 

21 

2219.52 

4235.00 

1109.80 

2117.50 

739.9171411.6? 

554.988 

1058.75 

444.040 

847.000 

22 

2220.47 

4236.67 

1110.27 

2118.33 

740.2321412.22 

555.225 

1059.1? 

444.229 

847.333 

23 

2221.41 

4238.33 

1110.75 

2119.17 

740.548 

1412.78 

555.461 

1059.58 

444.418 

847.667 

24 

2222.36 

4240.00 

1111.22 

2120.00 

740.803 

1413.33 

555.697 

1060.00 

444.608 

848.000 

25 

2223.33 

4241.6? 

1111.71 

2120.83 

741.187 

1413.89 

555.941 

1000.42 

444.802 

848.333 

36 

2224  31 

4243.33 

1112.19 

2121.67 

741.512 

1414.44 

556.185 

1060.83 

444.997 

848.667 

37 

2225.25 

4245.00 

1112.6? 

2122.50 

741.827 

1415.00 

556.421 

1061.25 

445.186 

849.000 

38 

2226.20 

4246.6? 

1113.14 

2123.33 

742.142 

1415.56 

556.657 

1061.67 

445.376 

849.333 

39 

2227.1? 

4248.33 

1113.63 

2124.17 

742.467 

1416.11 

556.901 

1062.08 

445.570 

849.667 

30 

2228.15 

4250.00 

1114.11 

2125.00 

742.792 

1416.67 

557.144 

1062.50 

445.765 

850.000 

31 

2229.09 

4251.6? 

1114.59 

2125.83 

743.107 

1417.22 

557.381 

1062.92 

445.955 

850.333 

33 

2230.04 

4253.33 

1115.06 

2126.6? 

7'43.422 

1417.78 

557.617 

1063.33 

446.144 

850.667 

33 

2231.01 

4255.00 

1115.55 

2127.50 

743.747 

1418.33 

557.861 

1063.75 

446.339 

851.000 

34 

2231.99 

4256.67 

1116.  as 

2128.33 

744.072 

1418.89 

558.104 

1064.17 

446  533 

851.333 

35 

2232.93 

4258.33 

1116.51 

2129.17 

744  387 

1419.44 

558.341 

1064.58 

446.723 

851.667 

36 

2233.88 

4200.00 

1116.98 

2130.00 

744.702 

1420.00 

558.577 

1065.00 

446.912 

852.000 

37 

2234.85 

4261.6? 

1117.4? 

•2130.83 

745.027 

1420.56 

558.821 

1065.4-2 

447.107 

852.333 

38 

2235.82 

4263.33 

1117.95 

2131.6? 

745.351 

1421.11 

559.064 

1065.83 

447.301 

852.667 

39 

2236.7? 

4265.00 

1118.43 

•213-2.50 

745.667 

1421.67 

559.301 

1066.25 

447.491 

853.000 

40 

2237.71 

4266.67 

1118.90 

2133.33 

745.982 

1422.22 

559.537 

1066.67 

447.680 

853.333 

41 

2-238.69 

4268.33 

1119.39 

2134.17 

746.306 

1422.78 

559.781 

1067.08 

447.875 

853.667 

43 

2239.66 

4270.00 

1119.87 

2135.00 

746.631 

1423.  33 

500.024 

1067.50 

448.069 

854.000 

43 

2240.61 

4271.67 

1120.35 

2135.83 

746.946 

1423.89 

560.261 

1067.92 

448.259 

854.333 

44   -2241.55 

4273.33 

1120.82 

2136.67 

747.261 

1424.44 

560.49? 

1068.33 

448.448 

854.667 

45 

2242.53 

4-275.00 

1121.30 

•2137.50 

747.586 

1425.00 

560.741 

1068.75 

448.643 

855.000 

46 

2243.50 

4276.  G7 

1121.79 

2138.33 

747.911 

1425.56 

560.984 

1069.17 

448.837 

855.333 

47 

2244  48 

4278.33 

1122  28 

2139.17 

748.236 

1426.11 

561.228 

1069.58 

449.032 

855.667 

48 

2-245.  4r> 

4280.00 

1122  77 

2140.00 

748.560 

1426.6? 

561.471 

1070.00 

449.227 

856.000 

49 

•2246.40 

4281.67 

1123^24 

•2140.83 

748.876 

1427.22 

561.708 

1070.42 

449.416 

856.333 

5O 

2247.34 

4283.33 

1123.71 

2141.67 

749.191 

1427.78 

561.944 

1070.83 

449.605 

856.667 

51 

2248.31 

4285.00 

11-24.20 

2142.50 

749.515 

1428.33 

562.188 

1071.25 

449.800 

857.000 

53   2249.2* 

4286.07 

1124.69 

•2143.33 

749.840 

1428.89 

562.431 

1071.67 

449.995 

857.333 

53  .2250.23 

4288.33 

1125.1(1 

2144.17 

750.155 

14-29.44 

562  OOS 

1072.08 

450.184 

857.667 

54  '  -2-251.  18 

4290.00 

1125.63 

•2145.00 

750.470 

1430.00 

50-2.904 

107-2.50 

450.373 

£58.000 

55  ;y25:2.i5 

4291.67 

1126.12 

2145.83 

750.795 

1430.50 

503.1  47 

107-2.92 

450  51  '8 

858.333 

56   2.  '53.  13 

4293.33 

1126.61 

2146.67 

751.120 

1431.11 

503.391 

1073.33 

450.7H3 

858.667 

57   2-254.07 

4295.00 

1127.08 

2147.50 

7  5  1.435  '143  1.0? 

5C3.0-2? 

1073.75 

450.95-2 

859.00) 

58   2  .'55.  0:2 

4296:67 

1127.55 

2148.33 

751.7501432.22 

503.801 

1074.1? 

451.141 

859.333 

59  2-255.99 

4298.33 

1128.04 

2149.1? 

752.  075  11432.  78 

564.  It--? 

1074  58 

451.336 

859.007 

130 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

42° 

Tail.       Arc. 

Tan. 

Arc.      Tan. 

Arc. 

Tan  . 

Arc. 

Tan. 

Arc. 

M. 

366.728700.000 

614  .  389  600  .  000  275  .  143  525  .  000 

244.  622  j  466.  667 

220.217 

420.000 

0 

366.891  700.27'H 

31  4  528  600  .  238  275  .  265  :  525  .  208 

244.731 

466.852 

220.314 

420.167 

1 

367.053 

700.556 

314.667600.476275.387 

525.417 

244.839 

467.037 

220.412 

420.333 

2 

367.  an 

700.833 

314.  8031600.  714  275.  505 

525.625 

244.944 

467.222 

220.506 

420.500 

3 

367.368 

701.111 

314.938 

600.952275.623 

525.833 

245.049 

467.407 

220.601 

420.667 

4 

367.531 

701.389 

315.077 

601.190275.745 

526.042 

245.158 

467.593 

220.698 

420.833 

5 

367.693 

701.667 

315.216 

601.429275.867 

526.250 

245.266 

467.778 

220.796 

421.000 

6 

367.851 

701.944 

315.351 

601.667!  275.  985 

526.458 

245.371 

467.963 

220.891 

421.167 

7 

368.008 

702.222 

315.486 

601.905 

276.104 

526.667 

245.476 

468.148 

220.985 

421.333 

8 

368.166 

7'02.500 

315.622 

602.143 

276.222 

526.875 

245.582 

468.333 

221.080 

421.500 

9 

368.324 

702.778 

315.757 

602.381 

276.340 

527.083 

245.687 

468.519 

221.175 

421.667 

10 

368.486 

703.056 

315.896 

602.619 

276.462 

527.292 

245.795 

468.704 

221.272 

421.833 

11 

368.649 

703.333 

316.035 

602.857 

276.584 

527.500 

245.903 

468.889 

221  .370 

422.000 

12 

368.806 

703.611 

316.170 

603.095 

276.702 

527.708 

246.008 

469.074 

221.464 

422.167 

13 

368.964 

703.889 

316.305 

603.333 

276.820 

527.917 

246.114 

469.259 

221.559 

422.  333 

14 

369.126 

704.167 

316.445 

603.571 

276.942 

528.125 

246.222 

469.444 

221.657 

422.500 

15 

369.289 

704.444 

316.584 

603.810 

277.064 

528.333 

246.330 

469.630 

221.754 

422.667 

16 

369.446 

704.722 

316.719 

604.048 

277.182 

528.542 

246.435 

469.815 

221.849 

422.833 

17 

369.604 

705.000 

316.854 

604.286 

277.301 

528.750 

246.541 

470.000 

221.943 

423.000 

18 

369.766 

705.278 

316.993 

604.524 

277.422 

528.958 

246.649 

470.185 

222.041 

423.167 

19 

369.929 

705.556 

317.133 

604.762 

277.544 

529.167 

246.757 

470.370 

222.138 

423.333 

2O 

370.086 

705.833 

317.268 

605.000 

277.663 

529.375 

246.862 

470.556 

222.233 

423.500 

21 

370.244 

706.111 

317.403 

605.238 

277.781 

529.583 

246.968 

470.741 

222.328 

423.667 

22 

370.402 

706.389 

317.538 

605.476 

277.899 

529.792 

247.073 

470.926 

222.422 

423.833 

23 

370.559 

706.667 

317.673 

605.714 

278.017 

530.000 

247.178 

471.111 

222.517 

424.000 

24 

370.722 

7'06.944 

317.812 

605.952 

278.139 

530.208 

247.286 

471.296 

222.615 

421.167 

25 

370.884 

707.222 

317.952 

606.190 

278.261 

530.417 

247.395 

471.481 

222.712 

424.333 

26 

371.042 

707.500 

318.087 

606.429 

278.379 

530.625 

247.500 

471.667 

222.807 

424.500 

27 

871.199 

707.778 

318.222 

606.667 

278.498 

530.833 

247.605 

471.852 

222.901 

424.667 

28 

371.362 

708.056 

318.361 

606.905 

278.620 

531.042 

247.713 

472.037 

222.999 

424.833 

29 

371.524 

708.333 

318.500 

607.143 

278.741 

531.250 

247.822 

472.222 

223.097 

425.000 

3O 

371.682 

708.611 

318.636 

607.381 

278.860 

531.458 

247.927 

4V2.407 

223.191 

425.167 

31 

371.840 

708.889 

318.771 

607.619 

278.978 

531.667 

248.032 

472.593 

223.286 

425.333 

32 

372.002 

709.167 

318.910 

607.857 

279.100 

531.875 

248.140 

472.778 

223.383 

425.500 

33 

372.164 

709.444 

319.049 

608.095 

279.222 

532.083 

248.248 

472.963 

223.481 

425.667 

34 

372.322 

709.722 

319.184 

608.333 

279.340 

532.292 

248.354 

473.148 

223.576 

425.833 

35 

372.480 

710.000 

319.319 

608.571 

279.458 

532.500 

248.459 

473.333 

223.670 

426.000 

36 

372.642 

710.278 

319.459 

608.810 

279.580 

532.708 

248.567 

473.519 

223.768 

426.167 

37 

372.804 

710.556 

3  i  9.  598 

609  048 

279.702 

532.917 

248.675 

473.7'04 

•223.865 

426.333 

38 

372.962 

710.833 

319.733 

609.286 

279.820 

533.125 

248.781 

473.889 

223.960 

426.500 

39 

373.120 

711.111 

319.868 

609.524 

279.938 

533.333 

248  886 

474.074 

224.055 

426.667 

40 

373.282 

711.389 

320.007 

609.762 

280.060 

533.542 

248.994 

474.259 

2-.M.152 

426.  833 

41 

373.445 

711.66; 

320.147 

610.000 

280.182 

533.750 

249.102 

474.444 

224.250 

427.000 

42 

373.602 

711.944 

320.282 

610.238 

280.300 

533.958 

249.208 

474.630 

224.344 

427.167 

43 

373.760 

712.222 

320.417 

610.476 

280.419 

534.167 

249.313 

474.815 

224.  43S 

427.333 

44 

373.922 

712.500 

320.556 

610.714 

280.540 

534,375 

249.421 

475.000 

224.536 

427.500 

45 

374.085 

712.778 

320.695 

610.952 

280.662 

534.583 

249.529 

475.185 

224.634 

427.667 

46 

374.247 

713.056 

320.835 

611.190280.784 

534.792 

249.638 

475.370 

224.732 

427.833 

47 

374.409 

713.333 

320.974 

611.429280.906 

535.000 

249.746 

475.556 

224.829 

428.000 

48 

374.567 

713.611 

321.109 

611.667 

281.024 

535.208 

249.851 

475.741 

224.924 

428.167 

49 

374.725 

713.889 

321.244 

611.905 

281.143 

535.417 

249.956 

475.926 

225.018 

428.333 

50 

374.887 

714.167 

321.383612.143281.264 

535.625 

250.065 

476.111 

225.116 

428.500 

51 

375.050 

714.444 

321.523 

612.38li281.386 

535.833 

250.173 

476.296 

225.213 

428.667 

52 

o75.207 

714.722 

321.658 

612.619281.505 

536.042 

250.278 

476.481 

225.308 

428.833 

53 

375.365 

715.0  0 

321.793 

612.857281.623 

536.250 

250.383 

476.667 

225.403 

429.000 

54 

375.527715.278 

321  932 

613.095281.745 

536.458 

250.492 

476.852 

225.500 

429.167 

55 

375.  090 

715.  ?56 

322.071 

613.333281.867 

536.667 

250.600 

477.037 

225.598 

429.333 

56 

375.847 

715.833 

322.207 

613.571  281.985 

536.875 

250.705 

477.222 

225.692 

429.500 

57 

376.005 

716.111 

322.342 

613.810282.103 

537.083 

250.810 

477.407 

225.787 

429.667 

58 

376.167 

716.389 

322.481 

614.048282.225 

537.292 

250.919 

477.593 

225.885 

429.  K33:  .r;l> 

131 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


43° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

—  f 
5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

2256.97 

4300.00 

1128.52 

2150.00 

"52.400 

1433.33 

364.351 

1075.00 

451.531 

860.000 

1 

2257.94 

4301.67 

129.0! 

2150.K3 

"52.724 

1433.89 

564.594 

1075.42 

451.726 

860.333 

3 

2258.91 

4303.33 

129  50 

2151.67 

753.049 

1434.44 

564.838 

1075.83 

451.921 

860.667 

3 

2259.80 

4305.00 

129.97 

2152.50 

"53.364 

1435.00 

565.074 

1076.25 

452.110 

861.000 

4 

2260.81 

4306.67 

130.44 

2153.33 

'53.679 

1435.56 

565.311 

076.67 

452.299 

861.333 

5 

2261.78 

4308.33 

130.93 

2154.17 

754.004  1436.11 

565.554 

1077.08 

452.494 

861.667 

6 

22(52.75 

4310.00 

131.42 

2155.00 

"54.329  1436.67 

565.798 

1077.50 

452.689 

862.000 

7 

2263.73 

4311.67 

131.91 

2155.83 

"54.654  1437.22 

566.041 

1077.92 

452.884 

862.333 

$ 

2264.70 

4313.33 

132.39 

2156.67 

"54.9781437.78 

566.285 

1078.  &3 

453.079 

862.667 

9 

2265.65 

4315.00 

1132.86 

2157.50 

755.293 

1438.33 

566.521 

1078.75 

453.268 

863.000 

10 

2266.59 

4316.67 

1133.34 

2158.33 

"55.609 

1438.89 

566.758 

1079.17 

453.457 

863.333 

11 

2267.57 

4318.33 

1133.82 

2159.17 

"55.933  1439.44 

567.001 

1079.58 

453.652 

863.667 

12 

2268.54 

1320.00 

134.31 

2160.00 

56.258  1440.00 

567.245 

1080.00 

453.847 

864.000 

13 

2269.49 

4321.67 

1134.78 

2160.83 

756.573  1440.56 

567.481 

1080.42 

454.036 

864.333 

14 

2270.43 

4323.33 

135.26 

2161.67 

"56.8881441.11 

567.718 

1080.83 

454.225 

864.667 

15 

2271.4! 

4325.00 

1135.74 

2162.50 

"57.213  1441.67 

367.965 

1081.25 

454.420 

865.000 

16 

2272.38 

4326.67 

1136.23 

21  63.  ;33 

57.538  1442.22 

568.205 

1081.67 

454.615 

865.333 

17 

2273.35 

4328.33 

1136.72 

2164.17 

"57.862 

1442.78 

368.448 

1082.08 

454.810 

865.667 

18 

2274.33 

4330.00 

1137.21 

2165.00 

"58.187 

1443.33 

568.692 

1082.  50  J455.004!  866.  000 

19 

2275.27 

4331.67 

1137.68 

2165.83 

'58.502 

1443.89 

568.928 

1082.92 

455.194 

866.333 

2O 

2276.22 

4333.33 

138.15 

2166.67 

"58.817 

1444.44 

569.165 

1083.33 

455.383 

866.667 

31 

2277.19 

4335.00 

1138.64 

2167.50 

"59.142  1445.00 

569.408 

1083.75 

455.578 

867.000 

83 

2278.17 

4336.67 

1139.12 

2168.33 

"59.46711445.56 

569.652 

1084.17 

455.772 

867.333 

83 

2279.14 

4338.33 

1139.61 

2169.17 

"59.792  1446  11 

569.895 

1084.58 

455.967 

867.667 

34 

2280.11 

4310.00 

1140.10 

2170.00 

760.116  1446.67 

570.139 

1085.00 

456.162 

868.000 

35 

2281.09 

4341.67 

1140.59 

2170.83 

"60.441  1447  22 

570.383 

1085.42 

456.357 

868.333 

36 

2282.06 

4343.33 

1141.07 

2171.67 

760.766  1447.78 

570.626 

1085.83 

456.552 

868.667 

37 

2283.01 

4345.00 

1141.55 

2172.50 

761.081  1448.33 

570.862 

1086.25 

456.741 

869.000 

38 

2283.95 

4346.67 

1142.02 

2173.33 

761.3961448.89 

571.099 

1086  67 

456.930 

869.333 

39 

2284.93 

4348.33 

1142.51 

2174.17 

761.721 

1449.44 

371.342 

1087.08 

457.125 

869.667 

30 

2285.90 

4350.00 

1142.99 

2175.00 

762.046 

1450  00 

571.586 

1087.50 

457.320 

870  000 

31 

2286.88 

4351.67 

1143.48 

2175.83 

762.370 

1450.56 

571.830 

1087.92 

457.515 

870.333 

33 

2287.85 

4353.33 

1143.97 

2176.67 

762.695 

1451.11 

572.073 

1088.33 

457.710 

870.667 

33 

2288.79 

4355.00 

1144.44 

2177.50 

763.010 

1451.67 

572.310 

1088.75 

457.899 

871.000 

34 

2289  74 

4356.67 

1144.91 

2178.33 

763.325 

1452.22 

572.546 

1089.17 

458.088871.333 

35 

2290.71 

4358.33 

1145.40 

2179.17 

763.650 

1452.78 

572.789 

1089.58 

458.283 

871.667 

36 

2291.69 

4360.00 

1145.89 

2180.00 

703.975 

1453.33 

573.033 

1090.00 

458.478 

87'2.000 

37 

2292.66 

4361.67 

1146.37 

2180.83 

764.299 

1453.89 

573.277 

1090.42 

458  672 

872.333 

38 

2293.64 

4363.33 

1146.86 

•2181.67 

764.624 

1454.44 

573.520 

1090.83 

458.867 

872.667 

39 

2294.61 

4365.00 

1147.35 

•2182.50 

764.949 

1455.00 

573.764 

1091.25 

459.062 

873.000 

4O 

2295.58 

4366.67 

1147.83 

2183.33 

765.274 

1455.56 

574.007 

1091.67 

459.257 

873.333 

41 

2296.53 

4368.33 

1148.31 

2184.17 

765.589 

1456.11 

.374.244 

1092.  08]  459.  446 

873.667 

48 

2297.48 

4370.00 

1148.78 

2185.00 

765.904 

1456.67 

574.481 

1092.50 

459.635 

874.000 

43 

2298.45 

4371  67 

1149.27 

^185.83 

766.229 

1457.22 

574.724 

1092.92 

459.830 

87'4.333 

44 

2299.42 

4373.33 

1149.75 

2186.67 

766.553 

1457.78 

574.967 

1093.33 

460  025 

874.667 

45 

2300.40 

4375.00 

1150.24 

2187.50 

766.878 

1458.33 

575  211 

1093.75 

460.220 

875.000 

46 

2301.37 

4376.67 

1150.73 

2188.33 

767.203 

1458.89 

575.454 

1094.17 

460.415 

875.333 

47 

2302.35 

4378.33 

1151.21 

2189.17 

767.527 

1459.44 

575.698 

1094.58 

460.610 

875.667 

48 

2303.32 

4380.00 

1151.70 

2190.00 

767.  &52  11460.00 

575.941 

1095.00 

460.805 

876.000 

49 

2304.29 

4381.67 

1152.19 

2190.83 

768.177 

1460.56 

576.185 

1095.42 

460.999 

876.333 

5O 

2305.27 

4383.33 

1152.68 

2191.67 

768.502 

1461.11 

576.428 

1095.83 

461.194 

876.667 

51 

2306.21 

4385  00 

1153.15 

2192.50 

768.817 

1461.67 

576.665 

1096.25 

461.383 

877.000 

2307.16 

4386.67 

1153.62 

2193.33 

769.132 

1462.22 

576.901 

1096.67 

461.573 

877.333 

53 

2308.134388.3*3 

1154.11 

2194.17 

769.457 

1462.78 

577.145 

1097.08 

461.767 

877.667 

54 

2309.11  4390.00 

1154.60 

2195.00 

769.781 

1463.33 

577.388 

1097  50 

461.962 

878.000 

55 

231J.084391.67 

1155.08 

2195.83 

770.106 

1463.89 

577.632 

1097.92 

462.157 

878.333 

56 

2311.054393.33 

1155.57 

2196.67 

770.431 

1464.44 

577.876 

1098.?3 

462.352 

878.667 

57 

2312.034395.00 

1156.06 

2197.50 

770.755 

1465.00 

57'8.119 

1098.75 

462.547 

879.000 

58 

2313.004396.67 

1156.54 

2198.33 

771.080 

1465.56 

578.363 

1099.17 

462.742 

879.333 

59 

2313.984398.3; 

1157.03 

2199.17 

771.4051  1466.  11  1578.  606 

1099.58 

462.937 

879.667 

132 


TATVLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

43° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

870.330716.667 

322.620614.286 

282.  347  i  537.  500 

251.027 

477.778 

225.982 

430.000 

0 

376.492716.944 

W2.  759  614.  524 

282.  469  i  537.  708 

251.135 

477.963 

226.080 

430.167 

1 

376.655 

717.222 

322.899614.762 

282.51)0537.917 

251.244 

478.148 

226.177 

430.333 

2 

376.812 

717.500 

J23.034  615.000 

282.  709  1538.1  25 

251.349 

478.333 

226.272 

430.500 

3 

376.970 

717.778 

323.  169  61  5.  238 

282.8271538.3:33 

251.454 

478.519 

226.367 

430.667 

4 

377.132 

718.056 

323.308 

615.476 

282.949538.542 

251.562 

478.704 

226.464 

430.  sas 

5 

377.295 

718.333 

323.447 

615.714 

283.071 

538.750 

251.671 

478.889 

226.562 

431.000 

6 

377.457 

718.611 

323.587 

615.952 

283.193 

538.958 

251.77'9 

479.074 

226.659 

431.167 

7 

377.619 

718.889 

323.726 

616.190 

283  314 

539.167 

251.887 

479.259 

226.757 

431.333 

8 

377.777 

719.167 

323.861 

616.429 

283.433 

539.375 

251.992 

479.444 

226.851 

431.500 

9 

377.935 

719.444 

323.996 

616.667 

283.551 

539.583 

252.098 

479.630 

226.946 

431.667 

10 

378.097 

719.722 

324.135 

616.905 

283.673 

539.792 

252.206 

479.815 

227.044 

431.833 

11 

378.260 

720.000 

324.275 

617.143 

283.795 

540.000 

252  314 

480.000 

227.141 

432.000 

12 

378.417 

720.278 

324.410 

617.381 

283.  91  3 

540.208 

252.419 

480.185 

227.236 

432.167 

13 

378.575 

720.556 

S24.545 

617.619 

284.031 

540.417 

252.525 

480.370 

227.330 

432.333 

14 

378.737 

720.833 

324.684 

617.857 

284.153 

540.625 

252.633 

480.556 

227.428 

432.500 

15 

378.900 

721.111 

324.823 

618.095 

284.275 

540.833 

252.741 

480.741 

227.525 

432.667 

16 

379.062 

721  .  389 

'324.963 

618.333 

284.397 

541.042 

252.850 

480.926 

227.623 

432.833 

17 

379.225 

721.667 

325.102 

618.571 

284.519 

541.250 

252.958 

481.111 

227.720 

433.000 

18 

379.382 

721.944 

325.237 

618.810 

284.637 

541.458 

253.063 

481.296 

227.815 

433.167 

19 

379.540 

722  222 

325.372 

619.048 

284.755 

541.667 

253.168 

481.481 

227.910 

433.333 

20 

379.702 

722  .'500 

•325.511 

619.286 

284.877 

541.875 

253.277 

481.667 

228.007 

433.500 

21 

379.865 

722.778 

325.650 

619  524 

284.999 

542.083 

253.385 

481.852 

228.105 

433.667 

22 

380.027 

723.056 

325.790 

619.762 

285.121 

5.42.292 

253.493 

482.037 

228.202 

433.833 

23 

380.189 

723.333 

325.929 

620.000 

285.243 

542.500 

253.602 

482.222 

228.300 

434.000 

24 

380.352 

723.611 

326.068 

620.238 

285.364 

542.708 

253.710 

482.407 

228.397 

434.167 

25 

380.514 

723.889 

326.207 

620.476 

285.486 

542.017 

253.818 

482.593 

228.495 

434.333 

2G 

380.672 

724.167 

326.343 

620.714 

285.605 

543.125 

253.923 

482.778 

228.590 

434.500 

27 

380.830 

724.444 

326.478 

620.952 

285.723 

543.333 

254.029 

482.963 

228.684 

434.667 

28 

380.992 

724.722 

326.617 

621.190 

285.845 

543.542 

254.137 

483.148 

228.782 

434.833 

29 

381.154 

725.000 

326.756 

621.429 

285.966 

543.750 

254.245 

483.333 

228.879 

435.000 

30 

381.317 

725.278 

326.895 

621.667 

286.  Oh8 

543.958 

254.354 

483  519 

228.977 

435.167 

31 

381.479 

725  556 

327.035 

621.905 

286.210 

544.167 

254.462 

483.704 

229.074 

435.333 

32 

381.637 

725.833 

327.170 

622.143 

286.328 

544.375 

254.567 

483.889 

229.169 

435.500 

33 

381.794 

726.111 

327.305 

622.381 

286.447 

544.583 

254.672 

484.074 

229.264 

435.667 

34 

381.957 

726.389 

327.444 

622.619 

286.569 

544.792 

254.780 

484.259 

229.361 

435.833 

35 

883.119 

726.667 

327.583 

622.857 

286.690 

545.000 

254.889 

484.444 

229  459 

436.000 

36 

382.282 

726.944 

327.723 

623.095 

286.812 

545.208 

254.997 

484.630 

229.556 

436.167 

37 

382.444 

727.222 

327.862 

623.333 

286.9:34 

545.417 

255.106 

484.815 

229.654 

436.333 

38 

382.607 

727.500 

328.001 

623.571 

287.056 

545.625 

255.214 

485.000 

229.751 

436.500 

39 

382.769 

727.778 

328.140 

623.810 

287.178 

545.833 

255.322 

485.185 

229.849 

436.667 

4O 

382.927 

728.056 

328.275 

624.048 

287.296 

546.042 

255.427 

485.370 

229.944 

436.833 

41 

383.084 

728.333 

328.411 

624.286 

287.414 

546.250 

255.532 

485.556 

230.038 

437.000 

42 

383.247 

728.611 

328.550 

624.524 

287.536 

546.458 

255.641 

485.741 

230.136 

437.167 

43 

383.409 

728.889 

328  689 

624.762 

287.658 

546.667 

255.749 

485.926 

230.233 

437.333 

44 

383.571 

729.167 

328.828 

625.000 

287.780 

546.875 

255.857 

486.111 

230.331 

437.500 

45 

383.734 

729.444 

328.968 

625.238 

287.902 

547.083 

255.966 

486.296 

230.428 

437.667 

46 

383.896 

729.72v> 

329.107 

625.476 

288.024 

547.292 

256.074 

486.481 

230.  P26 

437.833 

47 

384.059 

730.000 

329.246 

625.714 

288.146 

547.500 

256.182 

486.667 

230.623 

438.000 

48 

384.221 

730.278 

329.385 

625.952 

288.267 

547.708 

256.291 

486.852 

230.721 

438.167 

49 

384.384 

730.556 

329.524 

626.190 

288.  3S9 

547.917 

256.399 

487.037 

230.818 

438.333 

5O 

384.  541  1730.  833 

329.660 

626.429 

288.507 

548.125 

256.504 

487.222 

230.913 

438.500 

51 

384.699731.111 

329.795 

626.667 

288.626 

548  333 

256.609 

487.407 

231  .008 

438.667 

52 

384.861 

731.389 

329.934 

626.905 

288.748 

548.542 

256.718 

487.593 

231.105 

438.833 

53 

385.001 

731.667 

330.073 

627.143 

288.869 

548.750 

256.826 

487.778 

231.203 

439.000 

54 

385.186 

731.944 

330.212 

627.381 

288.991 

548.958 

256.934 

487.963 

231.300 

439.167 

55 

385.848 

732.222 

330.352 

627.619 

289.113 

549.167 

257.043 

488.148 

231.398 

439.383 

56 

385.511 

732.500 

330.491 

627.857 

289.235 

549.375 

257.151 

488.333 

231.495 

439.500 

57 

385.673 

732.778 

330.630 

628.095 

289.357549.583 

257.259 

488.519 

231.593 

439.667 

58 

385.836 

733.056 

330.769 

628.333 

289.479549.792 

257.368 

488.704 

231.690 

439.833 

59 

133 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


440 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve- 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc.      Tan. 

Arc. 

<) 

2314.95 

4400.00 

1157.52 

2200.00771.730 

1466.67 

578.850 

1100.00463.132880.000 

1 

•>315.90 

4401.67 

1157.992200.83772.045 

1467.22 

579.086 

1100.42463.321  880.333 

2 

2316.84 

4403.33 

1158.46 

2201.  671772.  360 

1467.78 

579.323 

1100.63463.510880.667 

3 

2317.82 

4405.00 

1158.95 

2202.50772.685 

1468.  33 

579.566 

1101.25463.705881.000 

4 

2318.79 

4406.67 

1159.44 

2203.33 

773.009 

1468.89 

579.810 

1101.  67  ;  463.  900 

881.333 

5 

2319.76 

4408.33 

1159.92 

2204.17 

773.334 

1469.44580.053 

1102.08:464.094 

881.667 

0 

2320.74 

4410.00 

1160.41 

2205.00 

773.659 

1470.00,580.297 

1102.  50|464.  289 

882.000 

7 

2321.71 

4411.67 

1160.90 

2205.83 

773.984 

1470.56 

580.540 

1102.92,464.484 

882.333 

8 

2322.60 

4413.33 

1161.39 

2206.  67J  774.  308 

1471.11 

580.784 

1103.33 

464.679 

882.667 

9 

•2323.66 

4415.00 

1161.87 

2207.50 

774.633 

1471.67 

581.027 

1103.75 

464.874 

883.000 

10 

2324.63 

4416.67 

1162.36 

2208.33 

774.958 

1472.22 

581.271 

1104.17 

465.069 

883.333 

11 

2325.61 

4418.33 

1162.85 

2209.17 

775.282 

1472.78 

581.515 

1104.58 

465.264 

883.667 

12 

2326.58 

4420.00 

1163.33 

2210.00 

775.607 

1473.33 

581.758 

1105.00 

465.458 

884.000 

13 

2327.56 

4421.67 

1163.82 

2210.83 

775.932 

1473.89 

582.002 

1105.42 

465.653 

884.3:53 

14 

2328.53 

4423.33 

1164.31 

2211.67 

776.257 

1474.44 

582.245 

1105.83465.848 

884.667 

15 

2329.50 

4425.00 

1164.79 

2212.50 

776.581 

1475.00 

582.489 

1106.25 

466.043 

885.000 

16 

2330.48 

4426.67 

1165.28 

2213.33 

776.906 

1475.56 

582.732 

1106.67 

466.238 

885.333 

17 

3331.42 

4428.33 

1165.75 

2214.17 

777.221 

1476.11 

582.969 

1107.08 

466.427 

885.667 

18 

2332.37 

4430.00 

1166.23 

2215.00 

777.536 

1476.67 

583.205 

1107.50 

466.616 

886.000 

19 

2333.34 

4431.67 

1166.71 

2215.83 

777.861 

1477.22 

583.449 

1107.92 

466.811 

886.333 

20 

2334.32 

4433.33 

1167.20 

2216.67 

778.186 

1477.78 

583.692 

1108.33 

467.006 

886.667 

21 

2:335.29 

4435.00 

1167.69 

2217.50 

778.510 

1478.33 

583.936 

1108.75 

467.201 

887.000 

22 

2336.26 

4436.67 

1168.18 

2218.33 

778.835 

1478.89 

584.179 

1109.17 

467.396 

887.333 

23 

2337.24 

4438.33 

1168.66 

2219.17 

779.160 

1479.44 

584.423 

1109.58 

467.591 

887.667 

24 

23:38.21 

4440.00 

1169.15 

2220.00 

779.485 

1480.00 

584.666 

1110.00 

467.785 

888.000 

25 

2339.19 

4441.67 

1169.64 

2220.83 

779.809 

1480.56 

584.910 

1110.42 

467.980 

888.333 

26 

2340.16 

4443.33 

1170.12 

2221.67 

780.134 

1481.11 

585.154 

1110.83 

468,175 

888.667 

27 

2341.13 

4445.00 

1170.61 

2222.50 

780.459 

1481.67 

585.397 

1111  25 

468.370 

889.000 

28 

2342.11 

4446.67 

1171.10 

2223.33 

780.783 

1482.22 

585.641 

1111.67 

468.565 

889.333 

29 

2343.08 

4448.33 

1171.58 

2224.17 

781.108 

1482.78 

585.884 

1112.08 

468.760 

889.667 

3O 

2344.06 

4450.00 

1172.07 

2225.00 

781.433 

1483.33 

586.128 

1112.50 

468.955 

890.000 

31 

2345.03 

4451.67 

1172.56 

2225.83 

781.758 

1483.89 

586.371 

1112.92 

469.149 

890.333 

32 

2346.01 

4453.33 

1173.05 

2226.67 

782.082 

1484.44 

586.615 

1113.33 

469.344 

890.667 

33 

2346.98 

4455.00 

1173.53 

2227.50 

782.407 

1485.00 

586.858 

1113.75 

469.539 

891.000 

34 

2347.95 

4456.67 

1174.02 

2228.33 

782.732 

1485.56 

587.102 

1114.17 

469.734 

891.333 

35 

2348.93 

4458.33 

1174.51 

2229.17 

783.056 

1486.11 

587.346 

1114.58 

469.929 

891.667 

36 

2319.90 

4460.00 

1174.99 

2230.00 

783.381 

1486.67 

587.589 

1115.00 

470.124 

892.000 

37 

2350.88 

4461.67 

1175.48 

2230.83 

783.706 

1487.22 

587  833 

1115.42 

470.319 

892.333 

38 

2351.85 

4463.33 

1175.97 

2231.67 

784.031 

1487.78 

588.076 

1115.83 

470.514 

892.667 

39 

2352.82 

4465.00 

1176.45 

2232.50 

784.355 

1488.33 

588.320 

1116.25 

470.708 

893.000 

40 

2353.80 

4466.67 

1176.94 

2233.33 

784.680 

1488.89 

588.563 

1116.67 

470.903 

893.333 

41 

23o4.77 

4468.33 

1177.43 

2234.17 

785.005 

1489.44 

588.807 

1117.08 

471.098 

893.667 

42 

2355.75 

4470.00 

1177.92 

2235.00 

785.329 

1490.00 

589.050 

1117.50 

471.293 

894.000 

43 

2856.78 

4471.67 

1178.40 

2235.83 

785.654 

1490.56 

589.294 

1117.92 

471.488 

894.333 

44 

2357.69 

4473.33 

1178.89 

2236.67 

785.979 

1491.11 

589.538 

1118.  as 

471.683 

894.667 

45 

2358.67 

4475.00 

1179.38 

2237.50 

786.304 

1491.67 

589.781 

1118.75 

471.878 

895.000 

46 

2359.64 

4476.67 

1179.86 

2238.35 

786.628 

1492.22 

590.025 

1119.17 

472.072 

895.333 

47 

2360.62 

4478.33 

1180.35 

2239.17 

786.953 

1492.78 

590.268 

1119.58 

472.267 

895.667 

48 

23>>1.59 

4480.00 

1180.84 

2240.00 

787.278 

1493.33 

590.512 

1120.00 

472.462 

896.000 

49 

2362.56 

4481.67 

1181.33 

2240.83 

787.602 

1493.89 

590.755 

1120.42 

472.657 

896.333 

50 

2363.54 

4483.33 

1181.81 

2241.67 

787.927 

1494.44 

590.999 

1120.83 

472.852 

896.667 

51 

2364.51 

4485.00 

1182.30 

2242.50 

788.252 

1495.00 

591.243 

1121.25 

473.047 

897.000 

52 

2365.49 

4486  67 

1182.79 

2243.33 

788.577 

1495.56 

591.486 

1121.67 

473.242 

897.333 

53 

2366.46 

4488.  33 

nas.  27 

2244.17 

788.901 

1496.11 

591.730 

1122.08 

473.437 

897.667 

54 

2367.43 

4490.00 

1183.76 

2245.00 

789.226 

1496.67 

591.973 

1122.50 

473.631 

898.000 

55 

2368.41 

4491.67 

1184.25 

2245.83 

789.551 

1497.22 

592.217 

1122.92 

473.826 

898.333 

56 

2369.38 

4493.33 

1184.73 

2246.67 

789.875 

1497.78 

592.460 

1123.33 

474.021 

S98.667 

57 

2370.36 

4495.00 

11&5.22 

2247.50 

790.200 

1498.33 

592.704 

1123.75 

474.216 

899.000 

58 

2371.33 

4496.67 

1185.71 

2248.33 

790.525 

1498.89 

592.947 

1124.17 

474.411 

899.  aS3 

59 

2372.30 

4498.  a3 

1186.20 

2249.17 

790.850 

1499.44 

593.191 

1124.58 

474.606 

899.667 

131 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

440 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

385.998 

733.838 

330.909 

628.571 

289.601 

550.000 

257.476 

488.889 

231.788 

440.000 

~o" 

386.156 

733.  611  1331.044 

628.810 

289.719550.208 

257.581s  489.  074 

281.888 

440.10? 

i 

386.313 

783.889 

331.179 

629.048 

289.837 

550.417 

257.  686  1  489.  259 

231.97? 

440.338 

<j 

386.476 

734.107 

331.318 

629.286 

289.959 

550.625 

257.795489.444 

232.075 

440.500 

3 

386.638 

734.444 

331.457 

629.524 

290.081 

550.833 

257.  903  1  489.  630 

232.172 

440.667 

4 

386.801 

734.722 

331.59? 

629.762 

290.203 

551.042 

258.011 

489.815 

232.270 

440.833 

5 

386.963 

735.000 

331.736 

630.000 

290.325 

551.250 

258.120 

490.000 

232  367 

441.000 

6 

387.125 

735.278 

331.875 

630.238 

290.446 

551.458 

258.228 

490.185 

23:3.465 

441.167 

7 

387.288 

735.556 

332.014 

630.476 

290.568 

551.667 

258.336 

490.370 

232.562 

441.333 

8 

387.450 

735.833 

332.154 

630.714 

290.690 

551.875 

258.445 

490.556 

232.660 

441.500 

9 

387.613 

736.111 

332.293 

630.952 

290.812 

552.083 

258.553 

490.741 

232.757 

441.667 

1O 

387.775 

736.389 

332.432 

631.190 

290.934 

552.292 

258.661 

490.926 

232.855 

441.833 

11 

387.937 

736.667 

332.571 

631.429 

291.056 

552.500 

258.770 

491.111 

232.953 

442.000 

13 

388.100 

736.944 

332.710 

631.667 

291.177 

552.708 

258.878 

491.296 

233.050 

442.167 

13 

388.262 

7*7.2-22 

332.850 

631.905 

291.299 

552.917 

258.986 

491.481 

233.148 

442.3:33 

14 

388.425 

737.500 

332.989 

632.143 

291.421 

553  125 

259.095 

491  667 

233.245 

442.500 

15 

388.587 

737.778 

333.128 

632.381 

291.543 

553.333 

259.203 

491.852 

233.343 

442.667 

16 

388.745 

738.056 

333.263 

632.619 

291.661 

553.542 

259.308 

492.037 

233.437 

442.833 

17 

388.902 

738.333 

333.398 

632.857 

291.780 

553.750 

259.413 

492.222 

233.532 

443.000 

18 

389.065 

738.611 

333.538 

633.095 

291.901 

553  958 

259.522 

492.407 

233.629 

443.167 

19 

389.227 

738.889 

333.677 

633.333 

292.023 

554.167 

259.630 

492.593 

233.727 

443.333 

2O 

389.390 

739.167 

333.816 

633.571 

292.145 

554  375 

259.738 

492.778 

233.825 

443.500 

31 

389.552 

739.444 

333.955 

633.810 

292.267 

554.583 

259.847 

492.963 

233.922 

443.66? 

22 

389.714 

739.722 

334.095 

634.048 

292.389 

554.792 

259.955 

493.148 

£34.020 

443.833 

23 

389.877 

740.000 

334.234 

634.280 

292.511 

555.000 

260.063 

493.333 

234.117 

444.000 

24 

390.039 

740.278 

334.373 

634.524 

292.633 

555.208 

260.172 

493.519 

234.215 

444.167 

25 

390.202 

740.556 

334.512 

634.762 

292  754 

555.417 

260.280 

493.704 

234.312 

444.333 

2G 

390.364 

740.833 

334.652 

635.000 

292.876 

555.625 

260.388 

493.889 

2:34.410 

444.500 

37 

390.527 

741.111 

334.791 

635.238 

292.998 

555.833 

260.497 

494.074 

234.507 

444.66? 

38 

390.689 

741.389 

334.930 

635.476 

293.120 

556.042 

260.605 

494.259 

2^34.605 

444.833 

29 

390  851 

741.667 

335.069 

635.714 

293.242 

556.250 

260.713 

494.444 

234.702 

445.000 

30 

391.014 

741.944 

335.208 

635.952 

293.364 

556.458 

260.822 

494.630 

234.800 

445.16? 

31 

391.176 

742.22V 

335.348 

636.190 

293.486 

556.667 

260.930 

494.815 

234.897 

445.333 

33 

391.339 

742.500 

335.487 

636.429 

293.607 

556.875 

261  038 

495.000 

234.995 

445.500 

33 

391.501 

742.778 

335.626 

636  667 

293.729 

557  083 

261.147 

495.185 

235.092 

445.667 

34 

391.663 

743.056 

335.765 

636.905 

293.851 

557.292 

261.255 

495.370 

235.190 

445.833 

35 

391.826 

743.333 

335.905 

637.143 

293.973 

557.500 

261.363 

495.556 

235.287 

446.000 

36 

391.  9S8 

743.611 

336.044 

637.381 

294.095 

557.708 

261.472 

495.741 

235.385 

446.167 

37 

392.151 

743.889 

336.183 

637.619 

294.217 

558.917 

261.580 

495.926 

235.482 

446.333 

38 

392.313 

744.167 

336.322 

637.857 

294.338 

558.125 

261.688 

496.111 

235.580 

446.500 

39 

392.475 

744.444 

336.462 

638  095 

294.460 

558.  333 

261.797 

496.296 

235.678 

446.667 

40 

392.638 

744.722 

336.601 

638.333 

294.582 

558.542 

261.905 

496.481 

235.775 

446.833 

41 

392.800 

745.000 

336.740 

638.571 

294.704 

558.750 

262.014 

496.667 

235.873 

447.000 

43 

392.963 

745.278 

336.879 

638.810 

294.826 

558  958 

262.122 

496.852 

235.970 

447.167 

43 

393.125 

393.288 

745.550 
715.833 

337.018 
337.158 

639.048 

639.286 

294.948 
295.070 

559.167 
559.375 

262.230 
262.339 

497.037 
497.222 

236.068 
236.165 

447.333 
447.500 

44 
45 

393.450 

746.111 

337.297 

639  524 

295.191 

5.MK583 

262.447 

497.40? 

236.263 

447.667 

46 

393.612 

7-16.389 

337.436 

639.762 

295.313 

559.792 

262.555 

497.593 

236.360 

447.833 

47 

393.775 

746.667 

347.575 

640.000 

295.435 

500.000 

262.664 

497.778 

236.458 

448.000 

48 

393.937 

746.944 

337.715 

640.238 

295.557 

560.208 

262.772 

497.963 

236.555 

448.167 

49 

394.100 

747.222 

337.854 

640.476 

295.679 

560.417 

262.880 

498.148 

236.653 

448.333 

50 

394.262 

747.500 

337.993 

640.714 

295.80! 

560.625 

202.989 

498.333 

236.750 

448  500 

51 

394.424 

747.778 

338.13. 

640.952 

295.923 

500.833 

203.097 

498.519 

236.848 

448.667 

53 

394.587 

748.056 

338.272 

641  190 

296.044 

501.042 

203.205 

498  704 

236.945 

448.833 

53 

394.749 

748333 

338.411 

641.429 

296.166 

561.250 

263.314 

498.889 

237.043 

449.000 

54 

394.912 

748.611 

338.550 

641.667 

296.288 

561.458 

263.422 

499.074 

237.140 

449  167 

55 

39.-,.  074 

748.889 

.338.6*9 

641  .  905 

296.410 

561.667 

263.530 

499.259 

237.238 

449.333 

56 

395.237 

749.167 

338.8-29 

642.143 

296.532 

561.875 

263.639 

499.444 

237.336 

449.500 

57 

395.399 

749.444 

338.968 

642.381 

296.654562.083 

263.747 

499.630 

837.433 

449.667 

58 

395.561 

749.722 

339.107 

G42.619 

296.  776  1562.  292 

263.855 

499.815 

237.531 

449.833 

59 

TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


45° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

o~ 

2373728 

4500.00 

1186.68 

2250.00 

791.174 

1500.00 

593.43o 

1125.00 

474.801 

900.000 

1 

2374.25 

4501.67 

1187.17 

2250.83 

791.499 

1500.56 

593.678 

1125.42 

474.996 

900.333 

2 

2375.23 

4503.33 

1187.66 

2251.67 

791.824 

1501.11 

593.922 

1125.83 

475.190 

900.667 

3 

2376.23 

4505.00 

1188.16 

2252.50 

792.158 

1501.67 

594.172 

1126.25 

475.391 

901.000 

4 

2377.23 

4506.67 

1188.66 

2253.33 

792.492 

1502.22 

594.423 

1126.67 

475.592 

901.333 

5 

2378.21 

4508.33 

1189.15 

2254.17 

792.817 

1502  78 

594.667 

1127.08 

475.786901.667 

6 

2379.18 

4510.00 

1189.63 

2255.00 

793.142 

1503.33 

594.910 

1127.50 

475.981 

902.000 

7 

2380.15 

4511.67 

1190.12 

2255.  83 

793.466  1503.89 

595.154 

1127.92 

476.176902.333 

8 

2381.13 

4513.33 

1190.61 

2256.67 

793.791  1504.44 

595.397 

1128.33 

476.371 

902.667 

9 

2382.10 

4515.00 

1191.09 

2257.50 

794.116  1505.00 

595.641 

1128.75 

476.566903.000 

10 

2383.08 

4516.67 

1191.58 

2258.33 

794.440 

1505.56 

595.884 

1129.17 

476.761  903  333 

11 

2384.05 

4518.33 

1192.07 

2259.17 

794.765 

1506.11 

596.128 

1129.58 

476.956903  667 

12 

2385.02 

4520.00 

1192.56 

2260.00 

795.090 

1506.67 

596.372 

1130.00 

477.151 

904  .  000 

13 

2386.00 

4521.67 

1193.04 

2260.83 

795.415 

1507.22 

596.615 

1130.42 

477.345904.333 

14 

2386.97 

4523.33 

1193.53 

2261.67 

795.739 

1507.78 

596.859 

1130.83 

477.540 

904.667 

15 

2387.95 

4525.00 

1194.02 

2262.50 

796.064 

1508.33 

597.102 

1131.25 

477.735905.000 

16 

2388.92 

4526.67 

1194.50 

2263  33 

796.389 

1508.89 

597.346 

1131.67 

477.930 

905.333 

17 

2389.89 

4528.33 

1194.99 

2264.17 

796.713 

1509.44 

597.589 

1132.08 

478.125905.667 

18 

2390.87 

4530.00 

1195.48 

2265.00 

797.038 

1510.00 

597.833 

1132.50 

478.320 

906.000 

19 

2391.87 

4531.67 

1195.98 

2265.83 

797.372 

1510.56 

598.084 

1132.92 

478.520 

906.333 

20 

2392.87 

4533  33 

1196.48 

2266.67 

797.707 

1511.11 

598.334 

1133.33 

478.721 

906.667 

21 

2393.85 

4535.00 

1196.97 

2267.50 

798.031 

1511.67 

598.578 

1133.75 

478.916 

907.000 

22 

2394.82 

4536.67 

1197.45 

2268.33 

798.356 

1512.22 

598.821 

1134.17 

479.111 

907.333 

23 

2395.80 

4538.33 

1197.94 

2269.17 

798.681 

1512.78 

599.065 

1134.58 

479.306907.667 

24 

2396.77 

4510.00 

1198.43 

2270.00 

799.006 

1513.33 

599.309 

1135.00 

479.500 

908.000 

25 

2397.74 

4541.67 

1198  92 

2270.83 

799.330 

1513.89 

599.552 

1135.42 

479.  695  :  908.  333 

26 

2398.72 

4543.33 

1199.40 

2271.67 

799.655 

1514.44 

599.796 

1135.83 

479.890 

908.667 

27 

2399.69 

4545.00 

1199.89 

2272.50 

799.980 

1515.00 

600.039 

1136.25 

480.0851909.000 

28 

2400.67 

4546.67 

1200.38 

2273.33 

800.304 

1515.56 

600.283 

1136.67 

480.280!909.333 

29 

2401.64 

4548.33 

1200.86 

2274.17 

800.629 

1516.11 

600.526 

1137.08 

480.475 

909.667 

30 

2402.61 

4550.00 

1201.35 

2275.00 

800.954 

1516.67 

600.770 

1137.50 

480  670 

910.000 

31 

2403.62 

4551.67 

1201.85 

2275.83 

801.288 

1517.22 

601.021 

1137  92 

480.  870^910.  333 

32 

2404.62 

4553.33 

1202.35 

2276.67 

801.622 

1517.78 

601.271 

1138.33 

481.071 

910.667 

33 

2405.59 

4555.00 

1202.84 

2277.50 

801.947 

1518.33 

601.515 

1138.75 

481.2661911.000 

34 

2406.57 

4556.67 

1203.33 

2278.  a3 

802.272 

1518.89 

601  .  758 

1139.17 

481.461 

911.333 

35 

2407.54 

4558.33 

1203.81 

2279.17 

802.597 

1519.44 

602.002 

1139.58 

481.655 

911.667 

36 

2108.52 

4560.00 

1204.30 

2280.00 

802.921 

1520.00 

602.246 

1140.00 

481.850912.000 

37 

2409.19 

4561.67 

1204.79 

2280.  as 

803  246 

1520.56 

602.489 

1140.42 

482.045 

912.333 

38 

2410.46 

4563.33 

1205.28 

2281.67 

803.571 

1521.11 

602.733 

1140.83 

482.240 

912.667 

39 

2411.47 

4565.00 

1205.78 

2282.50 

803.905 

1521.67 

602.983 

1141.25 

482.441 

913.000 

40 

2412.47 

4566.67 

1206.28 

2283.33 

804.239 

1522.22 

603.234 

1141.67 

4S2.641 

913.333 

41 

2413.44 

4568.33 

1206.77 

2284.17 

H04.564 

1522.78 

603.478 

1142.08 

482.836 

913.667 

42 

2414.42 

4570.00 

1207.25 

2285.00 

804.889 

1523.33 

603.721 

1142.50 

483.031 

914.000 

43 

2415.39 

4571.67 

1207.74 

2285.83 

805  213 

1523.89 

603.965 

1142.92 

483.226 

914.333 

44 

2416.37 

4573.33 

1208.23 

2286.67 

805.53S 

1524.44 

604.208 

1143.33 

483.421 

914.667 

45 

2417.34 

4575.00 

1208.71 

2287.50 

805  863 

1525.00 

604.452 

1143.75 

483.616 

915.000 

46 

2418.31 

4576.67 

1209.20 

2288.33 

806.187 

1525.56 

604.695 

1144.17 

483.810915.333 

47 

2119.32 

4578.33 

1209.70 

2289.17 

806.522 

1526.11 

604.946 

1144.58 

484.011 

915.667 

48 

2120.32 

4580.00 

1210.20 

2290.00 

806.856 

1526.67 

605.197 

1145.00 

484.2121916.000 

49 

2421.29 

4581.67 

1210.69 

2290.83 

807.181 

1527.22 

605.440 

1145.42 

484.406 

916.333 

50 

2422.27 

4583.33 

1211.18 

2291.67 

807.505 

1527.78 

605.684 

1145.83 

484.601 

916  6G7 

51 

2423.24 

4585.00 

1211.66 

2292.50 

807.830 

1528.33 

605.928 

1146.25 

484.796 

917.000 

52 

2424.21 

4586.67 

1212.15 

2293.33 

808.155 

1528.89 

606.171 

1146.67 

484.991 

917.333 

53 

2425.22 

4588.33 

1212.65 

2294.17 

808.489 

1529.44 

606.422 

1147.08 

485.192917.667 

54 

2426.22 

4590.00 

1213.15 

2295.00 

808.823 

1530  00 

606.673 

1147.50 

485.392918.000 

55 

2427.19 

4591.67 

1213.64 

2295.83 

809.148 

1530.56 

606.916 

1147.92 

485.587 

918.  333 

56 

2428.17 

4593.33 

1214.13 

2296.67 

809.473 

1531  .  1  1 

607.160 

1148.33 

485.782 

918.667 

57 

2429.14 

4595.00 

1214.62 

2297.50 

809.798 

1531.67 

607.403 

1148.75 

485.977 

919.000 

58 

2430.12 

4596.67 

1215.10 

2298.33 

810.122 

1532.22 

607.647 

1149.17 

486.172 

919.333 

59 

2431.09 

4598.33 

1215.59 

2299.17 

810.447 

1532.78 

607.890 

1149.58 

486.367,919.667 

136 


TABLE  XIV.— ACTUAL   TANGENTS,    ETC. 


6*  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

45° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |    Arc. 

Tan. 

Arc. 

M. 

395.724 

750.000 

339.246 

642.857 

296.897 

562.500  263.964  500.000 

237.628 

450.000 

O 

395.886 

750.278 

339.385 

643.095 

297.019 

562.708264.072500.185 

237.726 

450.167 

1 

396.049 

750.556 

339.525 

643.333 

297.141 

562.917 

264.180 

500.370 

237.823 

450.333 

2 

396.216 

750.833 

339.668 

643.571 

297.267 

563.125 

264.292 

500.556 

237.924 

450.500 

3 

396.383 

751.111 

339.811 

643.810 

297.392 

563.333 

264.403 

500.741 

238.0,  '4 

450.667 

4 

396.545 

751.389 

339.951 

644.048 

297.514563.542 

264.512 

500.926 

238.121 

450.833 

5 

396.708 

751.667 

340  090644.286 

297.636563.750 

264.620 

501.111 

238.219 

451.000 

6 

896.870 

751.944 

340.229644.524 

297.758563.958 

264.728 

501.2% 

238  317 

451.167 

7 

397.033 

752.222 

340.368|644.762 

297.879564.167 

264.837 

501.481 

238.414 

451.333 

8 

397.195 

752.500 

340.508 

645.000 

298.001 

564.375 

264.945 

501.667 

238.512 

451.500 

9 

397.357 

752.778 

340.647 

645.238 

298.123 

564.583 

265.053 

501.852 

238.609 

451.667 

10 

397.520 

753.056 

340.786 

645.476 

298.  245  1564.792 

265.162 

502.037 

238.707 

451.833 

11 

397.682 

753.333 

340.925 

645.714 

298.  367  i  565.  tOO 

265.270 

502.222 

238.804 

452.000 

12 

397.845 

753.611 

341.064 

645.952 

298.489 

565.208 

265.378 

502.407 

238.902 

452.167 

13 

398.007 

753.889 

341.204 

646.  19U 

298.610 

565.417 

265  487 

502.593 

238.999 

452.333 

14 

398  170 

754.167 

341.343 

646.429 

298.732 

565.625 

265.595 

502.778 

239.097 

452.500 

15 

398.332 

754.444 

341.482 

646.667 

298.854 

565  833 

265.703 

502.963 

239.194 

452.667 

16 

398.494 

754.722 

341.621 

646  905 

298.976 

566.042 

265.812 

503.148 

239.29-2 

452.833 

17 

398  .  657 

755.000 

341.761 

647.143 

299  098 

566.250 

265.920 

503.333 

•239.389 

453.000 

18 

398.824 

755.278 

341.904 

647.381 

299.223 

566.458 

266.031 

503.519 

239.490 

453.167 

19 

398.991 

755.556 

342.047 

647.619 

299.349 

566.  G67 

266.143 

503.704 

239.590 

453.333 

20 

399.154 

755.833 

342.186 

647.857 

299.471 

566.875 

266.251 

503.889 

239.688 

453.500 

21 

399.316 

756.111 

342.326 

648.095 

299.592 

567.083 

266  360 

504.074 

239.785 

453.667 

22 

399.478 

756.389 

342.465 

648.333 

299.714 

567.292 

266.468 

504.259 

239.883 

453.833 

23 

399.641 

756.667 

342.604 

648.571 

299.836 

567.500 

266.576 

504.444 

239.980 

454.000 

24 

399.803 

756.944 

342.743 

648.810 

299.958 

567.708 

266.685 

504.630 

240.078 

454.167 

25 

399.966 

757.222 

342.883 

649.048 

300.080 

567.917 

266.793 

504.815 

240.175 

454.333 

26 

400.128 

757.500 

343.022 

649.286 

300.202 

568.125 

266.901 

505.000 

240.273 

454.500 

37 

400.290 

757.778 

343.161 

049.524 

300.324 

568.333 

267.010 

505.185 

240.370 

454.667 

38 

400.453 

758.056 

343.300 

649.762 

300.445 

568.542 

267.118 

505.370 

240.468 

454.833 

29 

400.615 

758.333 

343.440 

650.000 

300.567 

568.750 

267.226 

505.556 

240.565 

455.000 

SO 

400.782 

758.611 

343.583 

650.238 

300.693 

568.958 

267.338 

505.741 

240.666 

455.167 

31 

400.950 

758.889 

343.726 

650.476 

300.818 

569.167 

267.449 

505.926 

240.766 

455.333 

32 

401.112 

759.167 

343.865 

650.714 

300.940 

569.375 

267.558 

506.  Ill 

240.864 

455.500 

33 

401.274 

759.444 

344.005 

650.952 

301.062 

569.583 

267.666 

506.296 

240.961 

455.667 

34 

401.437 

759.722 

344.144 

651.190 

301.184 

569.792 

267.774 

506.481 

241.059 

455.833 

35 

401.599 

760.000 

344  283 

651.429 

301.306 

570.000 

267.883 

506.667 

241.156 

456.000 

36 

401.762 

760.278 

344.422 

651.667 

301.427 

570.208 

267.991 

506.852 

241.254 

456.167 

37 

401.924 

760.556 

344.562 

651.905 

301.549 

570.417 

268.099 

507.037 

241.351 

456.333 

38 

402.091 

760.833 

344.705 

652.143 

301.675 

570.625 

268.211 

507.222 

241.452 

456.500 

39 

402.258 

761.111 

344.848 

652.381 

301.800 

570.833 

268.3'22 

507.407 

241.552 

456.667 

40 

402.421 

761.389 

344.988 

652.619 

301.922 

571.042 

268.431 

507.593 

241.650 

456.833 

41 

402.583 

761  667 

345.127 

652.857 

302.044 

571.250 

268.539 

507.77'8 

241.747 

457.000 

43 

402.746 

761.944 

345.266 

653.095 

302.166 

571.458 

268.647 

507.963 

241.845 

457.167 

43 

402.908 

762.222 

345.405 

653.333 

302.288 

571.667 

268  756 

508.148 

241.942 

457.333 

44 

403.071 

762.500 

345.544 

653.571 

302.409 

571.875 

268.864 

508.333 

242.040 

457.500 

45 

403.  233  !  762.  778 

345.684 

653.810 

302.531 

572.083 

268.972 

508.519 

242.137 

457.667 

46 

403.400!  763  056 

•345.827 

654.048 

302.657 

572.292 

2C9.084 

508.704 

242.238 

457.833 

47 

403  567763.333 

345.970 

654.  28G 

302.782 

572.500 

269.196 

508.889 

242.338 

458.000 

48 

403.730 

763.611 

346.110 

654.524 

302.904 

572.708 

269.304 

509.074 

242.436 

458.107 

49 

403.892 

763.889 

346.249 

654.762 

303.026 

572.917 

269.412 

509.259 

242.533 

458.333 

50 

404.055764.167 

346.  38S 

655.000 

303.  148  !573.  125 

269.521 

509.444 

242.631 

458.500 

51 

404.217764.444 

346  .  527 

655.238 

303.270573.333 

269.629 

509.630 

242.7'28 

458.607 

53 

404.384 

764.722346.671 

655.476 

303.  395  :  573.  542 

269.740 

509.815 

242.829 

458.833 

53 

404.551 

765.000 

346.814 

655.714 

303.520573.750 

269.852 

510.000 

242.929 

459.000 

54 

404.714 

765.278 

346.953 

655.952 

303.642573.958 

269.960 

510.185 

243.026 

459.167 

55 

404.876  765.556 

347.092 

656.190 

303.764574.167 

270.069 

510.370 

243.124 

459.333   56 

405.039  765.83^3 

347.232 

656.429 

303.886574.375 

270.177 

510.556 

243.222 

459.500   57 

405.201 

766.111 

347.371 

656.667 

304.008574  583 

270.285 

510.741 

243.319 

459.667  58 

405.363 

766.389 

347.510 

656.905 

304.130574.792 

270.394 

510.926243.417 

459.833|  59 

137 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


46° 

1°  Curve. 

3°  Curve. 

3°  Cvirve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

A  re. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

2433.06 

4GOO.OO 

1216.08 

2300.00810.772  1533.33 

608.134 

1150.00 

486.561 

920.000 

1 

2433.07 

4601.67 

1216.58 

2300.83811.106:1533.89 

008.385 

1150.42 

486.762 

920.333 

2 

2434.07 

4603.33 

1217.08 

2301.67811.440 

1534.44 

608.635 

1150.83 

486.963 

920.667 

3 

2435.04 

4605.00 

1217.57 

2302.50811.765 

1535.00 

608.879 

1151.25 

487.158 

921.000 

4 

2436.02 

4606.67 

1218.05 

2303.33812.090 

1535.56 

609.122 

1151.67 

487.352 

921.333 

5 

2437.02 

4608.33 

1218.56 

2304.17 

812.424 

1536.11 

609.373 

1152.08 

487.553 

921.607 

0 

2438.02 

4610.00 

1219.06 

2305.00 

812.758 

1536.67 

009  .  624 

1152.50 

487.754 

922.000 

7 

2439.00 

4611.67 

1219.54 

2305.83 

813.083 

1537.22 

00'.).  867 

1152.92 

487.948922.333 

8 

2439.97 

4613.33 

1220.03 

2306.67 

813.408 

1537.78 

(JlO.lll 

1153.33 

488.143922.607 

9 

2440.95 

4615.00 

1220.52 

2307.50 

813.732 

1538.33 

010.355 

1153.75 

488.338 

923.000 

1O 

2441.92 

4616.67 

1221.00 

2308.33 

814  057 

1538.89 

610.598 

1154.17 

488.533 

923.333 

11 

2442.92 

4618.33 

1221.51 

2309.17 

814.391 

1539.44 

010.849 

1154.58 

488.734 

923.607 

12 

2443.92 

4620.00 

1222.01 

2310.00 

814.726 

1540.00 

611.100 

1155.00 

488.934 

924.000 

13 

2444.90 

4621.67 

1222.49 

2310.83 

815.050 

1540.56 

611.343 

1155.42 

489.129 

924.333 

14 

2445.87 

4623.33 

1222.98 

2311.67 

815.375 

1541.11 

611.587 

1155.83 

489  324 

924.607 

15 

2446.85 

4625.00 

1223.47 

2312.50 

815.100 

1541.67 

611.830 

1156.25 

489.519 

925.000 

16 

2447.82 

4626.67 

1223.96 

2313.33 

816.024 

1542.22 

612.074 

1156.67 

489.714 

925.333 

17 

2448.82 

4628.33 

1224.46 

2314.17 

816.359 

1542  78 

612.325 

1157.08 

489.914 

925.667 

18 

2449.83 

4630.00 

1224.96 

2315.00 

816.693 

1543.33 

612.575 

1157.50 

490.115 

926.000 

19 

2450.80 

4631.67 

1225.45 

2315.83 

817.018 

1543.89 

612.819 

1157.92 

490.310 

926.333 

3O 

2451.77 

4633  33 

1225.93 

2316.67 

817.342 

1544.44 

613.062 

1158.33 

490.505 

926.667 

31 

2452.78 

4635.00 

1226.43 

2317.50 

817.677 

1545.00 

013.313 

1158.75 

490.705 

927.000 

22 

2453.78 

4636  67 

1226.93 

2318.33 

818.011 

1545.56 

613.564 

1159.17 

490.906 

927.333 

23 

2454.75 

4638.33 

1227.42 

2319.17 

818.336 

1546.11 

613.807 

1159.58 

491.101 

927  .  007 

34 

2455.73 

4640.00 

1227.91 

2320.00 

818.660 

1546.67 

614.051 

1160.00 

491.296 

928.000 

35 

2456.70 

4641.67 

1228.40 

2320.83 

818.985 

1547.22 

614.294 

1160.42 

491.490 

928.333 

36 

2457.68 

4643.33 

1228.88 

2321.67 

819.310 

1547.78 

614.538 

1100.83 

491.685 

928.607 

37 

2458.68 

4645.00 

1229.38 

2322.50 

819.644 

1548.33 

614.789 

1161.25 

491  .  880 

929.000 

38 

2459.68 

4646.67 

1229.89 

2323.33 

819.978 

1548.89 

615.039 

1161.67 

492.081 

929.333 

39 

2460.66 

4648.33 

1230.37 

2324.17 

820.303 

1549.44 

615.283 

1162.08 

492.281 

929.667 

30 

2461.63 

4650.00 

1230.86 

2325.00 

820.628 

1550.00 

615.527 

1162  50 

492.476 

930.000 

31 

2462  63 

4651.67 

1231.36 

2325.83 

820.962 

1550.56 

615.  777 

1162.92 

492.671 

930.333 

33 

2463.63 

4653.33 

1231.86 

2326.67 

821.296 

1551.11 

616.028 

11  03.  33 

492.877 

930.667 

33 

2464.61 

4655.00 

1232.35 

2327.50 

821.621 

1551.67 

616.272 

1163.75 

493.072 

931.000 

34 

2465.58 

4656.67 

1232.84 

2328.33 

821.946 

1552.22 

616.515 

1164.11 

493.267 

931.333 

35 

2466.59 

4658.33 

1233.34 

23J9.17 

822.280 

1552.78 

616.766 

1164.58 

493.468 

931.667 

36 

2467.59 

4660.00 

1233.84 

2330.00 

822.614 

1553.33 

617.017 

1165.00 

493.668 

932  000 

37 

2468.56 

4661.67 

1234.33 

2330.83 

822.939 

1553.89 

617.260 

1165.42 

493.863 

932.333 

38 

2469.54 

4663.33 

1234.81 

2331.67 

823.264 

1554.44 

617.504 

1165.83 

494.058 

932.007 

39 

2470.54 

4665.00 

1235.31 

2332.50 

823.598 

1555.00 

617.754 

1166.25 

494.259 

933.000 

40 

2471.54 

4666.67 

1235.82 

2333.33 

823  932 

1555.56 

618.005 

1166.67 

494.459 

933.333 

41 

2472.52 

4668.33 

1-^36.30 

2334.17 

824.257 

1556.11 

618.249 

1167.08 

494.654 

933.667 

43 

24^8.49 

4670.00 

1236.79 

2335.00 

824.582 

1556.61 

618.492 

1167.50 

494.849 

934.000 

43 

2474.49 

4671.67 

1237.29 

2335.  83 

824.916 

1557.22 

618.743 

1167.92 

495.050 

934.333 

44 

2475.50 

4673.33 

1237.79 

2336  67 

825.250 

1557.  7H 

618.994 

1168.33 

495.250 

934.667 

45 

2476.47 

4675.00 

1238.28 

2337.50 

825.575 

1558.33 

619.237 

1168.75 

495.445 

935.000 

46 

2477.44 

4676.67 

1238.77 

2338.33825.899 

1558.89 

619.481 

1169.17 

495.640 

935.333 

47 

2478.45 

4678.33 

1239.27 

2339.  1?|  826.  234 

1559.44 

619.732 

1169.58 

495.841 

935.607 

48 

2479.45 

4680.00 

1239.77 

2340.00826.568 

1560.0( 

619.982 

1170.00 

496.041 

936.000 

49 

2480.42 

4681.67 

1240.26 

2340.83 

826.893 

1560.56 

620.226 

1170.42 

496.236 

936.333 

50 

2481.40 

4683.33 

1240.74 

2341.67 

827.217 

1561.11 

620.469 

1170.83 

496.431 

936.607 

51 

2482.40 

4685.00 

1241.25 

2342.50 

827.552 

1561.67 

620.720 

1171.25 

496.632 

937.000 

53 

2483.40 

4686.67 

1241.75 

2343.33  827.886 

1562.22 

620.971 

1171.67 

496.832 

937.333 

53 

2484.40 

4688.33 

1242.25 

3344.  17  '828.220 

1562.78 

621.222 

1172.06 

497.033 

937.607 

54 

2485.41 

4690.00 

1242.75 

2345.00828.555 

1503.33 

621.412 

1172.50 

497.233 

938.000 

55 

2486.38 

4691.67 

1243.24 

2345.83828.879 

1563.89 

621.716 

1172.92 

497.428 

938.  3*3 

56 

2487.36 

4693.33 

1243.72 

2346.67829.204 

1564.44 

621.959 

1173.33 

497  623 

9.-S8.007 

57 

2488.36 

4695.00 

1244.22 

2347.  50  1829.538 

1565.00 

622.210 

1173.75 

497.824 

939.000 

58 

2489.36 

4696.67 

1244.73 

2348.33829.872 

1565.56 

622.461 

1174.11 

498.024 

939.333 

59 

2490.34 

4698.33 

1245  21 

2349.17830.197 

1566.11 

622.704 

1174.58 

498.219 

939.607 

138 


TABLE  XIV. — ACTUAL,  TANGENTS,  ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

46° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

IviT 

405.526 

766.667 

347.649 

657.143 

304.252 

575.000 

270.502511,111 

243.514 

460.000 

o 

405.693 

766.944 

347.793 

657.381 

304.377 

575.208 

270.613511.296 

243.615 

460.167 

i 

405.860 

767.222 

•347.930 

657.619 

304.502 

575.417 

270.725511.481 

243.715 

460.333 

2 

406.023 

767.500 

348.075 

657.857 

304.624 

575.625 

270.833511.667 

243.812 

460.500 

3 

406.185 

767.778 

348.214 

658.095 

304.746 

575.833 

270.  942!  51  1.852 

243.910 

460.667 

4 

406.352 

768.056 

348.358 

658.333 

304.872 

576.042 

271.053512.037 

244.010 

460.833 

5 

406.519 

768.333 

348.501 

658.571 

304.997 

576.250 

271.165 

512.222 

244.111 

461.000 

6 

406.  G82 

768.611 

348.640 

658.810 

305.119 

576.458 

271.273 

512.407 

244.208 

461.167 

7 

406.844 

768.889 

348.780 

659.048 

305.241 

576.667 

271.381 

512.593 

244.306 

461.333 

8 

407.007 

769.167 

348.919 

659.286 

305.363 

576.875 

271.490 

512.778 

244.403 

461.500 

9 

407.169 

769.444 

349.058 

659.524 

•305.484 

577.083 

271.598 

512.963 

244.501 

461.667 

10 

407.  ase 

769.722 

349.201 

659.762 

305  610  577.292 

271.710 

513.148 

244.601 

461.833 

11 

407.503 

770.000 

349.345 

660.000 

305.735 

577.500 

271.821 

513.3:33 

244.702 

462.000 

12 

407.666 

770.278 

349.484 

660.238 

305.857 

577.708 

271.929 

513.519 

244.799 

462.167 

13 

407.828 

770.556 

349.623 

660.476 

1305.979 

577.917 

272.038  513.704 

244.897 

462.333 

14 

407.991 

770.833 

349  762 

660.714 

306.101 

578.125 

272.146 

513.889 

244.994 

462.500 

15 

408.153 

771.111 

349.902 

660.952 

306.223 

578.333 

272.254 

514.074 

245.092 

462.667 

16 

408.320 

771.389 

350.045 

661.190 

306.348 

578.542 

272.366 

514.259 

245.192 

462.8:33 

17 

408.488 

771.667 

350.188 

661.429 

306.474 

578.750 

272.477 

514.444 

245.293 

463.000 

18 

408.650 

771.944 

350.328 

661.667 

306.595 

578.958 

272.586 

514.630 

245.390 

463.167 

19 

408.812 

772.222 

350.467 

661.905 

306.717 

579.167 

272.694 

514.815 

245.488 

463.333 

20 

408.980 

772.500 

350.610 

662.143 

306.  842  579  ."375 

272.806 

515.000 

245.588 

463.500 

21 

409.147 

772.778 

350.753 

662.381 

306.  968  579.583 

272  917 

515.185 

245.688 

463.667 

22 

409.309 
409.472 

773.056 
773.333 

350.893 
351.032 

(562.619 

662.857 

307.090579.792 
307  212i580.000 

273.026 
273.134 

515.370 
515.556 

245.786 
245.883 

463.833 
464.000 

23 
24 

409.634 

773.611 

351.171 

663  095 

307.334 

580.208 

273.242 

515.741 

245.981 

464.167 

25 

409.796 

773.889 

351.310 

663.333 

307.456 

580.417 

273.351 

515.926 

246.079 

464.333 

26 

409.964 

774.167 

351.454 

663.571 

307.581 

580.625 

273.462 

516.111 

246.179 

464.500 

27 

410.131 

774.444 

351.597 

663.810 

307.706 

580.833 

273.574 

516.296 

246.279 

464.667 

28 

410.293 

774.722 

351.730 

664.048 

307.828 

581.042 

273.682 

516.481 

246.377 

464.833 

29 

410.456 

775.000 

351.876 

664.286 

307.950 

581  .250 

273.790 

516.667 

246.474 

465.000 

30 

410.623 

775.278 

352.019 

664.524 

308.076 

581.458 

273  '.902 

516.852 

246.575 

465.167 

31 

410.790 

775.556 

352.162 

664.702 

308.201 

581.667 

274.013 

517.037 

246.675 

465.333 

32 

410.952 

775.833 

352.301 

665.000 

308.323 

581  875 

274.122 

517.222 

246.773 

465.500 

33 

411.115 

776.111 

352.441 

665.238 

308.445 

582.083 

274.230 

517.407 

246.870 

465.667 

34 

411.282 

776.389 

352.584 

665.476 

308.570 

582  292 

274.341 

517.593 

246  971 

465.833 

35 

411.449 

776.667 

352.727 

665.714 

308  696 

582.500 

274.453 

517.778 

247.071 

466.000 

36 

411.612 

776.944 

352.867 

665.952 

308.817 

582.708 

27'4.561 

517.963 

247,169 

466.167 

37 

411.774 

777.222 

353.006 

666.190 

308.939 

582.917 

274.670 

518.148 

247.266 

466.333 

38 

411.941 

777.500 

353.149 

666.429 

309.065 

583.125 

274.781 

518.333 

247.366 

466.500 

39 

412.108 

777.778 

353.292 

666.667 

309.190 

583.333 

274.893 

518.519 

247.467 

466.C67 

40 

412.271 

778.056 

353.432 

666.905 

309.312 

583.542 

275.001 

518.704 

247.564 

466.8-33 

41 

412.433 

778.333 

453.571 

667.143 

309.434 

583.750 

27'5  109 

518.889 

247.662 

467.000 

42 

412.600 

778.611 

353.714 

667.381 

309.559 

583.958 

^75.221 

519.074 

247.762 

467.167 

43 

412.768 

778.889 

353.  858 

667.619 

309.685 

584.167 

275.332 

519.259 

247.863 

467.333 

44 

412.930 

779.167 

353.997 

667.857 

309.807 

584.375 

275.441 

519.444 

247.960 

467.500 

45 

413.092 

779.444 

354.136 

668.095 

309.928 

584.583 

275.549 

519.630 

248.058 

467.667 

46 

413.260 

779.722 

354.279 

668.  333 

310.054 

584.792 

275.661 

519.815 

248.158 

467.833 

47 

413.427 

780.000 

354.423 

668.571 

310.179 

585.000 

275.772 

520.000 

248.259 

468.000 

48 

413.589 

780.278 

354.562 

668.810 

310.301 

585.208 

275.881 

520.185 

248.356 

468.167 

49 

413.752 

780.556 

354.701 

669.048 

310.423 

585.417 

275.989 

520  370 

248.454 

468.333 

50 

413.919 

780.833 

354.844 

669.286 

310.548 

585.  62f 

276.100 

520.556 

248.554 

468.500 

51 

414  086 

781.111 

354.988 

669.524 

310.674 

585.833 

276.212 

520.741 

248.654 

468.667 

52 

414.253 

781.389 

355.131 

069.762 

310.799586.042 

276.323 

520.  92f 

248.755 

468.833 

53 

414.420 

781  667 

355.274 

070.000 

310.925586.250 

276.435 

521.111 

248.855 

469.000 

54 

414.583 

781.944 

355.414 

670.238 

311.047586.458 

276.  543  521.  29C 

248.953 

469.167 

55 

414.745 

782.222 

355.553 

670.476 

311.168586.667 

276.  652  521.  4M 

249.050 

469.333 

56 

414  912 

782.500 

355.690 

670.714 

311.294586.875 

276.763521.667 

249.151 

469.500 

57 

415.080 

782.  778  1355.  840 

670.952 

311.  419  587.  C&3 

276.875521.852 

249.251 

469  667 

58 

415.242 

783.  0561355.  979 

671.190 

311.541587.292 

276.988522.087 

249.349 

469.833 

59 

TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


47° 

1°  Carve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Are. 

Tan. 

Arc. 

Tan.       Arc. 

~~O" 

249T731 

4700.00 

1245.70 

2350.00 

830.522 

1566.67 

622.948 

1175.00 

498.414940.000 

1 

2492.31 

4701.67 

1246.20 

2350.83 

830.856  1567.22 

623.199 

1175.42 

498.615  940.333 

2 

2493.31 

4703.33 

1246.70 

2351.67 

831.190  1567.78 

623.449 

1175.83 

498.815940.667 

3 

2494.29 

4705.00 

1247.19 

2352.50 

831.515  3568.33 

623.693 

1176.25 

499.010941.000 

4 

2495.26 

4706.67 

1247.68 

2353.33 

831.840 

1568.S9 

623.935 

1176.67 

499.205941.333 

5 

2496.27 

4708.33 

1248.18 

2354.17 

832.174 

1569.44 

624.187 

1177.08 

499.406941.667 

6 

2497.27 

4710.00 

1248.68 

2355.00 

832.508 

1570.00 

6<!4.438 

1177.50 

499.606942.000 

7 

2498.27 

4711.67 

1249.18 

2355.83 

832.843 

1570.56 

624.689 

1177.92 

499.807942.333 

8 

2499.27 

4713.33 

1249.68 

J356.67 

833.177 

1571.11 

624.939 

1178.33 

500.007942.667 

9 

2500.25 

4715.00 

1250.17 

2357.50 

833.502 

1571.67 

625.183 

1178.75 

500.202 

943.000 

10 

2501.22 

4716.67 

1250.66 

2358.33 

833.826 

1572.22 

625.426 

1179.17 

500.397 

943.333 

J  1 

2.502.22 

4718.33 

1251.16 

2359.17 

834.161 

1572.78 

625.677 

1179.58 

500.598 

943.667 

12 

2503.23 

4720.00 

1251.66 

2360.00 

834.495 

1573.33 

625.928 

1180.00 

500.798 

944.000 

13 

2504.23 

4721.67 

1252.16 

2360.83 

834.829 

1573.89 

626.179 

1180.42 

500.999 

944.333 

14 

2505.23 

4723.33 

1252.66 

2361.67 

8-35.103 

1574.44 

626.429 

1180.83 

501.199 

944.667 

15 

2506.21 

4725.00 

1253.15 

2362.50 

835.488 

1575.00 

026.673 

1181.25 

501.394 

945.000 

16 

2507  18 

4726.67 

1253.64 

2363.33 

835.813 

1575.50 

626.916 

1181.67 

501.589 

945.333 

17 

2508.18 

4728.33 

1254.14 

2364.1? 

836.147 

157d.ll 

627.167 

1182.08 

501.790 

945.667 

18 

2509.19 

4730.00 

1254.64 

2365.00 

836.481 

1576.67 

627.418 

1182.50 

501.990 

946.000 

19 

2510.19 

4731.67 

1255.14 

2365.83 

836.816 

1577.22 

627.669 

1182.92 

502.191 

946.333 

20 

2511.19 

47'33.33 

1255.64 

2366.67 

837.150 

1577.78 

627.919 

1183.33 

502.392 

946.667 

2  1 

2512.17 

4735.00 

1256.13 

2367.50 

837.475 

1578.33 

628.163 

1183.75 

502.586 

947.000 

22 

2513.14 

4736.67 

1256.62 

2368.33 

837.799 

1578.89 

628.  40(5 

1184.17 

502.781 

947.333 

23 

2514.14 

4738.33 

1257.12 

2369.17 

838.134 

1579.44 

628.657 

1184.58 

:>02.982 

947.667 

24 

2515.14 

4740.00 

1257.62 

2370.00 

838.  46S 

1580.00 

628.908 

1185.00 

503.183 

948.000 

25 

2516.15 

4741.67 

1258.12 

2370.83 

838.802 

1580.56 

629.159 

1185.42 

503.383 

948.333 

26 

2517.15 

4743.33 

1258.62 

2371.67 

839.136 

1581.11 

629.409 

1185.83 

503.584 

948.667 

27 

2518.12 

4745.00 

1259.11 

2372.50 

839.461 

1581.67 

629.653 

1186.25 

503.779 

949.000 

28 

2519.10 

4746.67 

1259.60 

2373.33 

839.78(5 

1582.2:3 

629.896 

1186.67 

503.973 

949.333 

29 

2520.10 

4748.33 

1260.10 

2374.17 

840.120 

1582.78 

630.147 

1187.08 

504.174 

949.667 

30 

2521.10 

4750.00 

1260.60 

2375.00 

840.454 

1583.33 

630.398 

1187.50 

504.375 

950.000 

31 

2522.11 

4751.67 

1261.10 

2375.83 

840.789 

1583.89 

(530.649 

1187.92 

504.575 

950.333 

32 

3523.11 

4753.33 

1261.60 

2376.67 

841.123 

1584.44 

630.899 

1188.33 

504.776 

950.667 

33 

2524.11 

4755.00 

1262.10 

2377.50 

841.457 

1585.00 

631.150 

1188.75 

504.97(5 

951.000 

34 

2525.11 

4756.67 

1262.60 

2378.33 

841.791 

1585.56 

631.401 

1189.17 

505.177 

951.333 

35 

2526.09 

4758.33 

1263.09 

2379.17 

842.116 

1586.11 

631.644 

1189.58 

505.372 

951.667 

36 

2527.06 

4760.00 

1263.58 

2380.00 

842.441 

1586.67 

631.888 

1190.00 

505.567 

952.000 

37 

2528.06 

4761.67 

1264.08 

2380.83 

842.775 

1587.22 

632.139 

1190.42 

505.707 

952.333 

38 

2529.07 

4763.33 

1264.58 

2381.67 

843.109 

1587.78 

632.389 

1190.83 

505.9(58 

952.667 

39 

2530.07 

4765.00 

1265.08 

2382.50 

843.444 

1588.33 

632.640 

1191.25 

506.160 

953.000 

4O 

2531.07 

4766.67 

1265.58 

2383.33 

843.778 

1588.89 

632.891 

1191.67 

506.369 

953.333 

41 

2532.08 

4768.33 

1-256.08 

2384.17 

844.112 

1589.44 

633.142 

1192.08 

506.570 

1)53.667 

42 

2533.08 

4770.00J12G6  59 

2385.00 

844.446 

1590.00 

033.392 

1192.50 

506.770 

954.000 

43 

2534.05 

4771.67 

1267.07 

2385.83 

844.771 

1590.56 

633.636 

1192.92 

506.965 

954.333 

44 

2535.03 

4773.33 

1267.56 

2386.67 

845.096 

1591.11 

633.879 

1193.33 

507.160 

954.0(57 

45 

2536.03 

4775.00 

1268.06 

2387.50 

845.430 

1591.67 

634.130 

1193.75 

507.361 

955.000 

46 

&37.08 

4776.67|1268.56 

2388.33 

845.764 

1592.22 

634.  881  11  194.1? 

507.561 

955.333 

47 

4538.03 

4778.33H269.06 

2389.17 

846.099 

1592.78 

634.6321194.58 

507.762 

055.6(57 

48 

2539.04 

4780.00  1269.57 

2-390.00 

846.433 

1593.33 

634.882  1195.00 

507.963 

956.000 

49 

2540.04 

4781.67 

1270.07 

2390.83 

846.767 

1593.89 

635.133 

1195.42 

508.163 

J56.333 

5O 

2541.04 

4783.33 

1270.57 

2391.67 

847.101 

1594.44 

635.384 

1195.83 

508.364 

956.667 

51 

2542.05 

4785.00  1271.07 

2392.50 

847.436 

1595.00 

635.6341196.25 

508  564 

957.000 

52 

2543  .  05  4786  .  67  i  1  271  .  57  2393  .  33 

847.770 

1595.56 

635.885  1196.67 

508.765 

)57.333 

53 

2544.02  4788.33  1272.06  2394.17 

848.  095)1596.  11 

036.129  1197.08 

508.  9CO 

957.667 

54  sJ545.004790.00  1272.542395.00 

848  419  '1596.  67 

636.3721197.50 

509.155 

958.000 

55 

2546  .  00  '  4791  .  67  1  273  .  05  2395  .  83 

848.754  1597.22 

636.6231197.92 

509.355 

958.333 

56 

53547.004793.33  1273.55  2396.67 

849.0881597.78 

636.8741198.33 

509.556 

958.667 

57  !  2548.  00  4795.  00  '1274  052397.50 

849.422  1598.33 

637.124  1198.75 

509.756 

K59.000 

58  25  4  9  .  0  1  4796  .  67  1  274  .  55  2398  33 

84  9.  75(5  1598.89 

537.375  1199.17 

509.957 

959.333 

59  2550.  01  14:98.33  1275.05  2399.17 

850.091  1599.44 

637.626  1199.58 

510.158 

J59.607 

140 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


G°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

47" 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

470.000 

M. 
~O~ 

415.404 

783.333 

356.118671.429 

311.663 

587.500 

277.091 

522.222 

249.446 

415.572 

783.611 

356.261  671.667 

311.788 

587.708 

277.203 

522.407 

249.546 

470.167 

1 

415.739 

783.889 

356.405671.905 

311.914 

587.917 

277.314 

522.593 

249.647 

470.333 

2 

415.901 

784.167 

356.544  672.143 

312.036 

588.125 

277.423 

522.778 

249.744 

470.500 

3 

416.004 

784.444 

356.683672.381 

312.158 

588.333 

277.531 

522.963 

249.842 

470.607 

4 

416.2-31 

784.722 

356.826672.619 

312.283 

588.542 

277.643 

523.148 

249.942 

470.833 

5 

416.398 

785.000 

356.970  672.857 

312.409 

588.750 

277.754 

523.333 

250.043 

471.000 

0 

416.565 

785.278 

357.113673.095 

312.534 

588.958 

277.866 

523.519 

250.143 

471.167 

7 

416.732 

785.556 

357.256  673.333 

312.659 

589.167 

277.977 

523.704 

250.244 

471.333 

8 

416.895 

785.833 

357.396 

673.571 

312.781 

589.375 

278.085 

523.889 

250.341 

471.500 

9 

417.057 

786.111 

357.535 

673.810 

312.903 

589.583 

278.194 

524.074 

250.439 

471  .  667 

1O 

417.224 

786.389 

357.678:674.048 

313.029589.792 

5578.306 

524.259 

250.539 

471.833 

11 

417.392 

786.667 

357.822  674.  286 

313.154590.000 

278.417 

524.444 

250.639 

472.000 

1  2 

417.559 

786.944 

357.965674.524 

313.279590.208 

278.528 

524.630 

250.740 

472.167 

13 

417.726 

787.222 

358.108674.762 

313.405590.417 

278.640 

524.815 

250.840 

472.333 

14 

417  888 

787.500 

358.247  675.000 

3  1  3.  527  i  590  625 

278.748 

525.000 

250.938 

472.500 

15 

418.051 

787.778 

358.387  675.238 

313.649590.833 

278.857 

525.185 

251.035 

472.667 

10 

418.218 

788.056 

358.5301675.476 

313.774591.042 

278.968 

525.370 

251.136 

472.833 

17 

418.385 

788.333 

358.673 

675.714 

313.899591.250 

279.080 

525.556 

251.230 

473.000 

18 

418.552 

788.611 

358.817 

675.952 

314.025 

591.458 

279.191 

525.741 

251.336 

473.167 

19 

418.720 

788.889 

358.960 

676.190 

314.150 

591.667 

279.303 

525.926 

251.437 

473.333 

2O 

418.882 

789.107 

359  099 

076.429 

314.272 

591.875 

279.411 

526.111 

251.534 

473.500 

21 

419.044 

789.444 

359.239 

676.667 

314.394 

592.083 

279.519 

526.290 

251.632 

473.667 

22 

419.212 

789  722 

359.382 

676.905 

314.519 

592.292 

279.631 

526.481 

251.732 

473.833 

23 

419.379 

;9o  !  ooo 

359.525 

677.143 

314.645 

592.500 

279.742 

526.667 

251.833 

474.000 

24 

419.546 

790.278 

359.668 

677.381 

314.770 

592.708 

27D.854 

526.852 

251.933 

474.167 

25 

419.713 

790.556 

359.812 

677.619 

314.896i592  917 

279.965 

527.037 

252.033 

474.333 

26 

419.87(5 

790.833 

359.951 

677.857 

315.018 

593.125 

280.074 

527.222 

252.131 

474.500 

37 

420.038 

791.111 

300.090 

678.095 

315.139 

593.333 

280.182 

527.40; 

252.228 

474.667 

28 

420.205 

791.389 

360.234 

678.333 

315.265 

593.542 

280.294 

527.593 

252.329 

474.833 

29 

420.372 

791.667 

360.377 

678  571 

315.390 

593.750 

280.405 

527.778 

252.429 

475.000 

30 

420.539 

791.944 

360.520 

678.810 

315.516 

593.958 

280.517 

527.963 

252.530 

475.167 

31 

420.707 

792.222 

360.664 

679.048 

315.641 

594.167 

280.628 

528.148 

252.630 

475.333 

32 

420.874 

792.500 

360.807 

679.286 

315.767 

594.375 

280.740 

528.333 

252.730 

475.500 

33 

421.011 

792.778 

360.950 

679.524 

315.892 

594.583 

280.851 

528.519 

252.831 

475.667 

34 

421.203 

793.056 

361.089 

679.762 

316.014 

594.792 

280.960 

528.704 

252.928 

475.833 

35 

421.300 

793.333 

361.229 

680.000 

316.136 

595.000 

281.068 

528.889 

253.020 

476.000 

36 

421  .  533 

793.611 

361.372 

680.238 

316.261 

595.208 

281.179 

529.074 

253.126 

476.167 

37 

421  .  700 

793.889 

361.515 

680.476 

316.387 

595.417 

281.291 

529.259 

253.227 

476.333 

38 

421.867 

794.167 

361.659 

680.714 

316.512 

595.625 

281.402 

529.444 

253.327 

476.500 

39 

422.035 

794.444 

361.802 

680.952 

316.638 

595.833 

281.514 

529.  63P 

253.428 

476.  6G7 

40 

422.202 

794.722 

361.945 

681.190 

316.763 

596.042 

281.625 

529.815 

253.528 

476.833 

41 

432.369 

795.000 

302.089 

681.429 

316.888 

596.250 

281.737 

530.000 

253.628 

477.000 

48 

422.531 

795.278 

362.228 

681.667 

317.010 

596.458 

281.845 

530.185 

253.726 

477.167 

43 

422.091 

795.556 

362.367 

681.905 

317.132 

596.667 

281.954 

530.370 

253.823 

477.333 

44 

422.8611795.833 

362.510 

682.143 

317.258 

596.875 

282.065 

530.556 

253.924 

477.500 

45 

423.028  1  796.  Ill 

362.654 

682.381 

317.383 

597.083 

282.177 

530.741 

254.024 

477.667 

46 

423.  195  796.  3S9 

362.797 

682.619 

317.508597.292 

282.288 

530.926 

254.125 

477.833 

47 

423.363796.667 

362.940 

682  857 

317.634597.500 

282.400 

531  111 

254.225 

478.000 

48 

423.530 

796.944 

363.084 

683.095 

317.759 

597.708 

282.511 

531.296 

254.325 

478.167 

49 

423.097 

797.222 

363.227 

683.333 

317.885 

597.917 

282.623 

531.481 

254.426 

478.333 

50 

423.861 

797.500 

363.  370  6K3.  571 

318.010598.125 

282.734 

531.667 

254.526 

478.500 

51 

424.031 

797.778363.514 

683.810 

318.136598.333 

282.846 

531.852254.627 

478.667 

53 

424.194 

798.050303.653684.048 

318.257598.542 

282.954 

532.037 

254.724 

478.833 

53 

424.350 

798  333363.7921684.286 

318  379598.750 

283.063 

532.222 

254.822 

479.000 

54 

424.523 

798  .611  363  936  684  .  524 

318.505598.958 

283.174 

532.407 

254.922 

479.167 

55 

424.691 

798.  889  364.  07  9  084.  7'02 

318.630599.167 

283.286 

532.593 

255.022 

479.333 

56 

434.858 

799.167364.222685.000 

318.756599.375 

283.397 

532.778 

255.123 

479.500  57 

425.025 

799  444364.366685.238 

318.881  599.588288.609 

532.963 

255.223 

479.667  58 

425.192 

799.722364.509685.476 

3  1  9  .  006  599  .  792  1  283  .  620 

533.148 

255.324 

479.833'  59 

141 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


48° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

o 

y.V>l  Ul'  4800.  00 

1275.55 

2400.00 

850  425 

1600.  00  637.  877  ;  1200.  00 

510.358 

960.000 

1 

&53.01 

4801.67 

1276  05 

2400.83 

850.759 

1600.50638.1271200.42 

510.559 

960.333 

53 

2553  02 

4803.33 

1276.56 

2401.67 

851.093 

1001.11 

038  378 

1200.83 

510.759 

960.607 

3 

2554.02 

4805.00 

1277.06 

2402.50 

851.428 

1001.67 

638.029 

1201.25 

510.960 

961.000 

4 

2555.02 

4806.67 

1277.56 

2403.33 

851.762 

1002.22 

038.879 

1201.67 

511.161 

961.333 

5 

2556.00 

4808.33 

1278.05 

2404.17 

852.087 

1602.78639.123 

1202.08 

511.356 

961.607 

(> 

3556.97 

4810.00 

1278.53 

•2405.00 

852.411 

1003.33 

03'J.367 

1202.50 

511.550 

962.000 

7 

•2557.97 

4811.67 

1279.03 

2405.83 

fe52.740 

16H3.89 

639.617 

1202.92 

511.751 

962.333 

8 

2558.98 

4813.33 

1279.54 

2406.67 

853.080 

1604.44 

639.868 

1203.33 

511.952 

962.607 

9 

2559.98 

4815.00 

1280.04 

2407.50 

853.414 

1605.00 

640.119 

1203.75 

512.152 

963.000 

10 

2560.98 

4816.67 

1280.54 

2408.33 

853.748 

1605.56 

640.369 

1204.17 

512.353 

963.333 

11 

2561  98 

4818.33 

1281.04 

2409.17 

854.083 

1600  11 

640.620 

1204.58 

512.553 

963  007 

13 

3562.99 

4820.00 

1281.54 

2410.00 

854.417 

1606.67 

640.871 

1205.00 

512.754 

904.000 

13 

3563.99 

4821.67 

1282.04 

2410.83 

854.751 

1007.22 

641  .  122 

1205.42 

512.955 

964.333 

14 

2564.99 

4823  33 

1282.54 

2411.67 

855.086 

1607.78 

641.372 

1205.83 

513.155 

964.607 

15 

2566.00 

4825.00 

1283.04 

2412.50 

855.420 

1008.33641.623 

1206.25 

513.356 

965.000 

1.6 

2567.00 

4826.67 

1283.55 

2413.33 

855.754 

1008.89 

641.874 

1206.67 

513.556 

965.333 

17 

2568.00 

4828.33 

1284.05 

2414.17 

856.088 

1609.  441642.  124 

1207.08 

513.757 

905.067 

18 

2569.00 

4830  00 

1284.55 

2415  00 

856.423 

1610.00 

642.375 

1207.50 

513.958 

906  000 

19 

2570.01 

4831.67 

1285.05 

2415.83 

856.757 

1610.50 

642.620 

1207.92 

514.158 

966.333 

30 

2571.01 

4833.33 

1285.55 

2416.67 

857.091 

1611.11 

642.877 

1208.33 

514.359 

966.667 

21 

2572.01 

4835.00 

1286.05 

2417.50 

857.425 

1611.67 

643.127 

1208.75 

514.559 

967.000 

33 

2573.01 

4836.67 

1286.55 

2418  33 

857.760 

1612.22643.378 

1209.17 

514.760 

967.333 

33 

2574.02 

4838.33 

1287.06 

2419.17 

858.094 

1612.78 

643.629 

1-209.58 

514.961 

907.0(57 

34 

2575.02 

4840.00 

1287.56 

2420.00 

858.428 

1613.33 

643.880 

1210.00 

515.101 

968.000 

35 

2576.02 

4841  67 

1288.06 

2420  83 

858.762 

1613.89 

644.130 

1210.42 

515.302 

908.333 

36 

2577.02 

4843.33 

1288.56 

•2421.67 

859.097 

1614.44!044.381 

1210.83 

515.562 

968.667 

37 

5278.03 

4845.00 

1289.06 

2422.50 

859.431 

1615.00 

044.632 

1211.25 

515.763 

909.000 

38 

2579.03 

4846.67 

1289.56 

2423.33 

859.765 

1615.  561044.  882il211.  67 

515.904 

969.333 

39 

2580.03 

4848.33 

1290.06 

2424.17 

860.099 

1616.11 

645.133 

1212.08 

516.164 

969.667 

30 

2581.04 

4850.00 

1290.57 

2425.00 

860.434 

1616.67 

645.384 

1212.50 

516.365 

970.000 

31 

2582.04 

4851.67 

1291.07 

2425.83 

860.768 

1617.22 

645.635 

1212.92 

516.565 

970.333 

33 

2583.04 

4853.33 

1291.57 

2426.67 

861.102 

1617.  78:645.  885 

1213.33 

516.766 

970.667 

33 

2584.04 

4855.00 

1292.07 

2427.50 

8517437 

1618.33 

646.130 

1213.75 

516.967 

971.000 

34 

2585.05 

4856.67 

1292.57 

2428.33 

861.771 

1618.89646.387 

1214.17 

517.167 

971.333 

35 

2586.05 

4858.33 

1293.07 

2429.17 

862.105 

1619.44 

646.637 

1214.58 

517.368 

971.667 

36 

2587.05 

4860.00 

1293.57 

2430.00 

862.439 

1620.00646.888 

1215.00 

517.568 

972.000 

37 

2588.05 

4861.67 

1294.07 

2430.83 

862  774 

1620.56 

647.139 

1215.42 

517.709 

972.333 

38 

2589.06 

4863.33 

1294.58 

2431.67 

863.108 

1621.11 

647.390 

1215.83 

517.970 

972.667 

39 

2590.06 

4865.00 

1295.08 

2432.50 

863.442 

1621.67 

647.640 

1216.25 

518.170 

973.000 

4O 

2591.06 

4866.67 

1295.58 

2433.33 

863  .  776 

1622.22 

647.891 

1216.67 

518.371 

973.333 

41 

2592.07 

4868.33 

1296.08 

2434.17 

864.111 

1622.78648.142 

1217.08 

518.571 

973.667 

43 

2593.07 

4870.00 

1296.58 

2435.00 

864.445 

1623.33 

648.393 

1217.50 

518.772 

974.000 

43 

2594.07 

4871.67 

1297.08 

2435.83 

864.779 

1623.89 

648.643 

1217.92 

518.973 

974.333 

44 

2595.07 

4873.33 

1297.58 

2436.67 

865.113 

1624.44 

648.894 

1218.33 

519.173 

974.667 

45 

2596.08 

4875.00 

1298.09 

2437.50 

865.448 

1625.00649.145 

1218.75 

519.374 

975.000 

46 

2597.08 

4876.67 

1298.59 

2438.  33 

865.782 

1625.56 

649.395 

1219.17 

519.574 

975.333 

47 

2598.08 

4878.  33 

1299.09 

2439.17 

866.116 

1626.11 

649.646 

1219.58 

519.775 

975.607 

48 

2599.08 

4880.00 

1299.59 

2440.00 

866.450 

1626.67 

649.897 

1220.00 

519.970 

976.000. 

49 

2600.09 

4881.67 

1300.09 

2440.83 

866.785 

1627.22,650.148 

1220.42 

520.176 

976.333 

5O 

2601.09 

4883.33 

1300.59 

2441.67 

867.119 

16-27.78650.398 

1220.83 

520.377 

976.667 

51 

2602.09 

4885.00 

1301.09 

2442.50 

867.458 

1628.33 

050.049 

1221.25 

520.577 

977.000 

53 

2603.09 

4886.67 

1301.59 

2443.33 

867.788 

1628.89650.900 

1221.07 

520.778 

977.333 

53 

2004.10 

4888.33 

1302.10 

2444.17 

868.122 

1629.44 

651.150 

1222.08 

520.979 

977.607 

54 

2605.10 

4890.00 

1302.60 

2445.00 

868.456 

1030.00 

651.401 

1222.50 

521.179 

978.000 

55 

2606.10 

4891.67 

1303.10 

•?445.83 

868.790 

1630.56651.652 

1222.92 

521.380 

978.333 

56 

2607.11 

4893.33 

1303.60 

2446.67 

869.125 

1631.11 

651.  90S 

12-23.33 

521.580 

978.667 

57 

2608.14 

4895.00 

1304.12 

2447.50 

869.468 

1631.67 

652.160 

1223.75 

521.787 

979.000 

58 

2609.17 

4896.67 

1304.63 

2448.33 

S69.812  1632.22 

652.4181224.17 

521  .  993 

979.333 

59 

2610.17 

4898.33 

1305.13 

2449.K 

870.146  1632.78  652.  66911224.  58 

522.194  979.667 

TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

48° 

Tan. 

Arc. 

Tan.  |   Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan  . 

Arc. 

M. 

425.859800.000 

364.652685.714 

319.132 

600.000283.732 

533.333 

255.424480.000 

O 

425.527j800.278 

364.  796  6S5.  952 

319.257 

600.  208  '283.  843 

533.519 

255.524 

480.167 

1 

425.  694*800.  566 

364.939686.190 

319.383 

600.417283.955 

533.704 

255.625 

480.333 

2 

425.b6l|800.S83 

365.082686.429 

319.508 

600.625284.066 

533.889 

255.725 

480.500 

3 

426.028801.111 

365.226686.667 

319.634 

600.833 

284.178 

534.074 

255.826 

480.667 

4 

4-26.191 

801.389 

365.365 

686.905 

319.756601.042 

284.286534.259 

255.923 

480.833 

5 

426.353 

801.667 

365.504 

687.143 

319.877:601.250 

284.394  534.444 

256.021 

481.000 

6 

426.520 

801.944 

365.647 

687.381 

320.003601.458 

284.506534.630 

256.121 

481.167 

7 

426.687 

802.222 

365.791 

687.619 

320.128601.667 

284.617534.815 

256.  2S1 

481  .333 

8 

426  854 

802.500 

365.934 

687.857 

320.254 

601.875 

284.729 

535.000 

256.322 

481.500 

0 

427.022 

802.778 

366.077 

688.095 

320.379 

602  083 

284.841 

535.185 

256.422 

481.667 

10 

427.181)803.056 

366.221 

688.333 

320.505 

602.292 

284.952  535.370 

256.523 

481.833 

11 

427  356  803.333 

366.364 

688.571 

320.630 

602.500 

285.064 

535.556 

256.623 

482.000 

12 

427.523803.611 

366.507 

688.810 

320.755 

602.708 

285.175 

535.741 

256.723 

482.167 

13 

427.690803.889 

366.651 

689.048 

320.881 

602.917 

285.287 

535.926 

256.824 

482.333 

14 

427.858804.167 

366.794 

689.286 

321.006 

603.125 

285.398 

536.111 

256.924 

482.500 

15 

428.025804.444 

366.937 

689.524 

321  132 

603.333 

285.510 

536.296 

257.025 

482.667 

1(J 

428.  192  ;804.  722 

367.081 

689.762 

321.257 

603.542 

285.621 

536.481 

257.125 

482.833 

17 

428.  359  1805.000 

367.224 

690.000 

321.383 

603.750 

285.733 

536.667 

257.225 

483.000 

18 

428.526 

805.278 

367.367 

690.238 

321.508 

603.958 

285.844 

536.852 

257.326 

483.167 

19 

428.694 

805.556 

367.511 

690.476 

321.633 

604.167 

285.956 

537.037 

257.426 

483.333 

2O 

428.861  805.833 

367.654 

690.714 

321.759 

604.375 

286.067 

537.222 

257.527 

483.500 

21 

429.028806.111 

367.797 

690.952 

321.884 

604.583 

286.179 

537.407 

257.627 

483.667 

22 

429.195806.389 

367  941 

691.190 

322.010 

604.792 

286.290 

537.593 

257.727 

483.833 

23 

429.362800.667 

368.084 

691.429 

322.135 

605.000 

286.402 

537.778 

257.828 

484.000 

24 

429.530806.944 

368.227 

691.667 

322.261 

605.208 

286.513 

537.963 

257.928 

484.167 

25 

429.697  807.  22< 

368.371 

691.905 

322.386 

605.417 

286.625 

538.148 

258.029 

484.333 

26 

429.864  807.  500 

368.514 

692.143 

322.512 

605.625 

286.736 

538.333 

258.129 

484.500 

27 

430.031  807.778 

368.657 

692.381 

322  637 

605.833 

286.848 

538.519 

258.229 

484.667 

28 

430.198 

808.056 

368.801 

692.619 

322.762 

606.042 

286.959 

538.704 

258.330 

484.833 

29 

430.365 

808.333 

368.944 

692.857 

322  888 

606.250 

287.071 

538.889 

258.430 

485.000 

3O 

430.533808.611 

369.087 

693.095 

323.013 

606.458 

287.182 

539.074 

258.530 

485.167 

31 

430.700808.889 

369.231 

693.333 

323.139 

606.667 

287.294 

539.259 

258.631 

485.333 

32 

430.867809.167 

369.374 

693.571 

323.264 

606.875 

287.406 

539.444 

258.731 

485.500 

33 

431.034  809.444 

369.517 

693.810 

323.390 

607.083 

287.517 

539.630 

258.832 

485.667 

34 

431.201  809.722 

369.661 

694.048 

323.515 

607.292 

287.629 

539.815 

258.932 

485.833 

35 

431.369810.000 

369.804 

694.286 

323.640 

607.500 

287.740 

540.000 

259.032 

486.000 

3G 

431.536 

810.278 

369.947 

694.524 

323.766 

607.708 

287.852 

540.185 

259.133 

486.167 

37 

431.703 

810.556 

370.091 

694.762 

323.891 

607.917 

287.963 

540.370 

259.233 

486.333 

38 

431.870 

810.833 

370.234 

695.000 

324.017 

608.125 

288.075 

540.556 

259.334 

486.500 

39 

432.037 

811.111 

370.377 

695.238 

324.142 

608.333 

288.186 

540.741 

259.434 

486.667 

4O 

432.205 

811.389 

370.521 

695.476 

324.268 

608.542 

288.298 

540.920 

259.534 

486.833 

41 

432.372 

811.667 

370.664 

695.714 

324.393 

608.750 

288  409 

541.111 

259.635 

487.000 

42 

432.539 

811.944 

370  807 

695.952 

324.519 

608  958 

288.521 

541.296 

259.735 

487.167 

43 

432.706 

812.222 

370.950 

696.190 

324.644 

609.167 

288.632 

541.481 

259.83(i 

J  87.  333 

44 

432.873 

812.500 

371.094 

696.429 

324.769 

609.375 

288.744 

541.667 

259  936 

487.500 

45 

433.041 

812.778 

371.237 

696.667 

324.895 

609.583 

288.855 

541.852 

260  036 

487.667 

4G 

433.208 

813.056 

371.380 

696.905 

325.020 

609.792 

288.967 

542.037 

260.137 

487.833 

47 

433.375 

813.333 

371.524 

697.143 

325.146 

610.000 

289.078 

542.222 

260.237 

488.000 

48 

433.542 

813.611 

371.667 

697.381 

325.271 

610.208 

289.190 

542.407 

260.338 

488.167 

49 

433.709 

813.889 

371.810 

697.  fil  9 

325.397 

610.417 

289.301 

542.593 

260.438 

488.333 

50 

433.876 

814.167 

371.954 

697.857 

325.522 

610.625 

289.  41  3  1542.778 

260.538 

488.500 

51 

434.041 

814.444 

372.097 

698.095 

325.647 

610.833 

289.524:542.96? 

260  639 

488.667 

52 

434.211 

814.  722J372.240 

698.333 

325.773 

611.042 

289.636543.148 

260.739 

488.833 

53 

434.378 

81  5.000'  372.  3841  698.  571 

325.898 

611.250 

289.747543.333 

260.840 

489.000;  54 

434.545 

81  5.  278  372.  5271  698.  810 

326.024 

611.458 

289.  859  543.  51  < 

260.940 

489.167;  55 

434.712 

815.556  372.670  699.048 

326.149 

611.667 

289.971  543.704 

261.040 

489.333   r>(> 

484.884 

815.833372.818699.286 

326.278 

611.875 

290.085543.889 

261.144 

489.500j  57 

435.056  816.111  372.965  699.524 
435  .  224  !  8  1  6  .  389  373  .  1  09  '  699  .  762 

326.407 
326.533 

612.083 
612.292 

290.200544.074 
290.311:544  259 

261.247 
261.347 

489.667  58 
489.833  59 

143 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


49° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

2611.17 

4900.00 

1305.632450.00 

870.481 

1633.33 

652.920 

1225.00 

522.394 

980.000 

1 

2612.18 

4901.67 

1306.14 

2450.83 

870.815 

1633.89 

653.171 

1225.42 

522.595 

980.333 

2 

2613.18 

4903.33 

1306.64 

2451.67 

871.149 

1634.44 

653.421 

1225.83 

52-2.795 

980.667 

3 

2614.18 

4905.00 

1307.14 

2452.50 

871.484 

16:35.00 

653.672 

1226.25 

522.996 

981.000 

4 

2615.18 

4906.67 

1307.64 

2453.33 

871.818 

1635.56 

653.  923  11'226.  67 

523.197 

981.333 

5 

2616.19 

4908.33 

1308.14 

2454.17 

872.152 

1636.11 

654.173 

1227.08 

523.397981.667 

6 

2617.19 

4910.00 

1308.64 

2455.00 

872.486 

1636.67 

654.424 

1227.50 

523.598982.000 

7 

2618.19 

4911.67 

1309.14 

2455.83 

872.821 

1637.22 

654.675 

1227.92 

523.798982.333 

8 

2619.19 

4913.33 

1309.65 

2456.67 

873.1551637.78 

654.926 

1228.33 

523.999982.667 

9 

2620.20 

4915.00 

1310.15 

2457.50 

873.489,1638.33 

655.176 

1228.75 

524.200983.000 

10 

2621.20 

4916.67 

1310.65 

2458.33 

873.8231638.89 

655.427 

1229.17 

524.400983.333 

11 

2622.23 

4918.33 

1311.16 

2459.17 

874.167 

1639.44 

655.685 

1229.58 

524.607983.667 

12 

2623.26 

4920.00 

1311.68 

2460.00 

874.511 

1640.00 

655.943 

1230.00 

524.813984.000 

13 

2624.27 

4921.67 

1312.18 

2460.83 

874.845 

1640.56 

656.194 

1230.42 

525.013984.333 

14 

2625.27 

4923.33 

1312.68 

2461.67 

875.180 

1641.11 

656.444 

1230.83 

525.214984.667 

15 

2626.27 

4925.00 

1313.18 

2462.50 

875.514 

1641.67 

656.695 

1231.25 

525.415985.000 

16 

2627.27 

4926.67 

1313.69 

2463.33 

875.848 

1642.22 

656.946 

1231.67 

525.615985.333 

17 

2628.28 

4928.33 

1314.19 

2464.17 

876.182 

1642.78 

657.196 

1232.08 

525.816985.667 

18 

2629.28 

4930.00 

1314.69 

2465.  OJ 

876.517 

1643.33 

657.447 

1232.50 

526.  01  6  :  986.  000 

19 

2630.28 

4931.67 

1315.19 

2465.83 

876.851 

1643.89 

657.698 

1232.92 

526.217 

986.333 

20 

2631.28 

4933.33 

1315.69 

2466.67 

877.185 

1644.44 

657.949 

1233.33 

526.418 

986.667 

21 

2632.32 

4935.00 

1316.21 

2467.50 

877.529 

1645.00 

658.206 

1233.75 

526.  624  1987.  000 

22 

2633.35 

4936.67 

1316.72 

2468.33 

877.873 

1645.56 

658.464 

1234.17 

526.  830  i  987.  3:33 

23 

2634.35 

4938.33 

1317.22 

2469.17 

878.207 

1646.11 

658.715 

1234.58 

527.031  987.667 

24 

2635.35 

4940.00 

1317.72 

2470.00 

878.541 

1646.67 

658.966 

1235.00 

527  2311988.000 

25 

2636.36 

4941.67 

1318.23 

2470.83 

878.876 

1647.22 

659.216 

1235.42 

527.432988.333 

26 

2637.36 

4913.33 

1318.73 

2471.67 

879.210 

1647.78 

659.467 

1235.83 

527.633988.667 

27 

2638.36 

4945.00 

1319.23 

2472.50 

879.544 

1648.33 

659.718 

1236.25 

527.8331989.000 

28 

2639.36 

4946.67 

1319.73 

2473.33 

879.878 

1648.89 

659.969 

1236.67 

528.034 

989.333 

29 

2640.39 

4948.33 

1320.25 

2474.17 

880.222 

1649.44 

660.227 

1237.08 

528.240 

989.667 

30 

2641.43 

4950.00 

1320.76 

2475.00 

880.566 

1650.00 

660.484 

1237.50 

528.447 

990.000 

31 

2642.43 

4951.67 

1321.26 

2475.83 

880.900 

1650.56 

660.735 

1237.92 

528.647 

990.333 

32 

2643.43 

4953.33 

1321.76 

2476.67 

881.235 

1651.11 

660.986 

1238.33 

528.848 

990.607 

33 

2644.43 

4955.00 

1332.27 

2477.50 

881.569 

1651.67 

661.237 

1-238.75 

5-29.048 

991.000 

34 

2645.44 

4956.67 

1322.77 

2478.33 

881.903 

1652.22 

661.487 

1239.17 

529.249 

991.333 

35 

2646.44 

4958.33 

1323  27 

2479.17 

882.237 

1652.78 

661,738 

1239.58 

5-29.450 

991.667 

36 

2647.44 

4960.00 

1323.77 

2480.00 

882.572 

1653.33 

661.989 

1240.00 

529.650 

992.000 

37 

2648.47 

4961.67 

1324.29 

2480.83 

882.915 

1653.89 

062.247 

1240.42 

529.856 

992.333 

38 

2649.50 

4963.33 

1324.80 

2481.67 

883.259 

1654.44 

662.505 

1240.83 

530.063 

992.607 

39 

2650.51 

4965.00 

1345.30 

2482.50 

883.593 

1655.00 

662.755 

1241.25 

530.203 

993.000 

4O 

2651.51 

4966.67 

1335  80 

2483.33 

883.928 

1655.56 

663.006 

1241.67 

530.464 

993.333 

41 

2652.51 

4968.33 

1326.31 

2484.17 

884.262 

1656.11 

663.257 

1242.08 

530.665 

993.607 

42 

2653.52 

497'0.00 

1326.81 

2485.00 

884.596 

1656.67 

063.507 

1242.50 

530.865 

994.000 

43 

2654.55 

4971.67 

1327.32 

2485.83 

884.940 

1657.22 

063.765 

1242.9-2 

531.072 

994.333 

44 

2655.58 

4973.33 

1327.84 

•2486.67 

885.284 

1657.78 

664.023 

1243.33 

531.278 

994.607 

45 

2656.58 

4975.00 

1328.34 

2487.50 

8S5.618 

1658.33 

664.274 

1243.75 

531.478 

995.000 

46 

2657.58 

4976.67 

13-28  84 

2488.33 

8S5.952 

1658.89 

664.525 

1244.17 

531.679 

995.333 

47 

2658.59 

4978.33 

1329.34 

2489.17 

886.287 

1659.44 

664.775 

1244.58 

531.880 

995.067 

48 

2659.59 

4980.00 

1329.84 

2490.00 

886.621 

1660.00 

065.026 

1245.00 

532.080 

996.000 

49 

2(360.62 

4981.67 

1330.36 

2490.83 

886.905 

1660.56 

665.284 

1245.42 

532.287 

996.333 

5O 

2661.65 

4983.33 

1330.87 

2491.67 

887.309 

1601.11 

665.542 

1245.83 

53-2.493 

996.607 

51 

2662.65 

4985.00 

1331.38 

241)2.50 

887.643 

1661.67 

665.793 

1246.25 

582.694997.000 

52 

2603.664986.67 

1331.88 

2493.33 

887.977 

1662.22 

666.043 

1246.67 

532.894  997.333 

53 

2664.694988.33 

1332.39 

2494.17 

S88.321 

1662.78 

666.301 

1247.08 

533.100997.607 

54 

2665.724990.00 

1332.91 

2495.00 

888.665 

1663.33 

666.559 

1247.50 

533.307998.000 

55 

2666.724991.67 

1333.41 

2495.83 

888.999 

1603.89 

606.810 

1247.92 

533.507998.333 

56 

2667.734993.33 

1333.91 

2496.67 

889.3331664.44 

667.060 

1248.33 

533.708998.667 

57 

2668.7:14995.00 

1334.41  2107.50 

889.66816(55.00 

667.311 

1248.75 

533.909  999.000 

58 

2669.734996.67 

1334.91  2498.33 

890.002  1665.56 

667.562 

1249.17 

534.109999.333 

59 

2670.764998.33 

1335.432499.17 

890.346  1666.11 

667.820 

1249.58 

534.315999.667 

144 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


G°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

49° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

A  re. 
544.444 

Tan. 

Arc. 

M. 

435.391 

816.667 

373.252 

700.000 

326.658 

612.500 

290.423 

261.448 

490.000 

0 

435.558 

816.944 

373.395 

700.238 

326.784 

612.708 

290.535 

544.630 

261.548 

490.167 

1 

435.725 

817.222 

373.539 

700.476 

326.909 

612.917 

290.646 

544.815 

261.648 

490.333 

2 

435.892 

817.500 

373.682 

700.714 

327.034 

613.125 

290.758 

545.000 

261.749 

490.500 

3 

436.059 

817.778 

373.825 

700.952 

327.160 

613.333 

290.869 

545.185 

261.849 

490.667 

4 

436.227 

818.056 

373.969 

701.190 

327.285 

613  542 

290.981 

545.370 

261.950 

490.833 

5 

436.394 

818.333 

374.112 

701.429 

327.411 

613.750 

291.092 

545.556 

262.050 

491.000 

0 

436.561 

818.611 

374.255 

701.667 

327.536 

613.958 

291.204 

545.741 

262.150 

491.167 

7 

436.728 

818.889 

37'4.399 

701.905 

327.662 

614.167 

291.315 

545.926 

262.251 

491.333 

8 

436.895 

819.167 

374.542 

702.143 

327.787 

614.375 

291.427 

546.111 

262.351 

491.500 

9 

437.063 

819.444 

374.685 

702.381 

327.912 

614.583 

291.538 

546.296 

262.452 

491.667 

10 

437.235 

819.722 

374.833 

702.619 

328.041 

614.792 

291.653 

546.481 

262.555 

491.833 

11 

437.407 

820.000 

374.980 

702  857 

328.171 

615.000 

291.768 

546.667 

262.658 

44)2.000 

12 

437.  57  i 

820.278 

375.123 

703.095 

328.296 

615.208 

291.879 

546.852 

262.759 

492.167 

13 

437.741 

820.556 

375.267 

703.333 

328.421 

615.417 

291.991 

547.037 

262.859 

492.333 

14 

437.908 

820.833 

375.410 

703.571 

328.547 

615.625 

292.102 

547.222 

262.959 

492.500 

15 

438.075 

821.111 

375.553 

703.810 

328.672 

615.833 

292.214 

547.407 

263.060 

492.667 

16 

438.242 

821.389 

375.697 

704.  048 

328.798 

616.042 

292.325 

547.593 

263.160 

492.833 

17 

438.410 

821.667 

375.840 

704.286 

328.923 

616.250 

292.437 

547.778 

263.261 

493.000 

18 

438.577 

821.944 

375.983 

704.524 

329.049 

616.458 

292.548 

547.963 

263.361 

493.167 

19 

438.744 

822.222 

376.127 

704.762 

329.174 

616.667 

292.660 

548.148 

263.461 

493.333 

2O 

438.916 

822.500 

376.274 

705.000 

329.303 

616.875 

292.775 

548.333 

263.565 

493.500 

21 

439.088 

822.778 

376.422 

705.238 

329.432 

617.083 

292.889 

548.519 

263.668 

493.667 

22 

439.255 

823.05*. 

376.565 

705.47T, 

329.557 

617.292 

293.001 

548.704 

263.768 

493.833 

23 

439.42',' 

823.333 

376.708 

705.714 

329.683 

617.  500 

293.112 

548.889 

263.869 

494.000 

24 

439.  590 

823.611 

376.852 

705.952 

329.808 

617.708 

293.224 

549.074 

263.969 

494.167 

25 

439.757 

823.889 

376.995 

706.190 

3-J9.934 

617.917 

293.335 

549.251) 

264.069 

494.333 

2G 

439.924 

824.16? 

377.  138 

706.429 

330  059 

618.125 

293.447 

549.444 

264.170 

494.500 

27 

440.091 

S>4.444 

477.282 

706.667 

330.185 

618.333 

293.558 

549.630 

264.270 

494.667 

28 

440.263 

824.722 

377.429 

706.905 

330.314 

618.542 

293.673 

549.815 

264.374 

494.833 

29 

440.435 

825.000 

377.576 

707.143 

330.443 

618.750 

293.788 

550.000 

264.477 

495.000 

30 

440.602 

825.278 

377  720 

707.381 

330.568 

618.958 

293.899 

550.185 

264  .  577 

495.167 

31 

440.769 

825.556 

377.863 

707.619 

330.694 

619.167 

294.011 

550.370 

264.678 

495.333 

32 

440.937 

825.833 

378.006 

707.  857 

330.819 

619.37'5 

294.122 

550.556 

264.778 

495.500 

33 

441.104 

826.111 

378.150 

708.095 

330.944 

619.583 

294.234 

550.741 

264.878 

495.667 

34 

441.271 

826.389 

378.293 

708.  333 

331.070 

619.792 

294.345 

550.926 

264.979 

495.833 

35 

441.438 

826.667 

37'8.436 

708.571 

331.195 

620.000 

294.457 

551.111 

265.079 

496.000 

36 

441.610 

826.944 

378.584 

708.810 

331.324 

620.208 

294.572 

551.296 

265.182 

496.167 

37 

441.782 

827.222 

378  731 

709.048 

331.453 

620.417 

294.680 

551.481 

265.286 

496.333 

38 

441.949 

827.500 

378.875 

709.286 

331.579 

620.625 

294.798 

551.667 

265.386 

496.500 

39 

442.117 

827.778 

379.018 

709.524 

331.704 

620.833 

294.909 

551.852 

265.486 

496.667 

40 

442.284 

828.056 

379.161 

709.762 

331.830 

621.042 

295.021 

552.037 

265.587 

496.833 

41 

442.451 

828.333 

379.304 

710.000 

331.955 

621.250 

295.132 

552.222 

265.687 

497.000 

42 

442.623 

828.611 

379.452 

710.238 

332.084 

621.458 

295.247 

552.407 

265.791 

497.167 

43 

442.795 

828.889 

379.599 

710.476 

332.213 

621.667 

295.362 

552.593 

265.894 

497.333 

44 

442.962 

829.167 

379.743 

710.714 

a3  2.  339 

621.875 

295.473 

552.778 

265.994 

497.500 

45 

443.129 

829.444 

379.886 

710.952 

332.464 

622.083 

295.585 

552.963 

266.095 

497.667 

46 

443.296 

829.722 

380.029 

711.190 

332.  5S9 

622.292 

295.696 

553.148 

266.195 

497.838 

47 

443  464 

830.000 

380.173 

711.429 

332.715 

622.500 

295.808 

553.333 

266.295 

498.000 

48 

443.636 

830.278 

380.320 

711.667 

332.844 

622.708 

295.923 

553.519 

266.399 

498.167 

49 

443.808 

830.556 

380.468 

711.905 

332.973 

622.917 

296.037 

553.704 

266.502 

498.333 

50 

443.975 

830.833 

380.611 

712.143 

333.098 

623.125 

296.149 

553.889 

266.602 

498.500 

51 

444.142 

831.111 

380.754 

712.381 

333.224 

623.3.33 

296.260 

554.074 

266.703 

498.667 

52 

444.314 

831.38!) 

380.902 

712.619 

333  353 

623.542 

296.375 

554.259,266.806 

498.833 

53 

444.486 

831.667 

381.049 

712.857 

333.482 

623.7'50 

296.490 

554.444266.909 

499.000 

54 

444.653 

831.944 

381.192 

713.095 

333.607 

623.958 

2J6.601 

554.630267.010 

499.167 

55 

444.8201832.222 

381.336 

713.333 

333.S  33 

624.167 

2156.713 

554.815267.110 

499.333 

56 

444.987 

832.500 

381.479 

713.571 

333.858 

621.375 

296.824 

555.000267.210 

499.500 

57 

445.155 

832.778 

381.622 

713.810 

333.984 

624.583 

296.936 

555.185267.311 

499.667 

58 

445.327833.056 

381.770 

714.048 

334.113 

624.792 

297.051 

555.370  267.414 

499.833 

59 

145 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


5O° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 
5000.00 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

2671.79 

13^5.95 

2500.00 

890.689 

1666.07 

068.078 

1250.00 

5:34.522 

1000.00 

1 

3672.80 

5001.67 

1336.45 

2500.83 

891  024 

1667.22 

668.328 

1250.42 

534.722 

1000.33 

3 

2(573.80 

5003.33 

1336.95 

2501.67 

891.358 

1667.78 

668.579 

1250.83 

534.923 

1000.67 

3 

2074.83 

5005.00 

1337.46 

2502.50 

891.702 

1668.33 

668.837 

1251.25 

535.129 

1001.00 

4 

2675.86 

501)6.67 

1337.98 

2503.33 

892.046 

1668.89 

669.095 

1251.67 

535.336 

1001.  33 

5 

2676.86 

5008.33 

1338.48 

2504.17 

892.380 

1669.44 

669.346 

1252.08 

535.536 

1001.67 

6 

2677.87 

5010.00 

13:38.98 

2505.00 

892.714 

1670.00 

669.596 

1252.50 

535.737 

1002.00 

7 

2678.87 

5011.67 

1339.48 

2505.83 

893.048 

1670.56 

669.847 

1252.92 

535.937 

1002.33 

8 

2679.87 

5013.33 

1339.99 

2506.67 

893.383 

1671.11 

670.098 

1253.33 

536.138 

1002.67 

9 

2680.90 

5015.00 

1340.50 

2507.50 

893.726 

1671.67 

670.356 

1253.75 

536.344 

1003.00 

10 

2681.93 

5016.67 

1341.02 

2508.  as 

894.070 

1672.22 

670.614 

1254.17 

536.551 

1003.  as 

11 

2682.94 

5018.33 

1341.52 

2509.17 

894.  405'  1672.  78 

670.864 

1254.58 

536.751 

1003.67 

13 

2683.94 

5020.00 

1342.02 

2510.00 

894.739  1673  33 

671.115 

1255.00 

536,952 

1004.00 

13 

2684.97 

5021.67 

1342.53 

2510.83 

895.083:1673.89 

671.373 

1255.42 

537.158 

1004.  as 

14 

2686.00 

5023.33 

1343.05 

2511.67 

895.  426;  1674.  44 

671.631 

1255.83 

537.365 

1004.67 

15 

2687.01 

5025.00 

1343.55 

2512.50 

895.761  1675.00 

671.881 

1256.25 

537.565 

1005.00 

16 

2688.01 

5026.67 

1344.05 

2513.33 

896.095 

1675.56 

672.132 

1256.67 

537.766 

1005.33 

17 

2689.04 

5028.33 

1344.57 

2514.17 

896.439 

1676.11 

672.390 

1257.08 

537.972 

1005.67 

18 

2690.07 

5030.00 

1345.08 

2515.00 

896.783 

1676.67 

672.648 

1257.50 

538.178 

1006.00 

19 

2691.07 

5031.67 

1345.59 

2515.83 

897.117 

1677.22 

672.899 

1257.92 

538.379 

1006.33 

20 

2692.08 

soas.as 

1346.09 

2516.67 

897.451 

1677.78 

673.149 

1258.33 

538.580 

1006.67 

21 

2693.11 

5035.00 

1346.60 

2517.50 

897.795 

1678.  as 

673.407 

1258.75 

538.786 

1007.00 

22 

2694.14 

5036.67 

1347.12 

2518.33 

898.139 

1678.89 

673.665 

1259.17 

538.992 

1007.33 

23 

2695.14 

5038.  as 

1347.62 

2519.17 

898.473 

1679.44 

673.916 

1259.58 

539.193 

1007.67 

24 

2696.14 

5040.00 

1348.12 

2520.00 

898.807 

1680.00 

674.167 

1260.00 

539.394 

1008.00 

25 

2697.18 

5041.67 

1348.64 

2520.83 

899.151 

1680.56 

674  424 

1260.42 

539.600 

1008.33 

26 

2698.21 

5043.33 

1349.15 

2521.67 

899.495 

1681.11 

074.682 

1260.83 

539.806 

1008.67 

27 

2699.24 

5045.00 

1349.67 

2522.50 

899.839 

1681.87 

674.940 

1261.25 

540.013 

1009.00 

28 

2700.27 

5046.67 

1350.18 

2523.33 

900.183 

1682.22 

675.198 

1261.67 

540.219 

1009.33 

29 

2701  .27 

5048.33 

1350.69 

2524.17 

900.517 

1682.78 

675.449 

1262.08 

540.419 

1009.67 

30 

2702.27 

5050.00 

1351.19 

2525.00 

900.851 

1683.33 

675.700 

1262.50 

540.620 

1010.00 

31 

2703.31 

5051.67 

ia51.70 

2525.83 

901.195 

1683.89 

075.957 

1262.92 

540.826 

1010.33 

32 

2704.34 

5053.  as 

1352.22 

2526.67 

901.539 

1684.44 

676.215 

1263.33 

541.033 

1010.67 

33 

2705.34 

5055.00 

ia52.72 

2527.50 

901.873 

1685.00 

676.466 

1263.75 

541.2:33 

1011.00 

34 

2706.34 

5056.67 

1353.22 

2528.  33 

902.207 

1685.56 

676.717 

1264.17 

541.434 

1011.33 

35 

2707.37 

5058.  as 

1353.74 

2529.17 

902.551 

1686.11 

676.975 

1264.58 

541.640 

1011.67 

36 

2708.41 

5060.00 

1354.25 

2530.00 

902  895 

1686.67 

677.233 

1265.00 

541.847 

1012.00 

37 

2709.41 

5061.67 

1354.75 

2530.83 

903.229 

1687.22 

677.483 

1265.42 

542.047 

1012.33 

38 

2710.41 

5063.  as 

1355.26 

2531.67 

903.563 

1687.78 

077.734 

1265.83 

542.248 

1012.67 

39 

2711.44 

5065.00 

1355.77 

2532.50 

903.907 

1688.3S 

677.992 

1266.25 

542.454 

1013.00 

4O 

2712.47 

5066.67 

1356.29 

2533.33 

904.251 

1688.89 

678.250 

1266.67 

542.660 

1013.33 

41 

2713.50 

5068.33 

1:356  80 

2534.17 

904.595 

1689.44 

078.508 

1267.08 

542.867 

1013.67 

42 

2714.54 

5070.00 

1357.32 

2535.00 

904.939 

1690.00 

678.766 

1267.50 

543.073 

1014.00 

43 
44 

2715.54 
2716.54 

5071.67 
5073.33 

1357.82 
ia58.32 

2535.83 
2536.67 

905.2731690.56 
905.6071091.11 

679.016 
679.267 

1267.92 
1268.33 

543.274 
543.474 

1014.33 
1014.67 

45 

2717.57 

5075.00 

1358.84 

2537.50 

905.951 

1691.67 

079.525 

1268.75 

543.681 

1015.00 

46 

2718.60 

5076.67 

1359.  a5 

2538.33 

906.295 

1692.22 

679.783 

1269.17 

543.887 

1015.  as 

47 

2719.61 

5078.33 

1359.85 

2539.17 

906.629 

1692.78 

680.033 

1269.58 

544.088 

1015.67 

48 

2720.61 

5080.00 

1360.35 

2540.00 

906.963 

1693.33 

680.284 

1270.00 

544.288 

1016.00 

49 

2721.64 

5081.67 

1360.87 

2540.83 

907.307 

1693.89 

680.542 

1270.42 

544.494 

1016.33 

5O 

2722.67 

5083.33 

1361,39 

2541.67 

907.651 

1694.44 

680.800 

1270.83 

544.701 

1016.67 

51 

2723.70 

5085.00 

1361.90 

2542.50 

907.995 

1695.00 

681.058 

1271.25 

544.907 

1017.00 

52 

2724.74 

5086.67 

1362.42 

2543.  as 

908.339 

1695.56 

681.316 

1271.67 

545.113 

1017.33 

53 

2725.74 

5088.  a3 

1362.92 

2544.17 

908.6731696.11 

681.566 

1272.08 

545.314 

1017.67 

54 

2726.74 

5090.00 

1363.42 

2545.00 

909.00711696.67 

681.817 

1272.50 

545.515 

1018.00 

55 

2727.77 

5091.67 

1:363.94 

2545.83 

909.  351  !  1697.  22 

082.075 

1-J72.92 

545.721)1018.33 

56 

2728.80 

5093.  as 

1364.45 

2546.  #? 

909.6951697.78 

682.3:33 

1273.  as 

545.  927  [101  8.  67 

57 

2729.83 

5095.00 

1364.97 

2547.50 

910.039  1698.  as 

082.591 

1273.75 

540.1:34  1019.  00 

58 

2730.87 

5096.67 

1365.48 

2548.33 

910.382  1698.89 

682.849 

1274.17 

M6.340J1019.33 

59 

2731.90 

5098.33 

1366.00 

2549.17 

910.726  1699.44 

683.107 

1274.58 

516.546il019.67 

146 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

5O° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

445.499 

833.333 

381.917 

714  286 

334  242625.000 

297.165555.556267.517 

500.000 

0 

445.666 

833.6111382.060 

714.524 

334.367625.208 

297.  27?  1555.  741  267.618 

500.16? 

1 

445.883 

833.8891382  204 

714.762 

334.493625.417 

297.  388  555.  920267.71  8 

500.333 

2 

446.005 

S34.167 

382.351 

715.000 

334.622625.625 

297.503556.111  207.821 

500.500 

3 

446.17? 

834.444 

382.499 

715.238 

334.751 

625  833 

297.618 

556.296267.925 

500.66? 

4 

446.344 
446  511 

834.722 
835.000 

382.642 
382.785 

715.476 
715.714 

334.876  626.042 
335.001  626  250 

297.729 
297.841 

556.481 
556.667 

208.025 
268.125 

500.833 
501.000 

5 
6 

446.678 

835.278 

382.929 

715.952 

335.127 

626.458 

297.952 

556.852 

268.226 

501.167 

7 

446.846 

835.556 

383.072 

716.190 

335.252 

626.667 

298.064 

557.037 

268.326 

501.333 

8 

447.018 

835.833 

383.219 

716.429 

335.381 

626-875 

298.179 

557.222 

268.430 

501.500 

9 

447.190 

836.111 

383.367 

716.667 

335.  510  |627.083 

298.293 

557.407 

268.533 

501  .  667 

10 

447.35? 

836.359 

383.510 

716.905 

335.636627.292 

298.405 

557.593 

268.633 

501.833 

11 

447.524 
447.696 

836.667 
836.944 

383.653 

383.801 

717.143 

717.381 

335.  761  S627.500 
335.890627.708 

298.516 
298.631 

557.778 
557.963 

268.734  502.000 
268.837502.167 

12 
13 

447.868 

837.222 

383.948 

717.619 

986.019 

627.917 

298.746 

558.118 

268.940502.333 

14 

448.035 

837.500 

384.092 

717.85? 

336.145 

628.125 

298.857 

558.333 

209.040502.500 

15 

448.202 

837.778 

384.235 

718.095 

336.270 

628.333 

298.969 

558.519 

269.141  502  667 

16 

448.374 

838.056 

384.382 

718.333 

886.899 

628.542 

299  084 

558.704 

269.244  502.833 

17 

448.546 

838.333 

384.530 

718.571 

336.528 

628.750 

299.198 

558.889 

269.347 

503.000 

18 

448.713 

838.611 

384.673 

718.810 

336.654 

628.958 

299.310 

559.074 

269.448 

503.167 

19 

448.881 

838.889 

384.816 

719.048 

336.779 

629.167 

299.421 

559.259 

269.548 

503.333 

2O 

449.053 

839.167 

284.964 

719.286 

336.908629.375 

299.536 

559.444 

269.651 

503.500 

21 

449.224 

839.444 

385.111 

719.524 

337.  037  1629.583 

299.651 

559.630 

269.755 

503.667 

22 

449.392 

839.722 

385.255 

719.762 

337.1631629.792 

299.762 

559.815 

269.855 

5Q3.833 

23 

449.559 

840.000 

385.398 

720.000 

337.  288;  630.  000 

299.874 

560.000 

269.956 

504.000 

24 

449.731 

840.278 

385.545 

720.238 

337.417630.208 

299.988 

560.185 

270.059 

504.167 

25 

449.903 

840.556 

385.693 

720.476 

337.546 

630.417 

300.103 

560.370 

270.162 

504.333 

26 

450.075 

840.833 

385.840 

720.714 

337.675630.625 

300.218 

560.556 

270.265 

504.500 

27 

450.247 

841.111 

385.988 

720.952 

337.804  630  833 

300.333 

560.741 

270.369 

504.667 

28 

450.414 

841.389 

386.131 

721.190 

337.929631.042 

300.444 

560.926 

270.469 

504.833 

29 

450.581 

841.667 

386.274 

721.429 

338.055 

631.250 

300.556 

561.111 

270.569 

505.000 

30 

450.753 

841.944 

386.422 

721.667 

338.184631.458 

800.670 

561.290 

270.673 

505.167 

31 

450.925 

842.222 

386.569 

721.905 

338.313631.667 

300.785 

561.481 

270.776 

505.333 

32 

451.092 

842.500 

386.713 

722.143 

338.438631.875 

300  897 

561  667 

270.876 

505.500 

33 

451.259 

842.778 

386.856 

722.381 

338.564  632.083 

301.008 

561.852 

270  977 

505.667 

34 

451.431 

843.056 

387.003 

722  619 

338.693632.292 

301.123 

562.037 

271.080 

505.833 

35 

451.603 

843.333 

387.151 

722.857 

338.822  632.500 

301.237 

562  222 

271.183 

506.000 

36 

451.771 

P43.611 

3S7.294 

723.095 

338.947  632  708 

301.349 

562.407 

271.284 

506.167 

37 

451.938 

843.889 

387.437 

723.033 

339.073632.91? 

301.461 

562.593 

271  384 

506.333 

38 

452.110 

844.167 

387.585 

723.571 

339.202 

633.125 

301.575 

562.778 

271.487 

5C6.500 

39 

452.282 

844.444 

387.732 

723.810 

339.331 

633.333 

301.690 

562.963 

271.591 

506.667 

40 

452.454 

844.722 

387.880 

724.048 

339.  460:633.  542 

301.805 

563.148 

271.694 

506.833 

41 

452.626 
452.793 

845.000 

845.278 

388.027 
388.170 

724.286 
724.524 

339.589033.750 
339.714  633  958 

301.919503.333271.797 
302.  031  1  563.  51  9  271.  897 

507.000 
507.167 

42 
43 

452.960 

845.556 

388.314 

724.762 

339.840634.167 

302.142563.704  271.998 

507.333 

44 

453.132 

845.833 

388.461 

725.000 

339.969  634  375 

302.257563.889272.101 

507.500 

45 

453,304 

846.111 

388.609 

725.238 

340.098 

634.583 

302  .  372  564  074  272  .  204 

507.667 

46 

453.471 

846.389 

388.752 

725.476 

340.223 

634.792 

302.483564.259272  305 

507.838 

47 

453.638 

846.66? 

388.895 

725.714 

340.349 

635.000 

302  .  595  j  564  .  444  272  .  405 

508.000 

48 

453.810 

846.944 

389.043 

725.952 

340.478 

635.208 

302.  710  564.  630  1  272.  518 

508.167 

49 

453.982 

847.222 

389.190 

726.190 

340  607 

635.417 

302.8.24564.815 

272.612 

508.333 

50 

454.154 

847.500 

389.337 

726.429 

340.73(> 

635.625 

302  .  939  505  .  000  272  .715 

508.500 

51 

454.326 

847.778 

389.485 

726.667 

340.865 

035.833 

303  .  054  565  .  1  85  27  2  .  S  18  508  .  667 

52 

454.498848.056 

389.628 

726.905 

340.990636.042 

303  .  1  65  565  .  370  272  .  9  1  9  508  .  833 

53 

454.661848.888 

389.772 

727.143 

341.116036.250 

303  .  277  565  .  556  273  .019  509  .  000 

54 

454.832848.611 

389.919 

727.381 

341.245636.458 

3,'»3  .  391  565  .  741  273  .  1  22  50!)  .  1  67 

55 

455.004848.889 

390.066 

727.  (i  19 

341.374636.607 

303.506  505.926  273.226  509.333 

56 

455.176849.167 

390.214  727.85? 

341.503636.875 

303.1.21  566.111  273.329  509.500 

57 

455.348849.444 

390.361 

728.095 

341.  632  1637.  083 

303.736  566.296  273.432  509.067 

r>8 

455.520849.722 

390.509  728.333 

341  .  761  i  637  .  292  303  .  850  566  .  481  273  .  535  509  .  K-J3   59 

147 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


51° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~0 

273:2.93 

5100.  00  11366.  51 

2550.00 

911.070 

1700.00 

683.364 

1275.00 

546.753  1020.00 

1 

2733.93 

5101.67 

1367.02 

2550.83 

911.404 

1700.56 

683.615 

1275.42 

546.9531020.33 

3 

2734.93 

5103.33 

1367.52 

2551.67 

1)11.738 

1701.11 

683.866 

1275.8:1 

547.154  1020.6;' 

3 

2735.97 

5105.00 

1368.03 

2552.50 

912.08-3 

1701.67 

684.124 

1276.25 

547.  300  10-21.03 

4 

2737.00 

5106.67 

1368.55 

2553.33 

912.426 

1702.22 

684.382 

1-376.6: 

547.566 

1021.33 

5 

2738.03 

5108.33 

1369.06 

2554.17 

912.770 

1702.78 

684.640 

1277.08 

547.773 

1021.67 

6  2739.06 

5110.00 

1369.58,2555.00 

913.114 

1703.33 

684.897 

1277.50 

547.979 

1022.0J 

7  2740.06 

5111.67 

1370.08 

2555.83 

913.448 

1703.89 

685.148 

1277.9-3 

548.180 

1022.33 

8  2741.06 

5113.33 

1370.58 

2556.67 

913.782 

1704.44 

685.399 

1278.33 

548.380 

1022.67 

9 

2742.10 

5115.00 

1371.10 

2557.50 

914.126 

1705.00 

685.657 

1278.75 

548.587 

1023.00 

10 

2743.13 

5116.67 

1371.61 

2558.33 

914.470 

1705.56 

685.915 

1279.17 

548.793 

1023.33 

11 

2744.16 

5118.33 

1372.13 

2559.17 

914.814 

1706.11 

686.173 

1279.58 

518.999  1023.67 

13 

2745.19 

5120.00 

1372.65 

2560.00 

915.158 

1706.67 

686.430 

1280.00 

549.2061024.00 

13 

2746.22 

5121.67 

1373.16 

2560.83 

915.501 

1707.22 

686.688 

1280.42 

549.412  1024.33 

14 

2747.25 

5123.33 

1373.68 

2561.67 

915.845 

1707.78 

686.946 

1280.83 

549.018  1024.67 

15 

2748.28 

5125.00 

1374.19 

2562.50 

916.189 

1708.33 

687.204 

1281.25 

549.825  1025.00 

16 

2749.32 

5126.67 

1374.71 

2563.33 

916.533 

1708.89 

687.462 

1281.67 

550.031  1025.33 

17 

2750.32 

5128.33 

1375.21 

2564.17 

916  867 

1709.44 

687.713 

1282.08 

550.232  1025.67 

18 

2751.32 

5130.00 

1375.71 

2565.00 

917.201 

1710.00 

687.963 

1282.50 

550.432  1026.00 

19 

2752.35 

5131.67 

1376.23 

•2565.83 

917.545 

1710.56 

688.221 

1282.92 

550.639 

1026.33 

20 

2753.38 

5133.33 

1376.74 

2566.67 

917.889 

1711.11 

688.479 

1283.33 

550.845 

1026.67 

21 

2754.41 

5135.00 

1377.26 

2567.50 

918.233 

1711.67 

688.737 

1283.75 

551.051  10-37.00 

*8 

2755.45 

5136.67 

1377.77 

25158.33 

91  S.  577 

1712.22 

688  99:> 

1284.17 

551.258  1027.33 

33 

2756-.  48 

5138.33 

1378.29 

2569.17 

918  920 

1712.78 

689.253 

1284.58 

551.4641027.67 

34 

2757.51 

5140.00 

1378.80 

2570.00 

919.264 

1713.33 

t>89.51' 

1285.00 

551.6701028.00 

35 

2758.54 

5141.67 

1379.32 

2570.83 

919.608 

1713.89 

689.769 

1285.42 

55  1.877  [10-38.  33 

36 

2759.57 

5143.33 

1379.84 

2571.67 

919.952 

1714.44 

690.026 

1285.83 

552.0831028.67 

37 

2760.57 

5145.00 

1380.34 

2572.50 

920.286 

1715.00 

690.277 

1286.25 

552.283:1029.00 

38 

2761.58 

5146.67 

138  J.  84 

2573.33 

920.620 

1715.56 

690.528 

1286.67 

552.484!  1029.  33 

39 

2762.61 

5148.33 

1381.35 

2574.17 

920.964 

1716.11 

690.786 

1287.08 

552.690 

1029.67 

30 

2763.64 

5150.00 

1381.87 

2575.00 

9-21.308 

1716.67 

691.044 

1287.50 

552.897 

1030.00 

31 

2764.67 

5151.67 

138-3.39 

2575.83 

931.652 

1717.22 

691.302 

1287.92 

553.103 

1030.33 

33 

2765.70 

5153.33 

1382.90 

2576.67 

921.996 

1717.78 

691.559 

1288.33 

553.309 

1030.67 

33 

2766.73 

5155.00 

1383  42 

2577.50 

93-3.  339 

1718.33 

691.817 

1288.75 

553.516 

1031.00 

34 

2767.76 

5156.67 

1383.93 

2578.33 

922.683 

1718.89 

(592.075 

1289.17 

553.722 

1031.33 

35 

2768.80 

5158.33 

1384.45 

2579.17 

923.027 

1719.44 

692.333 

1289.58 

553.928 

1031.67 

36 

2769  83 

5160.00 

1384.96 

2580.00 

923.371 

1720.00 

692.591 

1290.00 

554.135 

1032.00 

37 

2770.86 

5161.67 

1385.48 

2580.83 

933.715 

1720.56 

692.849 

1290.42 

554.341 

1032.33 

38 

2771.89 

5163.33 

1386.00 

2581.67 

924.059 

1721.11 

693.107 

1290.83 

554.547 

1032.67 

39 

2772.92 

511J5.00 

1385.51 

2582.50 

924.402 

1721.67 

693.365 

1291.25 

554.754 

1033.00 

40 

2773.95 

5166.67 

1387.03 

2583.33 

924.746 

1722.22 

693.623 

1291.67 

554.960 

1033.33 

41 

2774.98 

5168.33 

1387.54 

2584.17 

925.090 

1722.78 

693.880 

1292.08 

555.166 

1033.67 

43 

2776.02 

5170.00 

1388.06 

2585.00 

935.434 

1723.33 

694.138 

1292.50 

555.373 

1034.00 

43 

27J7.05 

5171.67 

1388.57 

2585.83 

925.778 

1723.89 

694.396 

1292.92 

555.579 

1034.33 

44 

2778.08 

5173.33 

1389.09 

2586.67 

926.121 

1724.44 

694.654 

1293.33 

555.785 

1034.67 

45 

2779.08 

5175.00 

1389.59 

2587.50 

926.456 

1725.00 

694.905 

1293.75 

555.986 

1035  00 

46 

2780.08 

5176.67 

1390.09 

2588.33 

926.790 

1725.56 

695.156 

1294.17 

556.187 

1035.33 

47 

2781.11 

5178.33 

1390  61 

2589.17 

927.134 

1726.11 

695.413 

1294.58 

556.393 

1035.67 

48 

2782.15 

5180.00 

1391.12 

2590.00 

927.478 

1726.67 

695.671 

1295.00 

556.599 

1036.00 

49 

2783.18 

5181.67 

1391.64 

2590.83 

927.821 

1727.22 

695.929 

1295.42 

556.806 

1036.33 

50 

2784.21 

5183.33 

1392.16 

2591.67 

928.165 

1727.78 

696.187 

1295.83 

557.012 

10-36.67 

51 

2785.24 

5185.00 

1392.67 

2592.50 

928.509 

1728.33 

696.445 

1296.25 

557.218 

1037.00 

53 

278(5.27 

5186.67 

1393.19 

2593.33 

928.853 

1728.89 

696.703 

1296.67 

557.425 

1037.33 

53 

2787.30 

5188.33 

1393.702594.17 

929.197 

1729.44 

696.961 

1297.  08  1  557.  631 

1037.67 

54 
55 

2788.33 
2789.  37 

5190.00 
5191.67 

1394.222595.00 
1394.  73  12595.  83 

929  .  540 
929.881 

1730.01* 
1730.56 

697.219 
697.476 

1297.50 
1297.92 

557.837 
558.043 

1038.00 
1038.33 

56 
57 

2790.40 
2791.43 

5193.33 
5195.00 

1395.  25  j  2596.  67 
1395.772597.50 

930.228 
930.57-3 

1731.11 
1731.67 

697  734 
697.992 

1298.33558.250 

1298.75558.456 

1038.67 
1039.00 

58 

2792.46 

5196.67 

1396.282598.33 

930.916 

1732.22 

698.2501299.17558.662 

1039.33 

59 

2793.49 

5198.33 

1396.8012599.17 

931.260 

173-3.78 

698.  .r;08l  1299.  58:558.  8(39 

1039.67 

148 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

51° 

Tan. 

Arc. 

Tan. 

Arc. 

Tail. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

455.69:; 

tso.coo 

390.656 

728.571 

341.890 

637.500 

303.965 

566.6671273.639 

510.000 

O 

455.  860 

850.278 

390.799 

728.810 

342.015 

637.708 

304.077566.852 

273.739 

510.167 

1 

456.02? 

850.556 

390.913 

729.048 

342.141 

637.917 

304.188 

567.037 

273.839 

510.333 

2 

456.199 

850.833 

391.090 

729.286 

342.270 

638.125 

304.303 

567.222 

273.943 

510.500 

3 

456.371 

8r>i.ni 

391.238 

729.524 

3  1  2.  399 

G38.333 

304.417 

567.407 

274.046 

.110.667 

4 

456.543 

851.389 

391.385 

729.762 

342.528 

638.542 

304.532 

567.593 

274.149 

510.833 

5 

456.715 

851.667 

391.532 

730.000 

342.657 

638.750 

•304.647 

567.778 

274.252 

511.000 

6 

456.882 

851.944 

391.676 

730.238 

S42.782 

638.958 

304.758 

567.963 

274.353 

511.167 

7 

457.  049 

852.222 

391.819 

730.476 

342.908 

639.167 

304.870 

568.148 

274.453 

511.333 

8 

457.221 

S52.500 

391.967 

730  714 

•343.037 

639.375 

304.985 

568.333 

274.557 

511.500 

9 

457.393 

852.77'S 

392.114 

730.952 

343.166 

639.583 

305.099 

568.519 

274.660 

511  667 

1O 

457.565 

853.056 

'392.261 

731  .  190 

343  295 

639.792 

305.214 

568.704 

274.763 

511.833 

11 

457.737 

853.333 

392.409 

731.429 

343.424 

640  000 

305.329 

56*.  889 

274.866 

512.000 

12 

457.909 

853.611 

392.556 

731.667 

343.553 

640.208 

305.443 

569.074 

274.970 

512.167 

13 

458.081 

853.889 

392.704 

731.905 

343.682 

640.417 

305.558 

569.259 

275.073 

512.333 

14 

458.253 

854.167 

392  851 

732.143 

343.811 

640.625 

305.673 

569.444 

275.176 

512.500 

15 

458.425 

854.444 

392.999 

732.381 

343.940 

640.833 

305.788 

569.630 

275.279 

512.667 

16 

458.592 

854.722 

393.142 

732.619 

314.065 

641.042 

305.899 

569.815 

275.380|512.833 

17 

458.759 

855.000 

393.285 

732.857 

344.191 

641.250 

306.011 

570.000 

275.480513.000 

18 

458.931 

855.278 

393.433 

733.095 

344.320 

641.458 

306.125 

570.185 

275.583 

513.167 

19 

459.103 

855.556 

393.580 

73-3.333 

344.449 

641.667 

306.240 

570.370 

275.687 

513.333 

20 

459.275 

855.833 

393.727 

733.571 

344.578 

641.875 

306.355 

570.556 

275.790513.500 

21 

459.447 

856.111 

393.875 

733.810 

344.707 

642.  083 

306.469 

570.741 

275.893 

513.667 

22 

459.619 

«56.389 

394.  (22 

734.048 

344.836 

642.292 

306.584 

570.926 

275.996 

513.833 

23 

459.791 

856.667 

394.170 

734.286 

344.965 

642.  5ul 

306.699 

571.111 

276.  100 

514.00C 

24 

459.963 

856.944 

394.317 

734.524 

345.094 

642.708 

306.814 

571.296 

276.203 

514.167 

25 

460.135 

857.222 

394.465 

734.  76L 

345.223 

642.917 

306.928 

571.481 

276.3d6 

514.333 

26 

460.302 

857.500 

394.608 

735.000 

345.348 

643.125 

307.040 

571.667 

276.407 

514.500 

21 

460.469 

857.778 

394.751 

735.  23b 

345.474 

643.333 

307.151 

571.852 

276.507 

514.667 

28 

460.  641 

858.056 

394.899 

735.476 

345.603 

643.542 

307.266 

572.037 

276.610 

514.833 

29 

460.813 

858.333 

395.046 

735.714 

345.732 

643.750 

307.381 

572.222 

276.714 

515.000 

3O 

460.985 

858.611 

395.193 

735.952 

345.861 

643.958 

307.495 

572.407 

276.817 

515.167 

31 

461.157 

858.889 

395.341 

736.190 

345.990 

644.167 

307.610 

572.593 

276.920 

515.333 

32 

461.329 

859.167 

395.488 

736.429 

346.119 

644.  37f 

307.725 

572.778277.023 

515.500 

33 

461.501 

859.444 

395.636 

736.6(57 

346.248 

644.  583 

307.840 

572.963 

277.127 

515.667 

34 

461.673 

859.722 

395.783 

736.905 

346.377 

644.792 

307.954 

573.148 

277.230 

515.833 

35 

461.845 

860.000 

395.931 

737.143 

346.506 

645.000 

308.069 

573.333 

277.333 

516.000 

36 

462.017 

860.278 

396.078 

737.381 

346.635 

645.208 

308.184 

573.519 

277.436 

516.167 

37 

462.189 

860.556 

396.225 

737.619 

340.764 

645.417 

308.298 

573.704 

277.540 

516,333 

38 

462.361 

860.833 

396.373 

737.857 

346.893 

645.625 

308.413 

573.889 

277.643 

516.500 

39 

462.533 

861.111 

396.520 

738.09? 

347.022 

645.833 

308  528 

574.074 

277.746 

516.667 

40 

462.705 

861.389 

396.668 

738.333 

347.151 

646.042 

308.643 

574.259 

277.849 

516.833 

41 

462.877 

861.667 

396.815 

738.571 

347.280 

646.250 

308.757 

574.444 

277.953 

517.000 

42 

463.049 

861.944 

396.963 

738.810 

347.409 

646.458 

308.872 

574.630 

278.056 

517.167 

43 

463.221 

862.222 

397.110 

739.048 

347.538 

646.667 

308.987 

574.815 

278.159 

517.333 

44 

463.388 

862.500 

397.253 

739.286 

347.663 

646.875 

309.098 

575.000 

278.260 

517.5CK 

45 

463.555 

862.778 

397.397 

7'39.524 

347.789 

647.083 

309.210 

575.  185 

278.360 

517.667 

46 

463.727 

863.056 

397.544 

739.762 

347.918 

647.292 

309.324 

575.370 

278.463 

517.833 

47 

463.899 

863.333 

397.691 

740.  (XX 

348.047 

647.500 

309.439 

575.556 

278.567 

518.000 

48 

464.071 

863.61J 

397.839 

740.238 

348.170 

647.708 

309.554 

575.741 

278.670 

518.167 

49 

464.243 

863.889 

397.986 

740.476 

348.305 

647.917 

309.669 

575.926 

278.773 

518.333 

50 

464.415 

864.16; 

398.134 

740.714 

348.434 

648.125 

309.783 

576.111i278.  876 

518.500 

51 

464.587 

864.444  398  281 

740.952 

348.563 

648.333 

309.898 

576.  296  '278.  980 

518.667 

52 

464.759 

864.722 

398.429 

741.190 

348.692 

648.542 

310.013 

576.  481  i279.083 

518.833 

53 

464  931 

865.  00!  i 

398.576 

741.429 

348.821 

648.750 

310.127 

576.667279.186 

519,000 

54 

465.103 

865.278 

398.723 

741.667 

348.950 

648.958 

310.242 

576.852279.289 

519.167 

55 

465.275 

865.556 

398.871 

741.905 

349.079 

649.167 

310.357 

577.037279.393 

519.333 

56 

465.447 

865.833 

399.018 

742.143 

349.208 

649.375 

310.472 

577.222279.490 

519.500 

57 

465.619 

866.111 

399.166 

742.381 

349.837 

649.583 

310.586 

577.407279.599 

519.667 

58 

465.  791  1866.389 

399.313 

742.619 

349.466 

649.792 

310.701 

577.593279.703 

519.833 

59 

149 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


53° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~O~ 

,2794.  52 

5200.00 

1397.31 

.'000.00,931.603 

1733.33 

698.706 

1300.00 

5.59.075 

1040.00 

1 

2795.55 

5-201.67 

1397.83 

2600.83 

931.947 

1733.89 

699.024 

1300.4-2 

559.281 

1040.33 

2 

2796.58 

5203.33 

1398.34 

'601.67 

932.291 

1734.44 

699.282 

1300.83 

559  488 

1040.67 

3 

2797.62 

5205.00 

1398.86 

2602.50 

932.635 

1785.00699.540 

1301.25 

559.694 

1041.00 

4 

2798.65 

5206.67 

1399.158 

2603.33 

932.971) 

1735.56699.797 

1301.67 

559.900 

1041.33 

5 

2799.68 

5208.33 

1399.89 

26i)4.17 

933.322 

1736.lli700.055 

1302.08 

560.107 

1041.67 

6 

2800.71 

5210.00 

1400.41 

2605.00 

933.666 

1736.  67(700.  31  3 

1302.50 

560.313 

1042.00 

7 

2801.74 

5211.67 

1400.92 

2605.83 

934.010 

1737.  22!700.  571 

1302.92 

500.519 

1042.33 

8 

2802.77 

5213.33 

1401.44 

2606.67 

9-34.354 

1737.78 

700  829 

1303.  33 

560.726 

1042.67 

9 

2803.80 

5215.00 

1401.95 

2607.50 

934.698 

1738.33 

701.087 

1303.75 

560.932 

1043.00 

1O 

2804.84 

5216.67 

1402.47 

2608.33 

9a5.041 

1738.89 

701.345 

1304.17 

561.138 

1043.33 

11 

2805.87 

5218.33 

1402.98 

2609.17 

935.385 

1739.44 

701.603 

1304.58 

561.345 

1043.67 

13 

2806.90 

5220.00 

1403.50 

2610.00 

935.729 

1740.00 

701.861 

1305.00 

561.551 

1044.00 

13 

2807.96 

5221.67 

1404.03 

2610.83 

936.082 

1740.56 

702.126 

1305.42 

561.763 

1044.  as 

14 

2809.02 

5223.33 

1404.56 

2611.67 

936.436 

1741.11 

702.391 

1305.83 

501.1)75 

1044.67 

15 

2810.05 

5225.00 

1405.08 

2612.50 

936.780 

1741.67 

702.648 

1306.25 

502.182 

1045.00 

16 

2811.08 

5226.67 

1405.59 

2613.33 

937.123 

1742.22 

702.906 

1306.67 

562.388 

1045.33 

17 

2812.11 

5228.33 

1406.11 

2614.17 

937.467 

1742.78 

703.164 

1307.08 

562.594 

1045.07 

18 

2813.14 

5230.00 

140(5.62 

2615.00 

937.811 

1743.33 

703.422 

1307.50 

562.  81  1 

1046.00 

19 

2814.1? 

5231.67 

1407.14 

2615.83 

938.155 

1743.89 

703.680 

1307.92 

563.007 

1046.33 

20 

2815.21 

5233.33 

1407.65 

2616.67 

938.499 

1744.44 

703.9.38 

1308.  as 

563.213 

1046.67 

21 

2816.24 

5235.00 

1408.17 

2617.50 

938.843 

1745.00 

704.196 

1308.75 

563.420 

1047.00 

22 

2817.2? 

5236.67 

1408.69 

2618.33 

9-59.186 

1745.56 

704.454 

1301).  17 

563.620 

1047.33 

23 

2818.30 

5238.33 

1409.20 

2619.17 

939.530 

1746.11 

704.712 

1309.58 

503.832 

1047.67 

34 

2819.33 

5240.00 

1409.72 

2620.00 

939.874 

1746.67 

704.969 

1310.00 

564.039 

1048.00 

35 

2820.36 

5241.67 

1410.23 

2620.83 

940.218 

1747.22 

705.227 

1310.42 

564.245 

1048.33 

36 

28-21.39 

5243.33 

1410.75 

2621.67 

940.562 

1747.78 

705.485 

1310.83 

564  451 

1048.67 

37 

2822.43 

5245.00 

1411.26 

262-2.50 

910.905 

1748.33 

705.743 

1311.25 

564.658 

1049.00 

28 

2823.46 

5246.67 

1411.78 

2623.3'} 

941.249 

1718.89 

700.001 

1311.67 

564.864 

10-19.  33 

39 

2824.52 

5248.33 

141.2.31 

2024.  i; 

U41.603 

1749.44 

70t5.260 

1312.08 

50.5.  071 

1049.67 

30 

2825.58 

5250.00 

1412.84 

2625.00 

941.056 

1750.00 

706.531 

1312.50 

565.288 

1050.00 

31 

2826.61 

5251  .  67 

1413  36 

2625.83 

942.300 

1750.50 

700.789 

1312.92 

50.5.494 

1050.33 

33 

2827.64 

5253.33 

1413.87 

2626.67 

942.644 

1751.11 

707.047 

1313.33 

56c.701 

1050.67 

33 

2828.67 

5255.00 

1414.39 

2627.50 

942.987 

1751.67 

707.305 

1313.75 

565.907 

1051.00 

34 

2829.70 

5256.67 

1414.90 

2628.33 

943.331 

1752.22 

707.  563 

1314.17 

566.113 

1051.33 

35 

2830.73 

5258.33 

1415.42 

<J629.17 

943.675 

1752.78 

707.820 

131  4.  58 

566.320 

1051.67 

36 

2831.76 

5260.00 

1415.93 

2630.00 

944.019 

1753.  as 

708.078 

1315.00 

566.526 

1052.00 

37 

2832.80 

5261.67 

1416.45 

2630.83 

944.303 

1753.89 

708.  336 

1315.45 

566.732 

1052.33 

38 

2833.83 

5263.33 

1416.97 

2631.67 

1)44.706 

1754.44 

708.594 

1315.83 

566.939 

1052.67 

39 

2834.86 

5265.00 

1417.48 

2632.50 

945.050 

1755.00 

708.852 

1316.  '25 

567.145 

1053.00 

40 

2835.89 

5266.67 

1418.00 

2633.33 

945.394 

1755.56 

709.110 

1316.67 

567.351 

1053.33 

41 

2830.95 

5268.33 

1418.53 

2634.17 

945.747 

1756.11 

709.375 

1317.08 

567.563 

1053.67 

43 

2838.01 

5270.00 

1419.06 

2635.00 

946.101 

1756.67 

709.640 

1317.50 

567.775 

1054.00 

43 

2839.04 

5271.67 

1419.57 

2685.83 

946.445 

1757.22 

709.898 

1317.92 

567.982 

1054.33 

44 

2840.07 

5273.33 

1420.09 

2636.67 

946.788 

1757.78 

710.150 

1318.33 

568.188 

1054.67 

45 

2841.10 

5275.00 

1420.60 

2637.50 

947.132 

1758.33 

710.414 

1318.75 

568.394 

1055.00 

46 

2842.14 

5276.67 

1421.12 

2638.33 

947.476 

1758.89 

710.672 

1319.17 

568.601 

1055.33 

47 

2843.17 

5278.  as 

1421.64 

2639.17 

947.820 

1759.44 

710.929 

1319.58 

568.807 

1055.67 

48 

2844.20 

5280.00 

1422.15 

2640.00 

948.164 

1760.00 

711.187 

1320.00 

569.013 

1056.00 

49 

•2845.26 

5281.67 

1422.68 

2640.83 

948.517 

1760.56 

711.452 

1320.42 

569.225 

1056.33 

5O 

2846.32 

5283.33 

1423.21 

2641.67 

948.870 

1761.11 

711.717 

1320.83 

569.438 

1056.67 

51 

2847.35 

5285.00 

1423.73 

2642.50 

949/214 

1761.67 

711.975 

1321.25 

563.644 

1057.00 

53 

2848.38 

5286.67 

1424.24 

2643.33 

949.558 

1762.22 

712.233 

1321.67 

569.850 

1057.33 

53 

2849.41 

5288.33 

1424.76 

2644.17 

949.902 

1762.78 

712.491 

1322.08 

570.057 

1057.67 

54 

•2850.44 

5290.00 

1425  27  j  2645.  00 

950.240 

1703.33 

712.749 

1322.50 

570.263 

1058.00 

55 

2851.50 

5291.67 

1425.80:26-45.83  950.591)  1763.89 

713.014  1  1322.  92 

570.475 

1058.33 

50 

2852.56 

5293.33 

1426.33,2646.67  950.95-2  1764.44  713.279 

1323.ai 

570.687 

1058.67 

57 

2853.59 

5295.00 

1426.85  2647.50  951.296  1765.00  713.537 

1323.75 

570.893 

1059.00 

58 

2854.  63 

5296.67 

1427.37  2648.33  9M.640  1765.50 

713.795 

1324.17 

571.100 

1059.33 

59 

2855.66 

5298.33 

1427.88,2649.17,951.98411766.11 

714  053 

1324  58 

571.306 

1059.67 

150 


TABLE  XIV. — ACTUAL  TANGENTS, ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve.        9°  Curve. 

10°  Curve.   \52° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  1   Arc. 

Tan. 

Arc. 

M. 

405.963 

866.667 

399.461 

742.857 

349.595 

650.  000  310.  816)577.  778 

279.  8C6 

520.0UO 

O 

466.135 

866.944 

399.608 

743*.  095 

349.724 

650.208310.930 

577.963 

279.909 

520.167 

1 

466.306 

867.222 

399.755 

743.333 

349.853 

650.417311.045 

578.148 

280.012 

520.333 

2 

466.478 

867.500 

399.903 

743.571 

349.982 

650.625311.160 

578.333 

280.116 

520.500 

3 

466.650 

867.778 

400.050 

743.810 

350.111 

650.833311.274 

578.519 

280.219 

520.667 

4 

466.822 

868.056 

400.198 

744.048 

350.240 

651.042311.389 

578.704 

280.322 

520.833 

5 

466.994 

8(18.333 

400.345 

744.286 

350.369 

651.250311.504 

578.889 

280.425 

521.000 

6 

467.166 

868.611 

400.493 

744.524 

350.498 

651.458:311.619 

579.074 

280.529 

521.167 

7 

467.3:38 

868.889 

400.640 

744.7C2 

350.627 

651.  667  131  1.733 

579.259 

280.632 

521.333 

8 

467.510 

869.167 

400.787 

7'45.000 

350.756 

651.875311.848 

579.444 

280.735 

521.500 

9 

467.682 

869.444 

400.935 

745.238 

350.  885 

652.083 

311.963 

579.630 

280.838 

521.667 

10 

467.854 

869.722 

401.082 

745.476 

351.014  652.292312  077  1  579.  81  5 

280.942 

521.833 

11 

468.026 

870.000 

401.230 

745.714 

351.143 

652.500312.192 

580.000 

281.045 

522.000 

12 

468.203 

870.278 

401.381 

745.952 

351.276 

652.708312.310 

580.185 

281.151 

522.167 

13 

468.380 

870.556 

401.533 

746.190 

351.409 

652.917|312.428 

580.370 

281.257 

522.333 

14 

468.552 

870.833 

401.G80 

746.429 

351.538 

653.125312.543 

580.556 

281.360 

522.500 

15 

468.724 

871.111 

401.828 

746.667 

351.667 

653.333312.657 

580.741 

281.464 

522.667 

16 

468.896 

871.389 

401.975 

746.905 

351.796 

653.542312.772 

580.926 

281.567 

522.833 

17 

469.068 

871.667 

402.122 

747.143 

351.925 

653.750312.887 

581.111 

281.670 

523.000 

18 

469.239 

871.944 

402.270 

747.381 

352.051 

653.958 

313.001 

581.296 

281.774 

523.167 

19 

469.411 

872.222 

402.417 

747.619 

352.183 

654.167 

313.116 

581.481 

281.877 

523.333 

20 

469.583 

872.500 

402.565 

747.857 

352.312 

654.375313.231 

581.667 

281.980 

523.500 

21 

469.755 

872.778 

402.712 

748.095 

352.441 

654.583313.346 

581.852 

282.083 

523.667 

22 

469.927 

873.056 

402.860 

748.333 

352.570 

654.792313.460 

582.037 

282.187 

523.833 

2*3 

470.099 

873.333 

403.007 

748.571 

358.699 

655.  0001313.  57  5 

582.222 

282.290 

524.000 

24: 

470.271 

873.611 

403.154 

748.810 

352.828 

655.208J313.690 

582.407 

282.398 

524.167 

25 

470.443 

873.889 

403.302 

749  048 

352.957 

655.417313.804 

582.593 

282.4% 

524.333 

26 

470.615 

874.167 

403.449 

749.286 

353.086 

655.625 

313.919 

582.778 

282.600 

524.500 

27 

470.787 

874.444 

403.597 

749.524 

353.215 

655.833314.034 

582.963 

282.703 

524.667 

28 

470.964 

874.  i&> 

403.748 

749.762 

353.347 

656.042314.152 

583.148 

282.809 

524.833 

29 

471.141 

875.000 

403.900 

750.000 

353.480 

056.250 

314.270 

583.333 

282.915 

525.000 

3O 

471.313 

875.278 

404.047 

750.238 

353.609 

H56.458 

314.384 

583.519 

283.018 

525.167 

31 

471.485 

875.550 

404.195 

750.476 

353.738 

656.667314.499 

583.704 

•^3.U'2 

525.333 

32 

471.657 

875.833 

404.342 

750.714 

353.867 

666.875814.614 

583.889 

283.225 

525.  5CO 

33 

471.829 

876.111 

404.489 

750.952 

353.996 

657.  083!  31  4.  728 

584.074 

283.328 

525.667 

34 

472.000 

876.389 

404  637 

751.190 

354.125 

657.2921314.843 

584.259 

283.431 

525.833 

35 

472.172 

876.667 

404.784 

751.429 

354.254 

657.500314.958 

584.444 

283.535 

526.000 

36 

472.344 

876.944 

404  932 

751.667 

854.888 

657.708 

315.073 

584.630 

283.638 

526.167 

37 

472.516 

877.222 

405.079 

751.905 

354.512 

657.917 

315.187 

584.  815 

283.741 

526.333 

38 

472.688 

877.500 

405.226 

752.143 

354.641 

658.125 

315.302 

585.000 

283.845 

526.500 

39 

472.860 

877.778 

405.374 

752.381 

354.770 

658.333315.417 

585.185 

283.948 

526.667 

40 

473.037 

878.056 

405.525 

752.619 

354.903 

658.  5421815.  535 

585.370 

284.054 

526.833 

41 

473  214 

878.333 

405.677 

752.857 

355.035 

658.750315.653 

585.556 

284.160 

527.000 

42 

473.386 

878.611 

405.824 

753.095 

355.164 

658.958 

315.767 

585.741 

284.263 

527.167 

43 

473.558 

87'8.8S9 

405.972 

753.333 

355.293 

659.167 

315.882 

585.926 

284  367 

527.333 

44 

473.730 

879.167 

406.119 

753.571 

355.422 

659.375 

315.997 

586.111 

284.470 

527.500 

45 

473.902 

879.444 

406.267 

753.810 

955.652 

659.583 

316.111 

586.296 

284.573 

527.667 

46 

474.074 

879.722 

406  414 

754.048 

355.681 

659.792 

316.226 

586.481 

284.676 

527.833 

47 

474.246 

880.  OTO 

406.561 

754.286 

355.810 

660.000 

316.341 

586.667 

284.780 

528.000 

48 

474.422 

880.278 

406.713 

754.524 

355.942 

660.208 

316.459 

586.852 

284.886 

528.167 

49 

474  599 

880.  r  56 

406.865 

754.762 

356.075 

660.417 

316.577 

587.037 

284.992 

528.333 

50 

474.771 

880.833 

407.012 

755.000 

356.204 

6(50.625 

316.691 

587.222 

285.095 

528.500 

51 

474.943 

881.111 

407.159 

755.238 

356.383 

660.833 

316.806 

587.407 

285.198 

528.667 

52 

475.115 

881.389 

407.307 

755.476  3515.462 

661.042 

316.921 

587.593285.302 

528.833 

53 

475.287 

881.667 

407.454 

755.714  356.591 

661.250 

317.035 

587.778*85.405 

52!).  000 

54 

475.464 

8S  1.1)44 

407.606 

755.902856  723 

(561.458 

317.153 

587.  9b3  285.  5  11 

5-/9.167 

55 

475.  640  1  882.  222 

407.757 

756.190356.856 

661.667 

317.271 

588.148285.617 

529.333 

56 

475.812882.500 

407.905 

756.429 

356.985 

661.875 

317.386 

588.333285.721 

529  .  f>00 

57 

475.984  8H2.778 

408.052 

756.667 

357.114 

662.083 

317.501 

588.519285.824 

529.6(57 

58 

476.156883.056 

408.200 

756.905 

357.243 

662.292317.615 

588.704  285.927  529.833 

59 

151 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


53° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

5300.00 

Tan. 

Arc. 

Tau. 
952.328 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

2856.69 

1428.40 

2650.00 

176H.07 

714.311 

1325.00 

571.512 

1000.00 

1 

2857.72 

5301.07 

1428.91 

2050.83 

1)52.672 

1707.22 

714.568 

1325.42 

571.719 

1000.33 

3 

2858.75 

5303.33 

1429.43 

2051.07 

953.015 

1707.78 

714.820 

1325.83 

571.925 

1060.67 

3  |  2859.81 

5305.00 

1429.96 

2652.50 

953.309 

1768.33 

715.091 

1326.25 

572.137 

1001.00 

4  2800.87 

5308.67 

1430.49 

2653.33 

953.722 

1708.89 

715.350 

1326.67 

572.349 

1001.33 

5  2801.90 

5308.  33 

1431.00 

2054.17 

954.006 

1709.44 

715.014 

1327.08 

572.555 

1061.07 

G 

2802.93 

5310.00 

1431.52 

2655.00 

9.54.410 

1770.00 

715.872 

1327.50 

572.702 

1062.00 

7 

2803.99 

5311.67 

1432.05 

2655.83 

954.703 

1770.56 

710.137 

1327.92 

572.974 

1002.33 

8 

2805.05 

5313.33 

1432.58 

2056.07 

955.110 

1771.11 

710.402 

1328.33 

573.180 

1002.07 

9 

2800.09 

5315.00 

1433.10 

2657.50 

955.400 

1771.67 

710.660 

1328.75 

573.392 

1003.00 

1O 

2867.12 

5316.67 

14-33.61 

2658.33 

955.804 

1772.22 

716.918 

1329.17 

573.599 

1003.33 

11 

2868.15 

5318.33 

1434.13 

2659.17 

956.148 

1772.78 

717.176 

1329.58 

573.805 

1003.07 

12 

2809.18 

5320.00 

1434.64 

2660.00 

956.492 

1773.33 

717.434 

1330700 

574.011 

1004.00 

13 

2870.24 

5321.07 

1435.17 

2600.83 

956.845 

1773.89 

717.699 

1330.42 

574.2231004.33 

14 

2871.30 

5323.33 

1435.70 

2661.67 

957.198 

1774.44 

717.964 

1330.83 

574.435  1004.67 

15 

2872.33 

5325.00 

1436.22 

2662.50 

957.542 

1775.00 

718.222 

1331.25 

574.6421065.00 

16 

2873.30 

5320.07 

1436.73 

2663.33 

957.886 

1775.56 

718.480 

1331.67 

574.848  1065.33 

17 

2874.39 

5328.33 

1437.25 

2604.17 

958.230 

1776.11 

718.738 

1332.08 

575.0541065.67 

18 

2875.42 

5330.00 

1437.77 

2665.00 

958.574 

1776.67 

718.995 

1332.50 

575.201  1006.00 

19 

2876.48 

5331.67 

1438.30 

2665.83 

958.927 

1777.22 

719.261 

1332.92 

575.473 

1066.33 

20 

2877.54 

5333.33 

1438.83 

2666.67 

959.280 

1777.78 

719.526 

1333.33 

575.085 

1066.67 

21 

2878.58 

5335.00 

1439  34 

2667.50 

959.024 

1778.33 

719.783 

1  333.75 

575.891  1007.00 

22 

2879.61 

5336.67 

1439.86 

2668.33 

959.908 

1778.89 

720.041 

1334.17 

.170.097(1007.33 

23 

2880.07 

5338.33 

1440.39 

2669.17 

900.321 

1779.44 

72^.306 

1334.58 

576.309  1067.67 

21 

2881.73 

5340.00 

1440.92 

2670.00 

900.675 

1780.00 

720.571 

1335.00 

576.522  1068.00 

25 

2882.70 

5341.67 

1441.43 

2670.83 

961.019 

1780.56 

720.829 

1335.42 

576.7281068.33 

2G 

2883.79 

5343.33 

1441.95 

2671.67 

1)61.888 

1781.11 

721.087 

1335.83 

576.934  1068.67 

21 

2884.85 

5345.00 

1442.48 

2072.50 

961.710 

1781.67 

721.352 

1336.25 

577.140  1069.00 

2$ 

2885.91 

5346.67 

1443.01 

2673.33 

903.069 

1782.22 

721.017 

1336  07 

577.358 

1009.33 

29 

288(5.94 

5348.33 

1443.52 

2674.17 

962.413 

1782.78 

721.875 

1337.08 

577.565 

1069.67 

30 

2887.97 

5350.00 

1444.04 

2675.00 

962.757 

1783.33 

722.133 

1337.50 

577.771 

1070.00 

31 

2889.03 

5351.67 

1444.57 

2075.83 

903.110 

1783.89 

722.398 

1337.92 

577.983 

1070.33 

32 

2890.09 

5353.33 

1445.10 

2076.67 

963.463 

1784.44 

722.063 

1338.33 

578.195 

1070.07 

33 

2891.12 

5355.00 

1445.62 

2677.50 

963.807 

1785.00 

722.921 

1338.75 

578.401 

1071.00 

34 

2892.10 

5356.67 

1446.13 

2078.33 

964.151 

1785.56 

723.179 

1339.17 

578.608 

1071.33 

35 

2893.22 

5358.33 

1446.66 

2679.17 

964.504 

1786.11 

723.444 

1339.58 

578.814 

1071.67 

36 

2894.  2S 

5360.00 

1447.19 

2680.00 

964.858 

1786.07 

723.709 

1340.00 

579.020  1072.00 

37 

2895.31 

5361.67 

1447.71 

2080.83 

965.202 

1787.22 

723.967 

1340.42 

579.23211072.33 

38 

2896.34 

5363.33 

1448.22 

2681.67 

965.545 

'787.78 

724.225 

1340.83 

579.415  1072.67 

39 

2897.40 

5365.00 

1448.75 

2682.50 

905.899 

788.33 

724.490 

1341.25 

579.657 

1073.00 

40 

2898.46 

5366.67 

1449.28 

2683.33 

963.252 

788.89 

724.755 

1341.67 

579.809 

1073.33 

41 

2899.49 

5368.33 

1449.80 

2084.17 

906.596 

789.44 

725.013 

1342.08 

580.075 

1073.07 

42 

29:>0.52 

5370.00 

1450.31 

2085.00 

960.940 

790.00 

725.271 

1342.50 

580.281 

1074.00 

43 

2901.58 

5371.67 

1450.84 

2085.83 

9(57.293 

1790.56 

725.530 

1342.92 

580.493  1074.33 

44   2902.64 

5373.33 

1451.37 

2086.67 

967.617 

1791.11 

725.801 

1313  33 

580.  705  '1074.  07 

45   2903.07 

5375.00 

1451.89 

2687.50 

967.990 

1791.67 

726.059 

1343  75 

580.9121075.00 

46   2904.70 

5376.67 

1452.40 

2688.33 

968.334 

1792.22 

726.317 

1344.17 

581.  11  8!  1075.  33 

47  [2905.76 

5378.33 

1452.93 

2689.17 

968.088 

1792.78 

726.582 

1344.58 

581.  330;  1075.  07 

48  '2006.82 

5380.00 

1453.46 

2690.00 

969.041 

1793.33 

726.847 

1345.00 

581.542  1076.00 

49 

2907.85 

5381.67 

1453.98 

2690.83 

969.385 

1793.89 

727.105 

1345.42 

581.749 

1076.33 

50 

2908.89 

5383.33 

1454.50 

2691.67 

969.729 

1794.44 

727.362 

1345.83 

581.955 

1076.67 

51 

2909.95 

5385.00 

1455.03 

2692.50 

970.082 

1795.00 

727.627 

1316.25 

58  J.I  07;  1077.  00 

52 

2911.01 

5386.67 

1455.56 

2693.33 

970.435 

1795.56 

727.892 

1346.07 

582.379  1077.33 

53 

2912.07 

5388.33 

1456.09 

2694.17 

970.789  1790.11 

728.  15S 

1347.08 

582.591  1077.07 

54 

2913.13 

5390.00 

1456.62 

2695.00 

971.1421796.07 

728  423 

1317  50 

582.  S03  1078.00 

55 

2914.16 

5391.67 

1457.13 

2095.83 

971.486  1797.22 

728.080  1347.92 

583.009  1078.33 

56 

2915.19 

5393.33 

1457.65 

2096.67 

971.8301797.78 

728.938  13l8.:J,3i583.216  1078.07 

57 

2916.25 

5395.00 

1458.18 

2097.50 

972.183  1798.33 

729  .  203  1  3  48  .  75  5«3  .  428  1  079  .  00 

58 

2917.31 

5396.67 

1458.71 

2698.33 

972.530  1798.89 

729  .  408  1  3  10.1  7  583  .(3401  01  9  .  33 

59 

2918.37 

5398.33 

1459.24 

2099  17 

972.890  1799.44 

729.733  1319.58!583.852  1079.07 

152 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

53- 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

476.328 

8837333 

408.347 

757.143 

357.372 

662.500 

317.730588.889 

286.030 

530.000 

O 

476.500 

883.611 

408.494 

757.381 

357.501 

662.7081317.845589.074 

286.134 

530.167 

1 

476.672 

883.889 

408.642 

757.619 

357.630 

662.917 

317.959589.259 

286.247 

530.333 

2 

476.849 

884.167 

408.793 

757.857 

357.763 

663.125 

318.077 

589.444 

286.343 

530.500 

3 

477.026 

884.444 

408.945 

758.095 

357.895 

663.333 

318.195 

589.630 

286.449 

530.667 

4 

477.198 

884.722 

409.092 

758.333 

358.024 

663.542 

318.310 

589.815 

286.552 

530.833 

5 

477.370 

885.000 

409.240 

758.571 

358.153 

663.750 

318.425 

590.000 

286.656 

531.000 

6 

477.546 

885.278 

409.391 

758.810 

358.286 

063.958 

318.543 

590.185 

286.762 

531.167 

7 

477.723 

885.556 

409.543 

759.048 

358.419 

664.167 

318.660 

590.370 

286.868 

531.333 

3 

477.895 

885.833 

409.690 

759.286 

358.548 

664.375 

318.775 

590.556 

286.971 

531.500 

9 

478.067 

886.111 

409.838 

759.524 

358.677 

664.583 

318.890 

590.741 

287.074 

531.667 

10 

478.239 

886.389 

409.985 

759.762 

358.806664.792 

319.005 

590.926 

287.178 

531.833 

11 

478.411 

886.667 

410.132 

760.000 

358.935665.000 

319.119 

591.111 

287.281 

532.000 

12 

478.588 

886.944 

410.284 

760.238 

359.0671665.208 

319.237 

591.296 

287.387 

532.167 

13 

478.765 

887.222 

410.435 

760.476 

359.  200  1665.417 

319.355 

591.481 

287.493 

532.333 

14 

478.936 

887.500 

410.583 

760.714 

359.329:665.625 

319.470 

591.667 

287.596 

532.  f,00 

15 

479.1  Ob 

887.778 

410.730 

760.952 

359.  458  1665.833 

319.584 

591.852 

287.700 

532.667 

16 

479.280 

888.056 

410.878 

761.190 

359.587 

666.042 

319.699 

592.037 

287.803 

532.833 

17 

479.452 

888.333 

411.025 

761.429 

359.716 

666.250 

319.814 

592.222 

287.906 

533.  OOC 

18 

479.629 

888.611 

411.177 

761.667 

359.849 

666.458 

319.932 

592.407 

288.012 

533.167 

19 

479.806 

888.889 

411.328 

761.905 

359.981 

666.667 

320.050 

592.593 

288.119 

533.333 

20 

479.978 

889.167 

411.476 

762.143 

360.110 

666.875 

320.164 

592.778 

288.222 

533.500 

21 

480.150 

889.444 

411.623 

762.381 

360.239 

667.083 

320.279 

592.963 

288.325 

533.667 

22 

480.327 

889.722 

411.775 

762.619 

360.372 

667.292 

320.397 

593.148 

288.431 

533.833 

23 

480.503 

890.  ('00 

411.926 

762.857 

360.504 

667.500 

320.515 

593.333 

288.537 

534.001 

24 

480.675 

890.278 

412.073 

763.095 

360.633 

667.708 

320.630 

593  519 

288.641 

534.167 

25 

480.847 

890.556 

412.221 

763.333 

360.762 

667.917 

320.744 

593.704 

288.744 

534.333 

26 

481.024 

890.833 

412.372 

763.571 

360.895 

668.125 

320.862 

593.889 

288.850 

534.  50( 

27 

481.201 

891.111 

412.524 

763.810 

361.028 

668.333 

320.980 

594.074 

288.956 

534.667 

28 

481.373 

891.389 

412.671 

764.048 

361.157 

668.542 

321.095 

594.259 

289.059 

534.833 

29 

481.545 

891.667 

412.819 

764.286 

361.286 

668.750 

321.210 

594.444 

289.163 

535.  00( 

30 

481.721 

891.944 

412.970 

764.524 

361.418 

668.958 

321.327 

594.630 

289.269 

535.167 

31 

481.898 

892.222 

413.122 

764.762 

361.551 

669.167 

321.445 

594.815 

289.375 

535.333 

32 

482.070 

892.500 

413.269 

765.  0()( 

361.680 

669.375 

321.560 

595.000 

289.478 

535.500 

33 

482.242 

892.778 

413.417 

765.238 

361.809 

669.583 

321.675 

595.185 

289.581 

535.667 

34 

482.419 

893.056 

413.568 

765.476 

361.942 

669.792 

321.793 

595.370 

289.688 

535.833 

35 

482.596 

893.333 

413.720 

765.714 

362.074 

670.000 

321.911 

595.556 

289.794 

536.000 

36 

482.768 

893.611 

413.867 

765.952 

362.203 

670.208 

322.025 

595.741 

289.897 

536.167 

37 

482.939 

893.889 

414.015 

766.190 

362.332 

670.417 

322.140 

595.926 

290.000 

536.333 

38 

483.116 

894.167 

414.166 

766.429 

362.465 

670.625 

322.258 

596.111 

290.106 

536.500 

39 

483.293 

894.444 

414.318 

766.667 

362.597 

670.833 

322.376 

596.296 

290.213 

536.667 

40 

4&3.46S 

894.722 

414.465 

766.905 

362.726 

671.042 

322.490 

596.481 

290.316 

536.833 

41 

483.637 

895.000 

414.612 

767.143 

362.855 

671.250 

322.605 

596.667 

290.419 

537.000 

42 

483.814 

895.278 

414.764 

767.381 

362.988 

671.458 

322.723 

596.852 

290.525 

537.167 

43 

483.990 

895.556 

414.915 

767.619 

363.121 

671.667 

322.841 

597.037 

290.631 

537.333 

44 

484  162 

895.833 

415.063 

767.857 

363.250 

671.875 

322.956 

597.222 

290.735 

537.500 

45 

484.334 

896.111 

415.210 

768.095 

363.379 

672.083 

323.070 

597.407 

290.838 

537.667 

46 

484.511 

896.389 

415.362 

768.333 

363.511 

672.292 

323.188 

597.593 

290.944 

537.833 

47 

484.688 

896.667415.513 

768.571 

363.644 

672.500 

323.306 

597.778 

291.050 

538.000 

48 

484.860 

896.944 

415.661 

768.810 

363.773 

672.708 

323.421 

597.963 

291.153 

538.167 

49 

485.032 

897.222 

415.808 

769.048 

363.902 

672.91? 

323.536 

598.148 

291.257 

538.333 

50 

485.208 

897.500 

415.960 

769.286 

364.035 

673.125 

323.653 

598.333 

291.363 

538.500 

51 

485.385 

897.778 

416.111 

769.524 

364.167 

673.333 

323.771 

598.519 

291.469 

538.667 

52 

485.562 

898.056 

416.263 

769.762 

364.300 

673.542 

323.889 

598.704 

291.575 

538.833 

53 

485.739 

898.333 

416.414 

770.000 

364.432 

673.750 

324.007 

598.889 

291.681 

539.000 

54 

485.911 

486.083 

898.611 
898.889 

416.562 
416.709 

770.238 
770.476 

364.561  673.958 
364.690674.167 

324.122 
324.237 

599.074 
599.259 

291.784 
291.888 

539.167 
539.333 

55 
56 

486.2591899.167 

416.861 

770.714  364.823  674.375 

324.354 

599.444 

291.994 

539.500 

57 

486.436899.444 

417.012 

770.952 

364.956674.583 

324.472 

599.630 

292.100 

539.667 

58 

486.613i899.722417.164 

771  .  190 

365.088674.792 

324.590 

599.815  292.206 

539.833 

59 

153 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


54° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M[7 

~o~ 

Tan. 
2919743 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

584.004 

Arc. 

5400.00 

1459.77 

2  -00.00 

973.243 

1SOO.OO 

729.999 

1350.00 

1080.00 

1 

2920.46 

5401.6? 

14i;0.2,s 

2?  00.  &i 

913.587 

IKK).  50 

730.250 

1350.42 

584.270 

1080.33 

3 

2921.49 

5403  33 

1400.80 

2?01.6: 

9  Hi.  931 

1801.11 

730.514 

1350.83 

584.477 

1080.07 

3 

2922.55 

5405  .  00 

1461.33 

2702.50 

J74.384 

1801.67. 

730.779 

1351.25 

584.089 

1081.00 

4 

2923.61 

5406.6? 

1461.86 

2703.33 

•J74.G37 

1802.22 

731.044 

1351.67 

584.901 

1081.33 

5 

2924.67 

5408.33 

1462  39 

2704.1? 

974.991 

1802.78 

731.309 

1352.08 

585.113  1(81.67 

6 

2925.73 

5410.00 

1462.92 

2705.0.1 

975.344 

1803.33 

731.574 

1352.50 

585.325 

1082.00 

7 

2926.76 

5411.6? 

1463.43 

2705.83 

975.688 

1803.89 

731.832 

1352.92 

585.531 

1083.33 

8 

2927.79 

5413.33 

1463.95 

2706.67 

976.032 

1804.44 

732.090 

1353.33 

585.738 

1082  67 

9 

2928.85 

5415.00 

1464.48 

2707.50 

976.385 

1805.00 

732.355 

1353.75 

585.950 

1083.00 

1O 

2929.91 

5416.67 

1465.01 

2708.33 

i)76.739 

1805.56 

732.620 

1354.17 

586.162 

1083.33 

11 

2930.97 

5418.33 

1465.54 

2709.1? 

977.092 

1806.11 

732.885 

1354.58 

586.374  1083.67 

12 

2932.03 

5420.00 

1466.07 

2710.00 

977.445 

1806.67 

733.150 

1355.00 

586.580:1084.00 

13 

2933.07 

5421.6? 

1466.5'J 

2710.83 

977.789 

1807.22 

733.408 

1355.42 

580.792  1084.33 

14 

2934.10 

5423.33 

1467  10 

2711.6? 

978.133 

1807.78 

733.666 

1355.83 

580.999  1084.67 

15 

2935.16 

5425.00 

1467.63 

2712.50 

978.486 

1808.33 

733.931 

1356.25 

587.211  1085.00 

16 

2936.22 

5426.67 

1468.16 

2713.83 

978.840 

1808.89 

734.190 

1356.6? 

587.4231085.33 

17 

2937.28 

5428  33 

1468.69 

2714.17 

979.193 

1809.44 

734.461 

1357.08 

587.635  1085.67 

18 

2938  34 

3  430.  00 

1469.22 

2715.00 

979.546 

1810.00 

734.726 

1357.50 

587.847  1086.00 

19 

2939.37 

5431.6? 

1469.74 

2715.83 

979.890 

1810.56 

734.984 

1357.92 

588.053 

1086.33 

30 

2940.40 

5433.33 

1470.25 

2716.67 

980.234 

1811.11 

735.242 

1358.33 

588.259 

1086.67 

31 

2941.46 

5435.00 

1470.78 

2717.50 

980.587 

1811.67 

735.50? 

1358.75 

588.  4?  1(1087.00 

33 

2942.52 

5436.67 

1471.31 

2718.33 

980.941 

1812.22 

735.772 

1359.17 

588.684J1087.33 

33 

2943.58 

54138.33 

1471.84 

2719.1? 

981.294 

1812.78 

736.037 

1359.58 

588.896 

1087.67 

34 

2944.64 

5440.00 

1472.37 

2720.00 

981.647 

1813.33 

736.302 

1360.00 

589.108 

1088.00 

35 

2945.70 

5441.6? 

1472.90 

2720.83 

982.001 

1813.89 

736.567 

1360.42 

589.320 

1088.33 

36 

2946.76 

5443.33 

1473.43 

2721.67 

982.354 

1814.44 

736.832 

1360.83 

589.532 

1088.67 

37 

2947.82 

5445.00 

1473.96 

2722.50 

982.708 

1815.00 

737.098 

1361  25 

589.744 

1089.00 

38 

2948.88 

5446.6? 

1474.49 

2723.33 

983.061 

1815.56 

737.303 

1301.67 

589.950 

1089.33 

39 

2949.91 

5448.33 

1475.01 

2724.1? 

983.405 

1816.11 

737.620 

1362.08 

590.162 

1089.67 

30 

2950.94 

5450.00 

1475.52 

2725.00 

983.749 

1816.67 

737.878 

1362.50 

590.309 

1090.00 

31 

2952.00 

5451.6? 

1476.05 

2725.83 

984.102 

1817.22 

738.143 

1362.92 

590.581 

1090.33 

33 

2953.06 

5453.33 

1476.58 

2726.67 

984.455 

1817.78 

738.408 

1363.33 

590.793 

1090.67 

33 

2954.12 

5455.00 

1477.11 

2727.50 

984.809 

1818.33 

738.673 

1363.75 

591.005 

1091.00 

34 

2955.18 

5456.67 

1477.64 

2728.33 

1)85.162 

1818.89 

738.939 

1364.17 

591.217 

1091.33 

35 

2956.24 

5458.33 

1478.17 

2729.17 

985.516 

1819.44 

739.204 

1364.58 

591.429 

1091.67 

36 

2957.30 

5460.00 

1478.70 

2730.00 

985.869 

1820.00 

739  469 

1365.00 

591.641 

1092.00 

37 

2958.36 

5461.6? 

1479.23 

2730.83 

986.222 

1820.56 

739.734 

1365.42 

591.853!  1092.  33 

38 

2959.42 

5463.33 

1479.76 

2131.6? 

986.575 

1821.11 

739.999 

1365.83 

592.065  1092.67 

39 

2960.48 

5465.00 

1480.30 

2732.50 

986.929 

1821.67 

740.264 

1366.25 

592.277 

1093.00 

40 

2961.54 

5466.67 

1480.83 

2733.33 

987.282 

1822.22 

740.529 

1366.6? 

592.489 

1093.33 

41 

2962.57 

5468.33 

1481.34 

2734.17 

987.626 

1822.78 

740.78? 

1367.08 

592.696  1093.67 

43 

2963.60 

5470.00 

1481.86 

2735.00 

987.970 

1823.33 

741.045 

1367.50 

592.902  1094.00 

43 

2964.66 

5471.67 

1482.39 

2735.83 

988.323 

1823.89741.310 

1367.92 

593.114  1  094.3  S 

44 

2965.72 

5473.33 

1482.92 

2736.67 

988.677 

1824.441741.575 

1368.331593.320 

1094.67 

45 

2966.78 

5475.00 

1483.45 

2737.50 

989.030 

1825.00:741.840 

1368.  75  1  593.  538 

1095.00 

46 

2967.84 

5476.67 

1483.98 

2738.33 

989.383 

1825.56 

742.105 

1369.17 

593.750  1095.33 

47 

2968.90 

5478.33 

1484.51 

2739.17 

989.737 

1826.11 

742.370 

1369.58 

593.962  1095.07 

48 

2969.96 

5480.00 

1485  04 

2740.00 

990.090 

1826.6? 

742.635 

1370.  00  594.1741  1096.  00 

49 

2971.02 

5481.67 

1485.57 

2740.83 

990.443 

1827.22 

742.900 

1370.42 

594.386 

1096.33 

5O 

2972.08 

5483.33 

1486.10 

2741.67 

990.797 

1827.78 

743.165 

1370.83 

594.598 

1096.67 

51 

2973.14 

5485.00 

1486.63 

2742.50 

991.150 

1828.33743.430 

1371.25:594.810 

1097.00 

53 

2974.20 

5486  67 

1487.16 

2743.33 

991.503 

1828.89743.695 

1371.67595.022 

1097.33 

53 

2975.26 

5488.33 

1487.69 

2744.17 

991.857 

1829.44743.960 

1372.08595.235 

1097.07 

54 

2976.32 

5490.00 

1488.22 

2745.00 

992.210 

1830.00744.225 

1  372.  50  :  595.  447 

1098.00 

55  2977.385491.67 

1488.752745.83 

992.564 

1830.56  744.490  1372.92  595.  659!  1098.  33 

5612978.445493.33 

1489.  28  [2746.  67 

992.917 

1  83  1  .  1  1  744  .  755  !  1  373  .  33  595  .  871  1  098  .  67 

57  3979.505495.00 

1489.81 

2747.50 

993  .  270  1  83  1  .  67  74  1  .  020  1  1  373  .  75  596  .  083  1  099  00 

58  2980.565496.67 

1490.34 

2748.33 

993  .  624  1832  .  22  745  .  285  j  1374  .  1  ?  5.  -6  .  295  1  099  .  33 

5912981.625498.33 

1490.8? 

2749  1  7 

993  .  9771  1  832  .  78  745  .  550!  1374  .  58  59(1  .  507  1  099  .  67 

154 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

54° 

Tan. 

Arc. 

Tan. 

417.315 

Arc. 

771  .429 

Tau. 
365.221 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

540.000 

M7 

~o" 

486.790 

JOO.OOO 

675.000 

324.708 

600.000 

292.312 

486.962 

900.  27S 

417.463 

771.667 

365.350 

675.208:324.823 

600.185 

292.415 

540.167 

i 

487.134 

900.550 

417.610 

771.905 

365.479 

675.  41  7  j  324.  938 

600.370 

292.519 

540.333 

2 

487.310 

900.833 

417.762 

772.143 

365  612 

675.625325.055 

600.556 

292.625 

540.500 

3 

487.487 

901.111 

417.913 

772.381 

365.744 

675.833 

325.173 

600.741 

292.731 

540.667 

4 

487.664 

901.3=9 

418.065 

772.619 

365.877 

676.042 

325.291 

600.  926'  292.  837 

540.833 

5 

487.841 

901.667 

418.216 

772.857 

366.009 

676.250 

325.409 

601.111 

292.943 

541.000 

6 

488.  012 

901.944 

418.364 

773.095 

366.138 

676.458 

325.524 

601.296 

293.047 

541.167 

7 

488.184 

902.222 

418.511 

773.333 

366.267 

676.667 

325.639 

601.481 

293.150 

541.333 

8 

488.361 

902.500 

418.662 

773.571 

366.400 

676.875 

325.756 

601.667 

293.256 

541.500 

9 

488.538 

902.778 

418.814 

773.810 

366.533 

677.083 

325.874 

601.852 

293.362 

541.667 

1O 

488.715903.056 

418.966 

774.048 

366.665 

677.292 

325.992 

602.037 

293.468 

541.833 

11 

488.891  903.333 

419.117 

774.280 

366.798 

677.500 

326.110 

602.222 

293.574 

542.000 

12 

489.063903.611 

419.264 

774.524 

366.927 

677.708 

326.225 

602.407 

293.678 

542.167 

13 

489.235903.889 

419  412 

774.762 

367.056 

677.917 

326.340 

602.593 

293.781 

542.333 

14 

489.412904.167 

419.563 

775.000 

367.188 

678.125 

326.45? 

602.778 

293.887 

542.500 

15 

489.589 

J04.444 

419.715 

775.238 

367.321 

678.333 

326.575 

602.963 

293.993 

542.667 

16 

489.766 

904.722 

419.866 

775.476 

367.454 

678.542 

326.693 

603.148 

294.099 

542.833 

17 

489.942 

905.000 

420.018 

775.714 

367.586 

678.750 

326.811 

603.333 

294.205 

543.000 

18 

490.114 

905.278 

420.165 

775.952 

367.715 

678.958 

326.926 

603.519 

294.309 

543.167 

19 

490.286 

905.556 

420.313 

776.190 

367.844 

679.167 

327.041 

603.704 

294.412 

543.333 

20 

490.463 

905.833 

420.464 

776.429 

367.977 

679  375 

327  158 

603.889 

294.518 

543.500 

21 

490.640 

906.111 

420.616 

776.667 

368.109 

679.583 

327.276 

604.074 

294.624 

543.667 

22 

490.817 

906.389 

420.767 

776.905 

368.242 

679.792 

327.394 

604.259 

294.730 

543.833 

23 

490.993 

906.667 

420.919 

777.143 

368.375 

680.000 

327.512 

604.444 

294.836 

544.000 

24 

491.170 

906.944 

421.070 

777.381 

368.507 

680.208 

327.630 

604.630 

294.943 

544.167 

25 

491.347 

907.22V 

421.222 

777.619 

368.640 

680.417 

327.748 

604.815 

295.049 

544.333 

26 

491.523 

907.500 

421.373 

777.857 

368.773 

680.625 

327.866 

605.000 

295.155 

544.500 

27 

491.700 

907.778 

421.525 

778.095 

368.905 

(580.833 

327.984 

605.185 

295.261 

544.667 

28 

491.872 

908.056 

421.672 

778.333 

369.034 

681.042 

328.098 

605.370 

295.364 

544.833 

29 

492.044 

908.333 

421.820 

778.571 

369.103 

681.250 

328.213 

605.556 

295.468 

545.000 

30 

492.221 

908.611 

421.971 

778.810 

369.296 

681.  45b 

328.331 

605.741 

295.574 

545.167 

31 

492.398 

908.889 

422.123 

779.048 

369.428 

681.667 

328.449 

605.926 

295.680 

545.333 

32 

492.574 

909.167 

422.274 

779.286 

369.561 

681.875 

328.507 

606.111 

295.786 

545.500 

33 

492.751 

909.444 

422.426 

779.524 

369.694 

682  083 

328.685 

606.296 

295.892 

545.667 

34 

492.928 

909.722 

422.577 

779.762 

369.826 

682.292 

328.803 

606.481 

295.998 

545.833 

35 

493.105 

910.000 

422.729 

780.000 

369.959 

682.500 

328.920 

606.667 

296.104 

546.000 

36 

493.281 

910.278 

422.880 

780.238 

370.091 

682.708 

329.038 

606.852 

296.210 

546.  16r 

37 

493.458 

1)10.556 

423.032 

780.476 

370.224 

682.917 

329.156 

607.037 

296.317 

546.333 

38 

493.635 

910.833 

423.183 

780.714 

370.357 

683.125 

329.274 

607.222 

296.423 

546.500 

39 

493.812 

911.111 

423.335 

780.952 

370.489 

683.333 

329.392 

607.407 

296.529 

546.66" 

40 

493.984 

911.389 

423.482 

781.190 

370.618 

683.542 

329.507 

607.593 

296.632 

546.833 

41 

494.156 

911.667 

423.630 

781.429 

370.747 

683.750 

329.621 

607.778 

296.735 

547.000 

42 

494.332 

911.944 

423.781 

781.667 

370  880 

683.958 

329.739 

607.963 

296.841 

547.  16r 

43 

494.509 

912.222 

423.933 

781.905 

371.012 

684.167 

329.857 

608.148 

296.948 

547.333 

44 

494.686 

912.500 

424.084 

782.143 

371.145 

684.375 

329.975 

608.333 

297.054 

547.500 

45 

494.863 

912.778 

424.236 

782.381 

371.278 

684.583 

330.093 

608.519 

297.160 

547.  66r 

46 

495.039 

913.056 

424.387 

782.619 

371.410 

684.792 

330.211 

608  704 

297.266 

547.833 

47 

495.216 

913.333 

424.539 

782.857 

371.543 

685.000 

330.329 

608.889 

297.372 

548.000 

48 

495.393 

913.611 

424.690 

783.095 

371.675 

685.208 

330.447 

609.074 

297.478 

548.16^ 

49 

495.569 

913.889 

424.842 

783.333 

371.808 

685.417 

330.565 

609.259 

297.584 

548.333 

50 

495.746 

914.167 

424.994 

783.571 

371.941 

685.625 

330.683 

609.444 

297.691 

548.500 

51 

495.923 

914.444 

425.145 

783.810 

372.073 

685.833330.800 

609.630 

297.797 

548.  66' 

52 

496.100 
496.276 

914.722 

915.000 

425.297 
425.448 

784.048 
784.286 

372.206 
372.  338 

686.042330.918 
686.250331.036 

609.815 
610.000 

297.903 
298.009 

548.833 
549.001. 

53 
54 

496.453915.278 

425.600 

784.524 

372.47 

686.458331.154 

610.185 

298.115 

549  167 

55 

496.630915.556 

425.751 

784.765, 

372.604 

686.667  331  .272  610.370 

298.221 

549.333 

56 

496.807 

915.833 

425.903 

785.000 

372.736 

686.875331.390610.556 

298.327 

549.500 

57 

496.983 

916.111 

426.054 

785  238 

372.869 

687  .  083  i  331  .  508  610  .  741 

298.433 

549.667 

58 

497.1601916.389 

426.206 

785.476 

373.002 

687.  292  331.  6261610.  926 

298.540 

549.833 

59 

155 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


55° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

59t)  .719 

Arc. 

O 

2982  68 

5500.00 

1491.40 

2750.00 

994.330 

1  8-13.33 

745.815 

1375.00 

1 

2983  '.74 

5501.67 

1491.93 

2750.83 

994.684 

1833.81) 

746.080 

1375.42 

596.931  1100.33 

2 

2984.80 

5503.33 

1492.46 

•2751.67 

995.037 

1834.44 

746.346 

1375.83 

597.143  1100.6? 

3 

2985.  8(3 

5505.00 

1492.99 

2752.50 

995.390 

1835.00 

746.611 

1376.25 

597.  355  !  1101.  00 

4 

•2986.92 

5506.67 

1493.52 

2753.33 

995.744 

18:45.56 

746.876 

1376.67 

597.  567)  1101.  33 

5 

2987.98 

5508.33 

1494.05 

2754.17 

996.097 

1836.11 

747.141 

1377.08 

597.779 

1101.6? 

6 

2989.04 

5510.00 

1494.58 

2755.00 

996.451 

1836.67 

747.406 

1377.50 

597.991 

1102.00 

7 

2990.10 

5511.67 

1495.11 

2755.83 

996.804 

1837.22 

747.671 

1377.92 

598.203 

1102.3:] 

8 

2991.16 

5513.33 

1495.64 

2756.67 

997.157 

1837.78 

747.936 

1378.33 

598.415 

1102.6? 

9 

2992.22 

5515.00 

1496.17 

2757.50 

997.511 

1838.33 

748.201 

1378.75 

598.628 

1103.00 

10 

2993.28 

5516.67 

1496.70 

2758.33 

997.864 

1838.89 

748.466 

1379.17 

598.840 

1103  33 

11 

2994.34 

5518.33 

1497.23 

2759.17 

998.217 

1839.44 

748.731 

1379.58 

599.052 

1103.6? 

12 

2995.40 

5520.00 

1497.76 

2760.00 

998.571 

1840.00 

748.996 

1380.00 

599.264 

1104.00 

13 

2996.46 

5521.67 

1498  29 

2760.83 

998.924 

1840.56 

749.261 

1380.42 

599.476 

1104.33 

14 

2997.52 

5523.33 

1498.82 

2761.67 

999.277 

1841.11 

749.526 

1380.83 

599.688 

1104.67 

15 

2998.58 

5525.00 

1499.35 

2762.50 

999.631 

1841.67 

749.791 

1381.25 

599.900 

1105.00 

16 

2999.64 

5526.67 

1499.8^ 

2763.33 

999.984 

1842.22 

750.056 

1381.67 

600.112 

1105.33 

17 

3000.70 

5528.  3  3 

1500.41 

•2764.17 

1000.34 

1842.78 

750.321 

1382.08 

600.324 

1105.6? 

18 

3001.76 

5530.00 

1500.94 

2765.00 

1000.69 

1843.33 

750.586 

1382.50 

600.536 

1106.00 

19 

3002.82 

5531.6? 

1501.47 

2765.83 

1001.04 

1843.89 

750.851 

1382.92 

600.748 

1106.33 

2O 

3003.88 

5533.33 

1502.00 

2766.67 

1001.40 

1844.44 

751.116 

1383.33 

600.960 

1106.6? 

21 

3004.94 

5535.00 

1502.53 

2767.50 

1001.75 

1845.00 

751.381 

1383.75 

601.172 

1107.00 

22 

3006.00 

5536.6? 

1503.06 

•2768.33 

1002.10 

1845.56 

751.646 

1384.17 

601.384 

1107.33 

23 

3007.06 

5538.33 

1503.59 

•2769.17 

1002.46 

1846.11 

751.912 

1384.58 

601.596 

1107.6? 

24 

3008.12 

5540.00 

1504.12 

2770.00 

1002.81 

1846.67 

752.177 

1385.00 

601.808 

1108.00 

25 

3009.18 

5541.67 

1504.66 

2770.83 

1003.16 

1847.22 

752.442 

1385.42 

602.021 

1108.33 

26 

3010.24 

5543.33 

1505.18 

2771.67 

1003.5-2 

1847.78 

7'52.707 

1385.83 

602.233 

1108.67 

27 

3011.30 

5545.00 

1505.71 

2772.50 

1003.87 

1848.33 

752.972 

1386.25 

602.445 

1109.00 

28 

3012.36 

5546.67 

1506.24 

2773.33 

1004.22 

1848.89 

753.237 

1386.67 

602.657 

1109.33 

29 

3013.45 

5548.33 

1506.78 

2774.17 

1004.59 

1849.44 

753  509 

1387.08 

602.875 

1109.67 

30 

3014.54 

5550.00 

1507.33 

2775.00 

1004.95 

1850.00 

753.781 

1387.50 

603.092 

1110.00 

31 

3015.60 

5551.67 

1507.86 

2775  .  83 

1005.30 

1850.56 

754.046 

1387.92 

603.304 

1110.33 

32 

3016.66 

5553.33 

1508.39 

2776.67 

1005.66 

1851.11 

754.311 

1388.38 

603.516 

1110.67 

33 

3017.72 

5555.00 

1508.92 

2777.50 

1006.01 

1851.67 

754.576 

1388.75 

603.728 

1111.00 

34 

3018.78 

5556.67 

1509.45 

2778.33 

1006.36 

1852.22 

754.841 

1389.17 

603.941 

1111.33 

35 

3019.84 

5558.33 

1509.98 

2779.17 

1006.72 

1852.78 

755.106 

1389.58 

604.153 

1111.67 

36 

3020.90 

5560.00 

1510.51 

2780.00 

1007.07 

1853.33 

755.371 

139J.OO 

604.365 

1112.00 

37 

3021.96 

5561.67 

1511.04 

2780.83 

1007.42 

1853.89 

755.637 

1390.42 

604.57? 

1112.33 

38 

3023.02 

5563.33 

1511.57 

2781.67 

1007.78 

1854,44 

755.902 

1390.83 

604.789 

1112.67 

39 

3024.08 

5565.00 

1512.10 

2782.50 

1008.13 

1855.00 

756.167 

1391.25 

605.001 

1133.00 

4O 

3025.14 

5568.67 

1512.63 

2783.33 

1008.48 

1855.56 

756.432 

1391.67 

605.213 

1113.33 

41 

3026.23 

5568.33 

1513.17 

2784.17 

1008.851856.11 

756.704 

1392.08 

605.431 

1113.67 

42 

3027.32 

5570.00 

1513.71 

2785.00 

1009.21  1856.67 

756.976 

1392.50 

605.649 

1114.00 

43 
44 

3028.38 
30-29.44 

5571.67 
5573.33 

1514.24 
1514.77 

2785.83 
2786.67 

1009.  56  [  1857.  22 
1009.92  1857.78 

757.241 
757.506 

1392.92 
1393.33 

605.861 
606.073 

1114.33 
1114.67 

45 

3030.50 

5575.00 

1515.30 

2787.50 

1010.27 

1858.33 

757.771 

1393.75 

606.285 

1115.00 

46 

3031.56 

5576  .  67 

1515.83 

2788.33 

1010.  62!  1858.  89 

758.036 

1394.17 

606.497 

1115.33 

47 

3032.62 

5578.33 

1516.36 

2789.17 

1010.98  1859.44 

758.301 

1394.58 

606.709 

1115.67 

48 

3033.68 

5580.00 

1516.89 

2790.00 

1011.331860.00 

758.566 

1395.00 

606.921 

1116.00 

49 

3034.77 

5581.67 

1517.44 

2790.83 

1011.69 

1860.56 

758.839 

1395.42 

607.139 

1116.33 

50 

3035.86 

5583.33 

1517.98 

2791.67 

1012.06 

1861.11 

759.111 

1395.83 

607.356 

1116.67 

51 

3036.92 

5585.00 

1518.51 

2792.50 

1012.4l|l861.67 

759.376 

1396.25 

607.569 

1117.00 

52 

3037.98 

5586.67 

1519.04 

2793.33 

1012.761862.22 

759.641  1396.67 

607.781 

1117.33 

53 

3J39.04 

5588.33 

1519.57 

2794.17 

1013.12  1862.78 

759.9061397.08 

607.993 

1117.67 

54 

3040.09 

5590.00 

15-20.10 

2795.00 

1013.  47  1  1868.  33 

760.171!  1397.  50 

608.205 

1118.00 

55 

3041.15 

5591.  67  11520.  63 

2795.83 

1013.82  1863  89 

760.4361397.92 

608.417 

1118.33 

50 

3042.21 

5593.331521.16 

2796.67 

1014.181864.44 

760.701  1398.33 

608.629 

1118.67 

57 

3043.30 

5595.00 

1521.71 

2797.50 

1014.54  1865.00 

760.973  1398.75 

608.847 

1119.00 

58 

3044.39 

5596.67 

1522.25 

2798.33 

1014.90  1865.56 

761.2461399.17 

609.064 

1119.33 

59  (3045.45 

5598.331522.78 

2799.17 

1015.261866.11 

761.511  1399.  58  609.  276 

1119.67 

.156 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

55° 

Tan. 
497^337 

Arc. 
916.667 

Tan. 

Arc. 

Tan. 

Arc. 

687.500 

Tan. 

Arc. 

Tan. 

Arc. 

31. 

426.357 

785.714 

373.134 

331.744 

611.111 

298.646 

550.000 

497.514 

916.944 

426.509 

785.952 

313.267687.708 

331.861 

611.296 

298.752550.16? 

1 

497.690 

917.222 

426.660 

786.190 

373.399  687.917 

331.979 

611.481 

298.858 

550.333 

497.867 

917.500 

426.812 

786.429 

373.532 

688.125 

332.097 

611.667 

298.964 

550.500 

3 

498.044 

917.778 

426.963 

786.66? 

373.665 

688.333 

332.215 

611.852;299.070 

550.667 

4 

498.221 

918.056 

427.115 

786  905 

373.797 

688.542 

332.333 

612.037 

299.176 

550.833 

5 

498.39? 

918.3:33 

427.266 

787.143 

373.930 

688.750 

332.451 

612.222 

299.283 

551.000 

6 

498.574 

918.611 

427.418 

787.381 

374.062688.958 

332.569 

612.407 

299.389 

551.167 

7 

498.751 

918.889 

427.569 

787.619 

374.195689.167 

332.68? 

612.593 

299.495 

551.333 

8 

498.928 

919.167 

427.721 

787.857 

374.328 

689.375 

332.805 

612.778 

299.601 

551.500 

9 

499.104 

919.444 

427.872 

788.095 

374.460 

689.583 

332.923 

612.963 

299.707 

551.667 

1O 

499.281 

919.722 

428.02! 

7S8.333 

374.593 

689.79;: 

333.040 

613.148 

299.813 

551.833 

11 

499.458 

920.000 

428.175 

788.571 

374.725 

690.  COO 

333.158 

613.333 

299.919 

552.000 

12 

499.635 

920.278 

428.327 

78S.810 

374.858 

690.208 

333.276 

613.519 

300.025 

•552  .  1  67 

13 

499.811 

920.556 

428.478 

789.048 

374.991 

690.417 

333.394 

613.701 

300.132 

552.333 

14 

499.988 

920.833 

428.630 

789.286 

375.123 

690.625 

333.512 

613.889 

300.238 

552.500 

15 

500.165 

921.111 

428.781 

789.524 

375.25S 

690  833 

333.630 

614.074 

300.344 

552.667 

16 

500.342 

921.389 

423.933 

789.762 

375.388 

691.042 

333.748 

614.259 

300.450 

552.833 

17 

500.518 

921.667 

429.085 

790.  000 

375.521 

691.250 

333.866 

614.444 

300.556 

553.000 

18 

500.695 

921.944 

429.236 

790.238 

375.654 

691.458 

333.984 

614.630 

300.662 

553.167 

19 

500.872 

922.222 

429.388 

790.476 

375.786 

691.667 

334.101 

614.815 

300.768 

553.333 

20 

501.049 

922.500 

429.539 

?'90.714 

375.919 

691.875 

334.219 

615.000 

300.875 

553.500 

21 

501.225 

922.778 

429.691 

790.952 

376.051 

692.083 

334.337 

615.185 

300.981 

553.66? 

22 

501.402 

923.056 

429.842 

791.190 

376.184 

692.292 

334.455 

615.370 

301.087 

553.833 

23 

501.579 

923.333 

429.994 

791.429 

376.317 

692.500 

334.573 

615.556 

301.193 

554.000 

24 

501.755 

923.611 

430.145 

791.667 

376.449 

692.708 

334.691 

615.741 

301.299 

554.167 

25 

501.932 

923.889 

430.297 

791.905 

376.582 

692.917 

334.809 

615.926 

301.405 

554.333 

26 

502.109 

924.167 

430.448 

792.143 

376.714 

693.125 

334.927 

616.111 

301.511 

554.500 

27 

502.286 

924.444 

430.600 

792.381 

376.847 

693.333 

335.045 

616.296 

301.617 

554.667 

28 

502.46? 

924.722 

430.755 

792.619 

376.983 

693.542 

335.166 

616.481 

301.726 

554.833 

29 

502.649 

9*5.000 

430.911 

792.857 

377.119 

693.750 

335.287 

616.667 

301.835 

555.000 

30 

502.826 

925.278 

431.062 

793.095 

377.252 

693.958 

335.405 

616.852 

301.942 

555.167 

31 

503.002 

925.556 

431.214 

793.333 

377.385 

694.16? 

335.523 

617.037 

302.048 

555.333 

32 

503.179 

J25.833 

431.365 

793.571 

377.517 

694.375 

335.640 

617.222 

302.154 

555.500 

33 

503.356 

J26.111 

431.517 

793.810 

377.650 

694.583 

335.758 

617.407 

302.260 

555.667 

34 

503.532 

926.389 

431.669 

794.048 

377.782 

694.792 

335.876 

617.5U3 

302.366 

555.833 

35 

503.709 

J26.667 

431.820 

794.286 

377.915 

695.000 

335.994 

617.778 

302.472 

556.000 

36 

503.886 

926.944 

431.972 

794.524 

378.048 

695.208 

336.112 

617.963 

302.578 

556.16? 

37 

504.063 

927.222 

432.123 

794.762 

378.180 

695.417 

336.230 

618.148 

302.685 

556.333 

38 

504.239 

927.500 

432.275 

795.000 

378.313 

695.625 

336.348 

618.333 

302.791 

556.500 

39 

504.416 

927.778 

432.426 

795.238 

378.445 

695.833 

336.466 

618.519 

302.897 

556.667 

4O 

504.598 

928.056 

432.582 

795.476 

378.582 

696.042 

336.58? 

618.704 

303.006 

556.833 

41 

504.779 

928.333 

432.737 

795  714 

378.718 

696.250 

336.708 

618.889 

303.115 

557.000 

42 

504.956 

928.611 

432.88<T 

795.952 

378.850 

696.458 

336.826 

619.074 

303.221 

557.167 

43 

505.133 

928.889 

433.040 

796.190 

378.983 

696.667 

336.944 

619.259 

303.327 

557.333 

44 

505.309 

929.167 

433.192 

796.42!) 

379.116 

696.875 

337.062 

619.444 

303.433 

557.500 

45 

505.486 

929.444 

433.343 

796.667 

379.248 

697.083 

337.180 

619.630 

303.539 

557.667 

46 

505.663 

929.722 

433.495 

?'96.905 

379.381 

697.292 

337.297 

619.815 

303.645 

557.833 

47 

505.840 

930.000 

433.646 

797.143 

379.513 

697.500 

337.415 

620.000 

303.752 

558.000 

48 

506.021 

930.278 

433.802 

797.381 

3r9.650 

697.708 

337.536 

620.185 

303.861 

558.167 

49 

506.203 

9°0.556 

433.958 

797  619 

379.786 

697.917 

337.657 

620.370 

303.970 

558.333 

50 

506.379 

930.833 

434.109 

797.857 

379.918 

698.125 

337.775 

620.556 

304.076 

558.500 

51 

506  .  556 

931.111 

434.261 

798.095 

380.051 

698.333 

337.893 

620.741 

304.182 

558.667 

53 

506.733 

931.389 

434.412 

798.333 

380.184 

698.542 

338.011 

620.926 

304.288 

558.833 

53 

506.910 

931.667 

434.564 

798.571 

380.316 

698.750 

338.129 

621.111 

304.394 

559.000 

54 

50  r.  086 

931.944 

434.715 

798.810 

380.449 

608.  95S 

338.247 

621.296 

304.500 

559.167 

55 

507.263 

932.222 

434.867 

799.048 

380.581 

699.167 

338.365 

621.481 

304.606 

559.333 

56 

507.445 

932.500 

435.022 

799.286 

380.718 

699.375 

338.486 

621.667 

304.715 

559.500 

57 

507.626 

932.778 

435.178 

799.524 

380.854  699  583 

338.607 

621.852 

304.824 

559.667 

58 

507.803 

933.056 

435.330  799.762 

380.986699.792 

338.725 

622.037 

304.931 

559.833 

59 

157 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


56° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

~o" 

Tan. 

Arc. 

Tan. 

Arc. 

2800.00 

Tan. 

Arc. 

Tan. 

Arc.       Tan. 

Arc. 

3046.51 

5600.00 

1523.31 

1015.61 

1866.67 

761.7761400.00609.489 

1120.00 

1   3047.57 

5601.67 

1523.842800.83 

1015.96 

1867.22 

762.  04  1|  1400.  42  609.  701 

1120.33 

2  3048.  63 

5603.33 

1524.37 

2801.67 

1016.32 

1867.78 

762.306 

1400.83:609.913 

1120.67 

3  13049.72 

5605.00 

1524.92 

2802.50 

1016.68 

1868.33 

762.578 

1401.25  610.130 

1121.00 

4 

3050.81 

5606.67 

1525.46 

2803.33 

1017  04 

1868.89 

762.850 

14U1.67610.348 

1121.33 

5 

3051.87 

5608.33 

1525.99 

2804.17 

1017.39 

1869.44 

763.115 

1402.08610.560 

1121.67 

6 

8052.93 

5610.00 

1526.52 

2805.00 

1017.75 

1870.00 

763.380 

14U2.50610.772 

1122.00 

7 

3053.99 

5611.67 

1527.05 

2805.83 

1018.10 

1870.56 

763.645 

1402.92  610.984 

1122.33 

8 

3055.05 

5613.33 

1527.58 

2806.67 

1018.45 

1871.11 

763.910 

1403.33611.196 

1122.67 

9 

3056.14 

5615.00 

1528.13 

2807.50 

1018.82 

1871.67 

764.183 

1403.75 

611.414 

1123.00 

10 

'3057.23 

5616.67 

1528.67 

2808.33 

1019.18 

1872.22 

764.455 

1404.17 

611.632 

1123.33 

11 

3058.29 

5618.33 

1529  20 

2809.17 

1019.53 

1872  78 

764.720 

1404.58 

611.844 

1123.67 

13 

3059.35 

5620.00 

1529.73:2810.00 

1019.89 

1873.33 

764.985 

1405.00 

612.056 

1124.00 

13 

3060.41 

5621.67 

15:30.2612810.83 

1020.24 

1873.89 

765.250 

1405.42 

612.268 

1124.33 

14 

3061  47 

5623.33 

1530.79 

2811.67 

1020.59 

1874.44 

765.515 

1405.83 

612.480 

1124.67 

15 

3062.56 

5625.00 

1531.33 

2812.50 

1020.96 

1875.00 

765.787 

1406.25 

612.698 

1125.00 

16 

3063.64 

5626.67 

1531.88 

2S13.33 

1021.32 

1875.56 

766.059 

1406.67 

612.916 

1125.33 

17 

3064.70 

5628.33 

1532.41 

2814.17 

1021.67 

1876.11 

766.3-24 

1407.08 

613.128 

1125.67 

18 

3065.  76  1  5630.  00 

1532.94 

2815.00 

1022  03 

1876.67 

766.589 

1407.50 

613.340 

1126.00 

19 

3066.85 

5631.67 

1533.48 

2815.83 

1022.39 

1877.22 

766.862 

1407.92 

613.558 

1126.33 

30 

3067.94 

5633  33 

1534.03 

2816.67 

1022.75 

1877.78 

767.134 

1408.33:613.776 

1126.67 

21 

3069.00 

5635.00 

1534  56 

2817.50 

1023.11 

1878.33767.399 

1408.75 

613.988 

1127.00 

22 

3070.06 

5636  67 

1535.09 

2818.33 

1023.46 

1878.89767.664 

1409.17 

614.200 

1127.33 

23 

3071.15 

5638.33 

1535.63 

2819.17 

1023.82 

1879.44767.936 

1409.58 

614.418 

1127.67 

24: 

3072.24 

5640.00 

1536.18 

2820.00 

1024.18 

1880.00;  7  68.  208 

1410.00 

614.635 

1128.00 

25 

3073.30 

5641.67 

1536.71 

2820.83 

1024.54 

1880.56768.473 

1410.42 

614.847 

1128.33 

26 

3074.36 

5643.33 

1537.24 

2821.67 

1024.89 

1881.11 

768.738 

1410.83 

615.059 

1128.67 

37 

3075.42 

5645.00 

1537.77 

2822.50 

1025.24 

1881.67 

769.004 

1411.25 

615.272 

1129.00 

28 

3076.48 

5646.67 

1  538.30 

2823.33 

1025.60 

1882.22 

769.269 

1411.67 

615.484 

1129.33 

29 

3077.57 

5648.33 

1538.84 

2824.17 

1025.96 

1882.78 

769.541 

1412.08 

615.701 

1129.67 

3O 

3078.66 

5650.00 

1539.38 

2825.00 

1026.32 

1883.33 

769.813 

1412.50 

615.919 

1130.00 

31 

3079.72 

5651.67 

1539.91 

2825.83 

1026.6S 

1883  89 

770.078 

1412.92 

616.131 

1130.33 

32 

3080.78 

5653.33 

1540.44 

2826.67 

1027.03 

1884.44 

770.343 

1413.33 

616.343 

1130.67 

33 

3081.86 

5655.00 

1540.99 

2827.50 

1027.39 

1885.00 

770.615 

1413.75 

616.561 

1131.00 

34 

3082.95 

5656.67 

1541.53 

2S28.33 

1027.76 

1885.56 

770.888 

1414.17 

616.779 

1131.33 

35 

'3084.01 

5658.  a3 

1542.06 

2829.17 

1028  11 

1886.11 

771.153 

1414.58'  616.  991 

1131.67 

36 

3085.07 

5660.00 

1542.59 

2830.00 

1028.46 

1886.67J771.418 

1415.00617.203 

1132  00 

37 

3086.16 

5661.67 

1543.14 

2830.83 

1028  83 

1887.22 

771.690 

1415.42617.421 

1132.33 

38 

3087.25 

5663.33 

1543.68 

2831.67 

1029.19 

1887.78 

771.962 

1415.83617.639 

1132.67 

39 

3088.34 

5665.  OU 

1544.23 

2832.50 

1029.55 

1888.33 

772.234 

1416.25 

617.856 

1133.00 

40 

3089.43 

5666.67 

1544.77 

2833.33 

1029.92 

1888.89 

772.506 

1416.67 

618.074 

1133.33 

41 

3090.49 

5668.33 

1545.30 

2834.17 

1030.27 

1889.44 

772.771 

1417.08 

618.286 

1133.67 

43 

3091.55 

5670.00 

1545.83 

2835.00 

1030.62 

1890.00 

773.037. 

1417.50 

618.498 

1134.00 

43 

3092.64 

5671.67 

1546.37 

2835.83 

1030.98 

1890.  56  (773.309 

1417.92 

618.716 

1134.33 

44 

3093.72 

5673.33 

1546.92 

2-'36  67 

1081.85 

1891.11 

773.581 

1418.33 

618.934 

1134.60 

45 

3094.78 

5675.00 

1547.45 

2837.50 

1031.70 

1891.67 

773.846 

1418.75 

619.146 

1135.07 

46 

3095.84 

5676.67 

1547.98 

2838.33 

1032.05 

1892.22 

774.111 

1419.17 

619.358 

1135.33 

47 

3096.93 

5678.33 

1548.52 

2839.17 

1053.42 

1892.78 

774.  383 

1419.58 

619.576lll35.67 

48 

3098.02 

5680.00 

1549.07 

2840.00 

1032.78 

1893.33 

774.655 

1420.00 

619.  7'94  1136.00 

49 

3099.08 

5681.67 

1549.60 

2840.83 

1033.13 

1893.89 

774.921 

1420.42 

620.006 

1136.33 

5O 

3100.14 

5683.33 

1550.13 

2841.67 

1033.49 

1894.44 

775.186 

1420.83 

620  218 

1136.67 

51 

8101.2:3 

5685.00 

1550.6? 

2842.50 

1033.85 

1895.00 

775.458 

1421.  25:620.  436 

1137.00 

53 

3102.32 

5686.67 

1551.22 

2843.33 

1034.21 

1895.56 

775.730 

1421.67620.653 

1137.33 

53 

3103.41 

5688.  ,33 

1551.76 

2844.17 

1034.5S 

1896.11 

776.002 

1422.08  620.  S71 

1137.67 

54 

3104.50 

5690.00 

1552.31 

2845.00 

1034.94 

1896.67 

776.274 

1422.  50!  621.  089 

1138.00 

55 

3105.56 

5691.67 

1552.84 

2845.83 

1035.29 

1897.22 

776.539 

1422.92621.301 

1138.33 

56 

3106.62 

5693.33 

1553.37 

2846.67 

1035.65 

1897.78 

776.805 

1423.33621.513 

1138.67 

57 

3107.70 

5695.00 

1553.91 

5847.60 

1036.01 

1898.33 

777.07? 

1423.75621.731 

1139.00 

58 

3108.79 

5696.67 

1554.45 

2848.33 

1036.37 

1898.89 

777.349 

1424.17 

621.949 

1139.33 

59 

3109.88 

5698.33 

1555.00 

2849.17 

1036.73 

1899.44 

777.621 

1424.58 

622.166 

1139.67 

158 


TABLE   XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

56° 

Tau.      Arc. 

Tan. 

Arc. 

Tan.       Arc. 

Tau. 

Arc. 

Tan. 

Arc. 

M7 

507.980933.333 

435.481 

800.000381.119700.000 

338.843 

622.222 

305.037 

560.000 

O 

508.1501933.011 

435  .  633  800  .  238  38  1  .  252  700  .  208 

338.961 

622.407 

305.143 

560.167 

1 

508.  333  !  933.  889 

435  .  784  800  .  476  :  381  .  384  700  .  4  1  7 

339.079 

622.593 

305.249 

560.3:33 

2 

508.515J93J.16? 

435  .  940  800  .  714  !  381  .  520  700  .  62£ 

339.200 

622.778 

305.358 

560.500 

3 

508.090 

934.441 

436.095800.952 

381.657 

700.833 

339.321 

622.963 

305.467 

560.667 

4 

508.873 

9:14.722 

436.2471801.190 

381.789 

701.042 

339.439 

623.148 

305.573 

560.833 

5 

509.050 

935.000 

436.398801.429 

381  922 

701.250 

339.557 

623.333 

305.679 

561.000 

6 

509.220 

935.2?'8 

436.550801.667 

382.054 

701.458 

339.674 

623.519 

305.785 

561.167 

7 

509.403 

935.550 

436.  701  1801.  905 

382.187 

701.667 

339.792 

623.704 

305.891 

561.333 

8 

600.585 

935.833 

436.857 

802.143 

382.323 

701.875 

339.913 

623.889 

306.000 

561.500 

9 

509.766 

936.111 

437.013 

802.381 

382.459 

702.083 

340.034 

624.074 

306.109 

561.667 

1O 

509.948 

936.389 

437.104  802.619 

382.592 

702.292 

340.152 

624.259 

306.216 

561.833 

11 

510.120 

936.66? 

437.316!802.857 

382.725 

702.500 

340.270 

624.444 

306.322 

562.000 

12 

510.297 

930.944 

437.4671803  095 

382.857 

702.708 

340.388 

624.630 

306.428 

562.167 

13 

510.473 

937.222 

437.619803.333 

382.990 

702.917 

340.506 

624.815 

306.534 

562.333 

14 

510.655 

937.  SOU 

43  r.  774 

803.571 

383.  126J703.  125 

340.627 

625.000 

306.643 

562.500 

15 

510.830 

937.778 

437.930 

803.810 

383.262 

703  333 

340.748 

625.185 

306.752 

502.667 

16 

511.013 

938.050 

438.081 

804.048 

383.395 

703.542 

340.866 

625.370 

306.858 

562.833 

17 

511.190 

938.333 

438.233 

804.286 

383.527 

703.750 

340.984 

625.556 

306.964 

563.000 

18 

511.371 

938.611 

438.389 

804.524 

383.664 

703.958 

341.105 

625.741 

307.073 

563.167 

19 

511.553 

938.889 

438.544 

804.762 

383.800 

704.167 

341.226 

625.926 

307.182 

563.333 

20 

511.730 

939.167 

438.696 

805.000 

383.932 

704.375 

341.344 

626.111 

307.288 

563.500 

21 

511.900 

939.444 

438.847 

805.238 

384.065 

704.583 

341.462 

626.296 

307.395 

563.667 

22 

512.088 

939.722 

439.003 

805.470 

384.201 

704.792 

341.583 

626.481 

307.504 

563.833 

33 

512.209 

940.000 

439.158 

805.714 

384.337 

705.000 

341.704 

626.667 

307.613 

564.000 

24 

512.440 

940.278 

439.310 

805.952 

384.470 

705.208 

341.822 

626.852 

307.719 

564.167 

25 

512.623 

940.556 

439.402 

806.190 

384.603 

705.417 

341.940 

627.037 

307.825 

564.333 

26 

512.800 

940  833 

439.013 

806.429 

384.735 

705.625 

342.058 

627.222 

307.931 

564.500 

27 

512.976 
513.158 

941.111 
941.389 

439  705 
439.920 

806.667 
806.905 

384.868 
385.004 

705.833 
?  06.  042 

342.176 
342.297 

627.407 
627.593 

308.037 
308.146 

564.667 
564.833 

28 
29 

513.339 

941.667 

440.076 

807.143 

385.140 

706.250 

342  418 

627.778 

308.255 

565.000 

30 

513.510 

941.944 

440.227 

807.381 

385.273 

706.458 

342.536 

027.963 

308.361 

565.167 

31 

513.693 

942.223 

440.379 

807.619 

385.405 

706.607 

342.654 

628.148 

308.467 

565.333 

32 

513.874 

942.500 

440.  534  1807.  85? 

385.542 

706  875 

342.775 

628.333 

308.576 

565.500 

33 

514.050 

942.778 

440.  690  1808.  095 

385.678 

707.083 

342.896 

628.519 

308.685 

565.667 

34 

514.233 

943.056 

440.842 

808.333 

385.810 

707  292 

343.014 

628.704 

308.791 

565.833 

35 

514.409 

943.333 

440.993 

808.571 

385.943 

707.500 

343.132 

628.889 

308.898 

566.000 

36 

514.591 

943.611 

441.149 

808.810 

386.079 

707.708 

343.253 

629.074 

309.007 

566.167 

37 

514.772 

943.889 

441.304 

809.048 

386.215 

707.917 

343  374 

629.259 

309.110 

566.333 

38 

514.954 

944.167 

441.460 

809.286 

386.352 

708.125 

343.495 

629.444 

309.225 

566.500 

39 

515.135 

944.444 

441.616 

809.524 

386.488 

708.333 

343.616 

629.630 

309.334 

566.667 

4O 

515.312 

944.722 

441.767 

809.762 

386.620 

708.542 

343.734 

629.815 

309.440 

566.833 

41 

515.489 

945.000 

441.919 

810.000 

386.753 

708.750 

343.852 

630.000 

309.546 

567.  000 

42 

515.67o 

945.278 

442  074 

810.238 

386.889 

708.958 

343.973 

630.185 

309.655 

567.167 

43 

515  852 

945.550 

442.230 

810.476 

387.025 

709.167 

344.094 

630  370 

309.764 

567.333 

44 

516.029 

945.833 

442.381 

810.714 

387.158 

709.375 

344.212 

630  556 

309  870 

567.500 

45 

516.205 

946.111 

442.533810.952 

387.291 

709.583 

344.  330 

630.741 

309.976 

567.667 

46 

510.387 

946  389 

442.688811.190 

387.427 

709.792 

344.451 

630.926 

310.085 

567.833 

47 

516.509 

940  607 

442.844  811.429 

387.563 

710.000 

344.572 

631.111 

310.194 

568.000 

48 

516.745 

946.941 

442.980 

811.667 

387.690 

710.208 

344.690 

631.296 

310  300 

568.167 

49 

516.922 

947.222 

443.147 

811.905 

387.8-^ 

710.417 

344.808 

631.481 

310.406 

568.333 

50 

517.104 

947.  500 

443.303812.143 

387.961 

710.625 

344.929 

631.667 

310.515 

568.500 

51 

517.285 

947.778 

448.458812.381 

388.100 

710.833 

345.050 

631.852 

3  10.  024  '568.  607 

52 

517.467 

948.050 

443.614 

812.619 

388.23? 

711.042 

345.171 

632.03? 

310.733 

568  833 

53 

517.648 

948.333 

443.770 

812.857 

888.878 

711.250 

345.292 

632.222 

310.842 

569.000 

54 

517.825 

948.611 

443.921  813.095 

388.505 

711.458 

345.410 

632.407310.949 

569.167 

55 

518.002 

948.889 

444.073813.333 

388.638 

711.067 

345.528 

632.593311.055 

569.333 

56 

518.183 

949.167 

444.228813.571 

388.774 

711.875 

345.649 

632.778311.164 

569.500 

57 

518.365 

949.444 

444.384813.810 

388.910 

712.083 

345.770 

032.963311.273 

569  007 

58 

518.546 

949.722 

444.539'814.048 

389.04? 

712.292 

345.891 

633.  148  1311.  382 

569.833 

59 

159 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


57° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Are. 

Tan. 

Arc. 

Tan. 

Arc.      Tan. 

Arc. 

Tan. 

Arc. 

O 

3110.97 

5700.00 

1555  54 

2850TOO 

1037.10 

1900.00777.893  1425.00 

622.384 

1140.00 

1 

3112.03 

5701.67 

1556.07 

28.50.83 

1037.45 

1900.56  778.158 

1425.42 

622.596  1140.33 

8 

3113.09 

5703.33 

1556.60 

2851  67 

1037.80 

1901.11  778.428 

1425.83 

622.8081140.67 

3 

3114.18 

5705.00 

1557.152852.50 

1038.17 

1901.67  778.696 

1426.25 

623  026  1141.00 

4 

3115.27 

5706  67 

1557.69 

2853.33 

1038.53 

1902.22778.968 

1426.67 

623.244  1141.33 

5 

8116.86 

5708.33 

1558.24 

2854.17 

1038.89 

1902.78  779.240 

1427.08 

623.462 

1141.07 

6 

3117.45 

5710.00 

1558.78 

2855.00 

1  039..  26 

1903.33779.512 

1427.50 

623.679 

1142.00 

7 

3118.51 

5711.67 

1559.31 

2855.83 

1039.61 

1903.89779.777 

1427.92 

623.892 

1142.33 

8 

3119.57 

5713.33 

1559.84 

J856.67 

1039.96 

1904.44 

780.042 

1428.33 

624.104 

1142.67 

0 

3120.65 

5715.00 

1560.38 

2857.50 

1040.33 

1905.00 

780.315 

1428.75 

624.321 

1143.00 

10 

3121.74 

5716.67 

1560.93 

2858.33 

1040.69 

1905.56 

780.587 

1429.17 

024.539 

1143.33 

11 

3122.83 

5718.33 

1561.47 

2859.17 

1041.05 

1906.11 

780.859 

1429.58 

624.757 

1143.07 

12 

31^3.92 

5720.00 

1562.0;! 

2860.00 

1041.4! 

1906.67 

781.131 

1430.00 

624.97o 

1144.00 

18 

3125.01 

5721.67 

1562.56 

2860.83 

1041.78 

1907.22 

781.403 

1430.42 

(525.1  93 

1144.33 

14 

3126.10 

5723.33 

1563.11 

2851.67 

1042.14 

1907.78 

7S  1.676 

1430.83 

025.410 

1144.67 

15 

3127.16 

5725.00 

1563.64 

2862.50 

1042.49 

1908.33 

781.941 

1431.25 

025.622 

1145.00 

10 

3128.22 

5726.67 

1564.17 

2863.33 

1042.85 

1908.89 

782.206 

1431.67 

025.834 

1145.33 

17 

3129.31 

5728.33 

1564.71 

2864.17 

1043.21 

1909.44 

782.478 

1432.08 

626.052 

1145.67 

18 

3130.39 

5730.00 

1565.25 

2865.00 

1043.57 

1910.00 

782.750 

1432.50 

626.270 

1146.00 

19 

3131.48 

5731.67 

1565.80 

2865.83 

1043.94 

1910.56 

783.022 

1432.92 

626.488 

1146.33 

20 

3132.57 

5733.33 

1566.34 

2866.67 

1044.30 

1911.11 

783.295 

1433.33 

626.706 

1146.67 

31 

3133.66 

5735.00 

1566.89 

2867.50 

1044.66 

1911.  G7 

783.  5G7 

1433.75 

026.923 

1147.00 

22 

3134.75 

5736.67 

1567.43 

2868.33 

1045.02 

1912.22783.839 

1434.17 

627.141 

1147.33 

33 

3135.81 

5738.33 

1567.96 

2869.17 

1045.38 

1912.78  784.104 

1434.58 

027.353 

1147.07 

34 

3136.87 

5740.00 

1568.49 

2870.00 

1045.73 

1913.33  784.309 

1435.00 

027.505 

1148.00 

35 

3137.96 

5741.67 

1569.04 

2870.83 

1046.09 

1913.89  784.641 

1435.42 

627.783 

1148.33 

30 

3139.05 

5743.33 

1569.58 

2871.67 

1046.46 

1914.44  784.914 

1435.83 

628.001 

1148.67 

37 

3140.13 

5745.00 

1570.12 

2872.50 

1046.82 

1915.00:785.186 

1436.25 

628.219 

1149.00 

38 

3141.22 

5746.67 

1570.67 

2873.33 

1017.18 

1915.  56  1785.458 

1436.67 

028.437 

1149.33 

39 

3142.31 

5748.33 

1571.21 

2874.17 

1047.55 

1916.11 

785.730 

1437.08 

628.654 

1149.67 

3O 

3143.40 

5750.00 

1571.76 

2875.00 

1047.91 

1916.67 

783.002 

1437.50 

628.872 

1150.00 

31 

3144.49 

5751.67 

1572.30 

2875.83 

1048.27 

1917.22 

786.275 

1437.92 

629.090 

1150.33 

33 

3145.58 

5?'53.33 

1572.85 

2876.67 

1018.63 

1917.78 

786.547 

1438.33 

629  308 

1150.67 

33 

3146.67 

5755.00 

1573.39 

2877.50 

1049.00 

1918.33 

786.819 

1438.75 

629  526 

1151.00 

34 

3147.76 

5756.67 

1573.94 

2878.33 

1049.36 

1918.89 

787.091 

1439.17 

629.743 

1151.33 

35 

3148.82 

5758.33 

1574.47 

2879.17 

1049.71 

1919.44 

787.356 

1439.58 

029.955 

1151.67 

36 

3149.88 

5760.00 

1575.00 

2880.00 

1050.07 

1920.00 

787.621 

1440.00 

630.167 

1152.00 

37 

3150.96 

5761.67 

1575.54 

2880.83 

1050.43 

1920.56 

787.894 

1440.42 

630.385 

1152.33 

38 

3152.05 

5763.33 

1576.08 

2881.67 

1050.79 

1921.11 

788.166 

1440.83 

630.603 

1152.67 

39 

3153.14 

5765.00 

1576.63 

2882.50 

1051.16 

1921.67 

788.438 

1441.25 

630.821 

1153.00 

40 

3154.23 

5766.67 

1577.17 

2883.33 

1051.52 

1922.22 

788.710 

1441.67 

631  .039 

1153.33 

41 

3155.32 

5768.33 

1577.72 

2884.17 

1051.88 

1922.78 

788.982 

1442.08 

031.250 

1153.67 

43 

3156.41 

5770.00 

1578.26 

2885.00 

1052.24 

1923.33 

789.255 

1442.50 

631.474 

1154.00 

43 

3157.50 

5771.67 

1578  81 

2885.83 

1052.61 

1923.89 

789.527 

1442.92 

031.  092  1154.33 

44 

3158.58 

5773.33 

1579.35 

2886.67 

1052.  97  11924.  44 

789.799 

1443.33 

631.91HM154.07 

45 

3159.67 

5775.00 

1579.89 

2887.50 

1053.33 

1925.0J 

790.071 

1443.75 

632.1-2S 

1155.00 

4(J 

3160.76 

5776.67 

1580.44 

2888  .-33 

1053.70 

1  1)25.56 

790.343 

1444.17 

632.345 

1155.33 

47 

3161.85 

5778.33 

1580.98 

2889.17 

1054.06 

1926.11 

790.616 

1444.58 

632.503  1155.67 

48 

3162.94 

5780.00 

1581.53 

2890.00 

1054.42 

1926.67 

790.888 

1445.00 

632.781 

1156.00 

49 

3164.03 

5781.67 

1582.07 

2890.83 

1054.78 

1927.22 

791  .  160 

1445.42 

632.999 

1156.33 

50 

3165.12 

5783.33 

1582.62 

'891.67 

1055.15 

1927.78 

791.432 

1445.83 

633.217 

1156.67 

51 

3166,20 

5785.00 

1583.16 

2892.50 

1055.51 

1928.33 

791.704 

1446.25 

033.434 

1157.00 

53 

3167.29 

5786.67 

1583.70 

2893.33 

1055.87 

1928.89 

791.977 

1446.67 

633.652 

1157.33 

53 

3168.38 

5788.33 

1584  2.') 

2894.17 

1056.24 

1929.44 

792.249 

1447.08 

633.87'0 

1157.67 

54 

3169.47 

5790.00 

1584.79 

2895.00 

1056.60 

1930.00 

792.521 

1447.50 

634.088 

1158.00 

55 

3170.56 

5791.67 

1585.34 

3895.83 

1056.96 

1930.56 

792.793 

1447.92 

634.30611158.33 

56 

3171.65 

5793.33 

1585.88 

2896.67 

1057.32 

1931.11 

793.066 

1448.33 

634.  523!  11  58.  67 

57 

3172.74 

5795.00 

1586.43 

2897.50 

1057.69 

1931.67 

793.338 

1448.75 

634.741  1159.00 

58 

3173.83 

5796.67 

1586.97 

2898.33 

1058  05 

1932.22 

793.610 

1449.17 

634.959 

1159.33 

59 

3174.91 

5798.33 

1587.52 

2899.17 

1058.41 

1932.78 

793.882 

1449.58 

635.177 

1159.67 

160 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

57° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

518.728 

950.000 

444.695 

814.286 

389.183712  500 

340.  U12 

633.333 

311.491 

570.000 

o 

518.904 

950.278 

444.847814.524 

389.315712.708 

346  130 

633.519 

311.597 

570.167 

1 

519.081 

950.556 

444.998i814.762 

389.448 

712.917 

346.248 

633.704 

311.703 

570.333 

2 

519.203 

950.833 

445.154815.000 

389.584 

713.125 

346.369 

633.889 

311.812 

570.500 

3 

519.444 

951.111 

445.309 

815.238 

389.720 

713.333 

346.490 

634.074 

311.921 

570.607 

4 

51  9.  626!  95  1.389 

445.465 

815.476 

389.857 

713.542 

346.611 

634.259 

312.030 

570.833 

5 

519.  8071951.  667 
51  9.  984  !  951.  944 

445.621  815.714 
445.772815.952 

389.993 
390.125 

713.750 
713.958 

346.732 
346.850 

634.444 
634.630 

312.139 
312.245 

571.000 
571.10? 

G 

7 

520.161  952.233 

445.924 

816.190 

390.258 

714.167 

346.968 

634.815 

312  351 

571.333 

8 

520.312 

952.500 

446.079 

816.429 

390.394 

714.375 

347.089 

635.000 

312.460 

571.500 

9 

520.524 

952.778 

446.235 

816.667 

390.530 

714.583 

347.210 

635.185 

312.569 

571.66? 

10 

520.705953.056 

446.390 

816.905 

390.667 

714.792 

347.331 

635.370 

312.678 

571.833 

1  1 

520.887 

953.3:33 

446.546 

817.143 

390.803 

715.000 

347.452 

635.556 

312.787 

572.000 

12 

521.068 

953.611 

446.702 

817.381 

390.939 

715.208 

347.573 

035.741 

312.896 

572.16? 

13 

521.250 

953.889 

446.857 

817.619 

391.075 

715.417 

347.694 

635.926 

313.005 

572.333 

14 

521.427 

954.167 

447.009 

817.857 

391.208 

715  625 

347.812 

636.111 

313.111 

572.500 

15 

521.603 

954.444 

447.160 

818.095 

391.340 

715.833 

347.930 

636.290 

313.21? 

572.66? 

16 

521.785 

954.722 

447.316 

818.3:33 

391.477 

716.042 

348.051 

636.481 

313.326 

572.833 

17 

521.96(5 

955.000 

447.472 

818  571 

391.613 

716.250 

348.172 

636.66? 

313.435 

573.000 

18 

522.  H  8 

955.278 

447.627 

818.810 

391.749 

716.458 

348.293 

636.852 

313.544 

573.167 

19 

522.329 

955.556 

447.783 

819.048 

391.885 

716.667 

348.415 

637.03? 

313.653 

573.333 

2O 

522.511 

955.833 

447.938 

819.286 

392.021 

716.875 

348.536 

637.222 

313.702 

573.500 

21 

522.092 

956.111 

448.094 

819.524 

392.157 

717.083 

348.657 

637.407 

313.871 

573.667 

22 

522.86'.) 

956.389 

448.240 

819.762 

392.290 

717.292 

348.775 

637.593 

313.978 

573.833 

23 

523.046 

956.667 

448.397 

820.000 

392.423 

717.500 

348.893 

637.778 

314.084 

574.000 

24 

523.227 

956.944 

448.553 

820.238 

392.559 

717.708 

349.014 

037.963 

314.193 

574.16? 

25 

523  409 

957.222 

448.708 

820.476 

392.695 

717  917 

349.135 

638.148 

314.302 

574.333 

26 

523.590 

957.500 

448.864 

820.714 

392.831 

718.125 

319.250 

638.333 

314.411 

574.500 

27 

523.772 

957.778 

449.019 

820.952 

392.967 

718.333 

349.377 

638.519 

314.520 

574.667 

28 

523.954 

958.056 

449.175 

821.190 

393.104 

718.542 

349.498 

038.704 

314.629 

574.833 

29 

524.135 

958.333 

449.  S3  1 

821.429 

393.  S40 

718.750 

349.619 

638.889 

314.738 

575.000 

30 

524.317 

958.611 

449.480 

821.667 

393.376 

718.958 

349.740 

639.074 

314.847 

575.16? 

31 

524.498 

958.889 

449.642 

821.905 

393.512 

719.167 

349.861 

639.259 

314.956 

575.333 

32 

524.680 

959.167 

449.798 

822.143 

393.648 

719.375 

349.982 

039.444 

315.065 

575.500 

33 

524.861 

959.444 

449.953 

822.1381 

393.785 

719.583 

350.103 

639.630 

315.174 

575.667 

34 

525.038 

959.722 

450.105 

822.619 

393.917 

719.792 

350.221 

039.815 

315.280 

575.833 

35 

525.215 

900.000 

450.256 

822  857 

394.050 

720.000 

350.339 

640.000 

315.386 

576.000 

36 

525.396 

960.278 

450.412 

823.095 

394.186 

720.208 

350.460 

640.185 

315.495 

576.167 

37 

525.578 

900.556 

450.567 

823.333 

394.322 

720.417 

350.581 

640.370 

315.604 

576.333 

38 

525.759 

960.833 

450.723 

823.571 

394.458 

720.625 

350.702 

640.556 

315.713 

576.500 

39 

525.941 

961.111 

450.879 

823.810 

394.595 

720.833 

350.823 

640.741 

315.822 

576.66? 

40 

526.122 

901.389 

451.034 

824.048 

394.731 

721.042 

350.945 

640.926 

315.931 

576.833 

41 

526.304 

901  .607 

451.190 

824.280 

394.807 

721.250 

351.066 

641.111 

316.040 

577.000 

42 

526.485 

901.941 

-151.345 

824.524 

395.003 

721.  -458 

351.18? 

641.296 

316.149 

577.167 

43 

526  667 

902.22.' 

451.501  824.762 

395.139 

721.66? 

351.308 

641.481 

316.258 

577.333 

44 

526.848 

902.500 

451.  65?  1825.  000 

395.275 

721.875 

351.429 

641.66? 

316.307 

577.500 

45 

527.030 

902.778 

451.812 

825.238 

395.412 

722.083 

351.550 

641.852 

316.476 

577.667 

46 

527.211 

903.050 

451.968 

825.476 

395.548 

722.292 

351.671 

642.03? 

316.585 

577.833 

47 

527.393 

9(>:'»  333 

452.124 

825.714 

395.084 

722.500 

351.792 

642.222 

316.694 

578.000 

48 

527.574 

903.611 

452.279 

825.952 

395.820 

722.708 

351.913 

642.407 

316.803 

578.16? 

49 

527.750 

903.889 

452.435 

826.190 

395.950 

722.917 

352.034 

642.593 

316.912 

578.333 

50 

527.937 

904.167 

452.590 

820.420 

3%.  093 

723.125 

352.155 

642.778 

317.021 

578.500 

51 

528.119 

!tf54  444 

452.746 

826.667 

396.229 

723.333 

352.276 

642.963 

317.130 

578.607 

52 

528.300 

1)04.722 

452.902 

826.905 

390  305 

723.542 

352.398 

643.148 

317.239 

578.833 

53 

528.482 

965.000 

453.057 

827.143 

396  501 

723.750 

352.519 

643.333 

317.348 

579.000 

54 

528.663 

965.278 

453.213 

827.381 

396.637 

723.958 

352.640 

643  519 

317.457 

579.167 

55 

528.845 

965.556 

453.368 

827.619 

396.774 

724.167 

352.761 

643.704 

317.566 

579.333 

56 

529.027 

965.833 

453.524 

827.857 

396.910 

724.375 

352.882 

643.889 

317.675 

579.500 

57 

529.208 

966.111 

453.680 

828.095 

397.046 

724.583 

353.003 

644.074 

317.784 

579.667 

58 

529.390 

966.389 

453.835 

828.333 

397.182 

724.792 

353.124 

644.259 

317.893 

579.833 

59 

161 


TABLE   XIV.— ACTUAL  TANGENTS,    ETC. 


58° 
M7 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

o 

3176.00 

5800.00 

1588.06 

2900.00 

1058.78 

1933.33 

794.154 

1450.00 

635.394:1160.00 

1 

3177.09 

5801.67 

1588.60 

2900.83 

1059.14 

1933.89 

794.427 

1450.42 

635.012  1160.33 

2 

3178.18 

5803.33 

1589.15 

2901.67 

1059.50 

1934.44 

794.699 

1450.83 

635.8301160.67 

3 

3179.27 

5805.00 

1589.69 

2902.50 

1059.87 

1935.00 

794.971 

1451.25 

636.0481161.00 

4 

3180.36 

5806.67 

1590.24 

2903.33 

1060.23 

1935.56 

795.243 

1451.07 

636.266  1161.33 

5 

3181.45 

5808.33 

1590.78 

2904.17 

1060.59 

1936.11 

795.515 

1452.08 

636.48311161.67 

« 

3182.53 

5810.00 

1591.33 

2905.00 

1060.95 

1936.67 

795.788 

1452.50 

636.701  1162.00 

7 

3183.62 

5811.67 

1591.87 

2905.83 

1061.32 

1937.22 

796.060 

1452.92 

636.919  1162.33 

8 

3184.71 

5813.33 

1592.41 

2906.67 

1061.68 

1937.78 

796.332 

1453.33 

637.137 

1162.67 

9 

3185.80 

5815.00 

1592.96 

2907.50 

1062.04 

1938.33 

796.604 

1453.75 

637.355 

1163.00 

1O 

3186.89 

5816.67 

1593.50 

2908.33 

1062.41 

1938.89 

796.877 

1454.17 

637.572 

1163.33 

11 

3187.98 

5818.33 

1594.05 

2909.17 

1062.771939.44 

797.149 

1454.58 

037.790!  1163.  67 

12 

3189.07 

5820.00 

1594.59 

2910.00 

1063.131940.00 

797.421 

1455.00 

638.008  1164.00 

13 

3190.15 

5821.67 

1595.14 

2910.83 

1063.491940.56 

797.693 

1455.42 

638.226 

1164.33 

14 

3191.24 

5823  33 

1595.68 

2911.67 

1063.86  1941.11 

797.965 

1455.83 

638.444 

1164.67 

15 

3192.36 

5825.00 

1596.24 

2912.50 

1064.23:1941.67 

798.245 

1456.25 

6:38.667 

1165.00 

16 

3193.48 

5826.67 

1596.80 

2913.33 

1064.60  1942.22 

798.524 

1456.67 

638.891 

1165.33 

17 

3194.57 

5828.33 

1597.34 

2914.17 

1064.97 

1942.78 

798.796 

1457.08 

639.1081165.67 

18 

3195.65 

5830.00 

1597.89 

2915.00 

1065.33 

1943.33 

799.069 

1457.50 

639.3261166.00 

19 

3196.74 

5831.67 

1598.43 

2915.83 

1065.69 

1943.89 

799.341 

1457.92 

639.544 

1166.33 

20 

3197.83 

5833.33 

1598.97 

2916.67 

1066.05 

1944.44 

799.613 

1458.33 

639.762 

1166.67 

21 

3198.92 

5835.00 

1599.52 

2917.50 

1066.42 

1945.00 

799.885 

1458.75 

639.  980|  1167.  00 

22 

3200.01 

5836.67 

1600.06 

2918.33 

1066.78 

1945.56 

800.157 

1459.17 

640.197 

1167.33 

23 

3201.10 

5838.33 

1600.61 

2919.17 

1067.14 

1946.11 

800.430 

1459.58 

640.415 

1167.67 

24= 

3202.19 

5840.00 

1601.15 

2920.00 

1067.51 

1946.67 

800.702 

1460.00 

640.633 

1168.00 

25 

3203.28 

5841  67 

1601.70 

2920  83 

1067.87 

1947.22 

800.974 

1460.42 

640.851 

1108.33 

26 

3204.36 

5843.33 

1602.24 

2921.67 

1068.23 

1947.78 

801.246 

1460.83 

641.  069!  1188.  67 

37 

3205.45 

5845.00 

1602.79 

2922.50 

1068.59 

1948.  as 

801.518 

1461.25 

641.2861169.00 

28 

3206.54 

5846.67 

1603.33 

2923.33 

1068.96 

1948.89 

801.791 

1461.67 

641.504lll69.33 

29 

3207.66 

5848.33 

1603.89 

2924.17 

1069.33 

1949.44 

802.070 

1462.08 

641.728 

1169.67 

30 

3208.78 

5850.00 

1604.45 

2925.00 

1069.70 

1950.00 

802.349 

1462.50 

641.951 

1170.00 

31 

3209.86 

5851.67 

1604.99 

2925.83 

1070.07 

1950.56 

802.622 

1462.92 

642.1691170.33 

32 

3210.95 

5853.33 

1605.54 

2926.67 

1070.43 

1951.11 

802.894 

1403.33 

642.387J1170.67 

33 

3212.04 

5855.00 

1606.08 

2927.50 

1070.79 

1951.67 

803.166 

1463.75 

642.605|  1171.  00 

34 
35 

3213.13 
3214.22 

5856.67 
5858.33 

1606.62 
1607.17 

2928.33 
2929.17 

1071.15 
1071.52 

1952.22 
1952.78 

803.438 
803.710 

1464.17 
1464.58 

642.  822  i  1171.  33 
643.040  1171.67 

36 

3215.31 

5860.00 

1607.71 

2930.00 

1071  88 

1953.33 

803.983 

1465.00 

643.258  1172.00 

37 

3216.42 

5861.67 

1608.27 

2930.83 

1072.25 

1953.89 

804.262 

1465.42 

643.48111172.33 

38 

3217.54 

5863.33 

1608.83 

2931.67 

1072.62 

1954.44 

804.541 

1405.83 

643.705:1172.67 

39 

3218.63 

5865.00 

1609.37 

2932.50 

1072.99 

1955.00 

804.814 

1466.25 

643.923  1173.00 

40 

3219.72 

5866.67 

1609.92 

2933.33 

1073.35 

1955.56 

805.086 

1406.67 

644.141 

1173.33 

41 

3280.81 

5868.33 

1610.40 

20:34.17 

1073.71 

1956.11 

805.358 

1467.08 

644.358  1173.67 

4:2 

3221.90 

-)870.00 

1611.01 

2935.00 

1074.08 

1956.67 

805.630 

1407.50 

644.576 

1174.00 

43 

3222.99 

5871  .  67 

1611.55 

2935.83 

1074.44 

1957.22 

805.902 

1407.92 

044.794 

1174.33 

44 

3224.07 

5873.38 

1612.10 

2936.67 

1074.80 

1957.78 

806.175 

1408.33 

645.012 

1174.67 

45 

3225.19 

5S75.00 

1612.65 

2937.50 

1075.17 

1958.33 

806.454 

1408.75 

645.235 

1175.00 

£6 

3226.31 

5876.67 

1613.21 

2938.33 

1075.55 

1958.89 

806.733 

1409.17 

045.459 

1175.33 

--7 

3227.40 

5878.33 

1613.76 

2939.17 

1075.91 

1959.44 

807.006 

1469.58 

645.677 

1175.67 

48 

3228.49 

5880.00 

1614.30 

2940.00 

1076.27 

1960.00 

807.278 

1470.00 

645.894 

1176.00 

49 

3229.57 

5881.67 

1614.85 

2940.83 

1076.64 

1960.56 

807.550 

1470.42 

646.112 

1176.33 

5O 

3230.66 

5883.33 

1615.39 

2941.67 

1077.00 

1961.11 

807.822 

1470.83 

643.330 

1176.67 

51 

53 

8281.78 

3232.90 

5885.00 

5886.67 

1615.95 
1616  51 

2942.50 
2943.33 

1077.37 
1077.74 

1961.67 
1962.22 

808.102 
808.381 

1471.25 
1471.67 

640.554  1177.00 
040.  77711177.  33 

53 

3233.99 

5888.33 

1617.05 

2944.17 

1078.11 

1962.78 

808.653 

1472.08 

646.9951177.67 

54 

3235.07 

5890.00 

1617.60 

2945.00 

1078.47 

IJ'03.33 

808.925 

1472.50 

647.2131178.00 

55 

838.19 

5891.67 

1618.16 

2945.83 

1078.84 

19(53.89 

809.205 

1472.92 

647.436  1178.33 

56 

3237.31 

5893.33 

1618.71 

2946.67 

1079.21 

1964.44 

S09.484 

1473.33 

047.6001178.67 

57 

3238.40 

5895.00 

1619.26 

2947.50 

1079.58 

1905.  00 

809.756 

1473.75 

647.877  1179.00 

58 

3239:49  5896.67 

1619.80 

2948.33 

1079.94 

1965.56 

810.029 

1474.17 

648.095 

1179.33 

59  3240.  581  5898.  33  1620.352949.17  1080.301906.11 

810.301  1474.58 

048.3131179.67 

162 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

58° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Ivii7 

529.571 

966.667 

453.991 

828.571 

397.318 

725.000 

353.245 

644.444 

318.002 

580.000 

~~0~ 

529.753 

966.944 

454.147 

828.810 

397.454 

725.208 

353.366 

644.630 

318.111 

580.167 

1 

529.934 

967.222 

454.302 

829.048 

397.591 

725.417 

353.487 

644.815 

318.220 

580.333 

2 

530.116 

967.500 

454.458 

829.286 

397.727 

725.625 

353.608 

645.000 

318.329 

580.500 

3 

530.297 

967.778 

454.613 

829.524 

397.863 

725.833 

353.729 

645.185 

318.438 

580.667 

4 

530.479 

968.056 

454.769 

829.762 

397.999 

726.042 

353.850 

645.370 

318.547 

580.833 

5 

530.800 

968.333 

454.925 

830.000 

398.135 

726.250 

353.972 

645.550 

318.656 

581.000 

6 

530.842 

968.611 

455.08,' 

630.238 

31(8.272 

726.458 

354.093 

645.741 

318.765 

581.167 

7 

531.023 

968.889 

455.236 

830.476 

398.408 

726.667 

354.214 

645.926 

318.874 

581  .333 

8 

531.205 

969.167 

455.391 

830.714 

398.544 

726.875 

354.335 

646.111 

318.983 

581.500 

9 

531.386 

969.444 

455.547 

830.952 

398.680 

727  083 

354.456 

646.296 

319.092 

581  667 

10 

531.5681969.722 

455.703 

831.190 

398.816 

727.292 

354.577 

646.481 

319.201 

581.833 

11 

531.749970.000 

455.  85b 

831.429 

398.953 

727.500 

354.698 

646.667 

319.310 

582.000 

12 

531.931  970.278 

456.014 

831.667 

.99.089 

727.708 

354.819 

646.852 

319.419 

582  167 

13 

532.112970.556 

456.170 

831.905 

399.225 

727.917 

354.940 

647.037 

319.528 

582.333 

14 

532.299970.833 

456.329 

832.143 

399.365 

728.125 

355.064 

647.222 

319.640 

582.500 

15 

532.485 

971.111 

456.489 

832.381 

399.504 

728.333 

355.189 

647.407 

319.752 

582  667 

16 

532.666 

971.389 

456.645 

832.619 

399.641 

7'28.542 

355.310 

647.593 

319.861 

582.833 

17 

532.848 

971.667 

456.800 

832.857 

399.777 

7'28.750 

355.431 

647.778 

319.970 

583.000 

18 

533.030 

971.944 

456.956 

833.095 

399.913 

728.958 

355.552 

647.963 

320.079 

583.167 

19 

533.211 

972.222 

457.111 

833.333 

400.049 

729.167 

355.673 

648.148 

320.188 

583.333 

2O 

533.393 
533.574 

972.500 
972.778 

457.267 
457.423 

833.571 

833.810 

400.185 
400.322 

729.375 
729.583 

355.794 
355.915 

648.  333  !  320.  297 
648.519320.406 

583.500 
583.667 

21 

22 

633.756 

973.056 

457.573 

834.048 

400.458 

729.792 

356.036 

648.704 

320.515 

583.833 

23 

533.937 

973.333 

457.734 

834.286 

400.594 

730.000 

356.157 

648.889 

320.624 

584.000 

24 

534.119 

973.611 

457.889 

834  .  524 

400.730 

730.208 

356.278 

649.074 

320.733 

584.167 

25 

534.300973.889 
534.  482  974.167 

458.045 
458.201 

834.762 
835.000 

400  866 
401.003 

730.417 
730.625 

356.400 
356.521 

649  259 
649.444 

320.842 
320.951 

584.333 
584.500 

26 

27 

534.663 

974.444 

458.356 

835.238 

401.139 

730.833 

356.642 

649.630 

821.060 

584.667 

28 

534.850 

974.722 

458.516 

835.476 

401.278 

731.042 

356.766 

649.815 

321.172 

584.833 

29 

535.036 

975.000 

458.676 

835.714 

401.418 

731.250 

356.890 

650.000 

321.284 

585.000 

30 

535.217 

975.278 

458.831 

835.952 

401.554 

731.458 

357.011 

650.185 

321.393 

585.167 

31 

535.399 

975.556 

458.987 

836.190 

401.691 

731.667 

357.132 

650.370 

321.502 

585.333 

32 

535.580 

975.833459.143 

836.429 

401.827 

731.875 

357.254 

650.550 

321.611 

585.500 

33 

535.762 

976.111459.298 

836.667 

401.963 

732.083 

357.375 

650.741 

321.720 

585.667 

34 

535.943 

976.389 

459.454 

&36.905 

402.099 

732.292 

357.496 

650.920 

321.829 

585.833 

35 

536.125 

976.667 

459.609 

837.143 

402.235 

732.500 

357.617 

651.111 

321.938 

586.000 

36 

536.311 

976.944 

459.769 

837.38! 

402.375 

732.708 

357.741 

651.296 

322.049 

586.167 

37 

536.498 

977.222459.929 

837.619 

402.515 

732.917 

357.865 

651  481 

322.161 

586.333 

38 

536.679 

977.500 

460.084 

83Z.857 

402.651 

733.125 

357.986 

651.667 

322.270 

586.500 

39 

536.861 

977.778 

460.240 

838.095 

402.787 

733.333 

358  107 

651.852 

322.379 

586.667 

40 

537.042 

978.056460.396 

838  333 

402.923 

733.542 

•358.229 

052.037 

322.488 

586.833 

41 

537.224 

978.333460.551 

838.571 

403.060 

733.750 

358  350 

€52  222 

322.597 

587.000 

42 

537.405 

978.611460.707 

838.810 

403.196 

733  958 

,358.471 

652.407 

322.700 

587.167 

43 

537.587 

97S.  889  460.  863 

839.048 

403.332 

734.167 

358-.  592 

652.593 

322.815 

587.333 

44 

537.773 

979.167:461.022 

839.280 

403.472 

734.375 

358.716 

052.778 

322.927 

587.500 

45 

537.959 

979.444'461.182 

839.524 

403.612 

734.  sas 

358.840 

652.963 

323.031) 

587.607 

46 

538.141 

979.722461.338 

839.762 

403.748 

734.792 

358.961 

653.148 

323.148 

587.833 

47 

538.322 

980.000461.493 

840.000 

403.884 

735.000 

359.082 

653.333 

323.257 

588.000 

48 

538.504 

980.278 

461.649 

840.238 

404.020 

735.208 

359.204 

653.519 

323.300 

588.167 

49 

538.685 

980.556 

461.804 

840.470 

404.150 

735.417 

&59.325 

053.704 

323.475 

588.333 

5O 

538.872 

980.833461.964 

840.714 

404.296 

735.625 

359.449 

053.889 

323.587 

588.500 

51 

5:59.058 

981.111  462  124 

840.952 

404.430 

735.833 

&59.573 

054.074 

323.099 

588.667 

52 

539.239 

981.  389;  462.  2?  9 

841.190 

404.572 

736.042 

359.694 

654  259 

323.  8C8 

588.833 

53 

539.421 

981.667402.435 

841.429 

404.708 

736.250 

359.815 

654.444 

323.917 

589.000 

54 

539.607 

981.  94  4  !  462.  595 

841.667 

404.848 

736.458 

359.940 

054.630 

324.029 

589.167 

55 

539.794 

982.222462.754 

841.905 

404.988 

736.667 

360.064 

654.815 

324.141 

589.333 

56 

539.975 

982.500,462.910 

842.143 

405.124 

736.875 

300.185 

655.000 

324.250 

589.500 

57 

540.157 

982.778463.066 

842.381 

405.260 

737.083 

360.306 

655.185 

324.359 

589.667 

58 

540.338 

983.056463.221 

842.619 

405.396 

737.292 

300.427 

055.370 

324.468 

589.833 

59 

163 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


59° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 
*Wl.fl6 

Arc. 

Tan. 

Arc. 
2950.00 

Tan. 

1080.67 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

5900.0011620.89 

1966.67 

810.573 

1475.00648.531 

1180.00 

1 

3242.78 

5901.67 

1621.45 

2950.83 

1081.04 

1967.22 

810.852 

1475.42648.754!ll80.33 

9 

3243.  9  J 

5903.33 

1622.01 

2951  .  67 

1081.41 

1967.78 

811.132 

1475.83648.978  1180.67 

3 

3244.99 

5905.00 

1622.55 

2952.50 

1081.77 

11)68.33 

811.404 

1476.25649.196  1181.00 

4 

1246.08 

5906.67 

1623.10 

2953.33 

1082.14 

1968.89 

81  1  .  67  6 

1476.67.649.4131181.33 

5 

3247.19 

5008.83 

1623.66 

2954.17 

1082.51 

1969.44 

811.956 

1477.08649.637;1181.S7 

6 

3248.31 

5910.00 

1624.21 

2955.00 

1082.88 

1970.00 

812.235 

1477.  50  649.  861  '1182.00 

7 

3249.40 

5911.67 

1624.76 

2955.83 

1083.24 

1970.56 

812.507 

1477.92650.078  1182.33 

8 

3250.49 

5913.33 

1625.30 

2956.67 

1083.61 

1971.11 

812.779 

1478.33  650.296  1182.67 

9 

3251.58 

5915.  OU 

1625.85 

2957.50 

1083.97 

1971.67 

813.052 

1478.75 

650.514 

1183.00 

10 

3253.67 

5916  67 

1626.39 

2958.  ^3 

1084.33 

1972.22 

813  324 

1479.17 

650.732 

1183.33 

11 

325:3.78 

5918.33 

1626  95 

2959.1; 

1084.71 

1972.78 

813.603 

1479.58650.955!1183.67 

12 

325  4.  9U 

5920.00 

1627.51 

2960.00 

1085.08 

1973.133 

813.883 

1480.  00^51.  179 

1184.00 

13 

3*65.99 

5921.67 

1628.05 

2960.8:} 

1085.44 

1973.89 

814.155 

1480.42651.397 

1184.33 

14 

3257.08 

5923.33 

1628  60 

2961.67 

1085.80 

1974.44 

814.427 

1480.83651.614 

1184.67 

15 

1*58.19 

5925.  OU 

1629.16 

2962.50 

1086.18 

1975.00 

814.706 

1481.25651.838 

1185.00 

16 

3259.31 

5926.67 

1629.72 

29G3.3-3 

1086.55 

1975.56 

814.986 

1481.67  652.061 

1185.33 

17 

32(50.40 

5928.33 

1630.26 

2964.17 

1086  91 

1976.11 

815.258 

1482.08652.279 

1185.67 

18 

3261.49 

5930.00 

1630.80 

2965.  OJ 

1087.27 

1976.67 

815.530 

1482.50652.497 

1186.00 

19 

3262.61 

.3931.67 

1631.3(5 

2965.  83 

1087.65 

1977.22 

815.810 

1482.92 

652.720 

1186.33 

20 

3203.72 

->933.33 

1631  92 

2966.67 

1088.02 

1977.78 

816.089 

1483.33 

652.944 

1186.67 

21 

3264.81 

5935.00 

163.1.47 

2967.50 

1088.38 

1978.33 

816.361 

1483.75653.16-2 

1187.00 

22 

3265.90 

5936.67 

1633.01 

2968.33 

1088.75 

1978.89 

816.633 

1484.17  653.380 

1187.33 

23 

3267  02 

5938.33 

1633.57 

2969.17 

1089.12 

1979.44 

816.913 

1484.58653  603 

1187.67 

24 

3268  14 

940.00 

1634  13 

2970.00 

1089.49 

1980.00 

817.192 

1485.00653.82; 

1188.00 

25 

3269.2.') 

5941.67 

1634.69 

2970.83 

1089.86 

1980.56 

817.471 

1485.42  654.050 

1188.33 

26 

3*70.81 

5913.33 

1635.24 

2971.67 

1090.24 

1981.11 

817.751 

1485.83654.274 

1188.67 

27 

3271.46 

5945.00 

1635.79 

2972.50 

1090.60 

1981.67 

818.02:3 

1486.25 

654.491 

1189.00 

28 

3272.55 

5946.67 

1636.33 

2973.33 

1090.96 

1982.22 

818.295 

1486.67 

654.7'09 

1189.33 

29 

3273.66 

5948.33 

1636.89 

2974.17 

1091.33 

1984.78 

818.575 

1187.08 

654.933 

1189.67 

30 

3274.78 

5950.00 

1637.45 

2975.00 

1091.71 

1983.33 

818.854 

1487.50 

655.156 

1190.00 

31 

3275.87 

5951.67 

1638.00 

2975.83 

1092  07 

1983.89 

819.126 

1487.92655  374 

1190.33 

32 

3276.96 

5953.33 

1638.54 

2976.67 

1092.43 

1984.44 

819.398 

1488.33655.59-2 

1190.67 

33 

3278.08 

5955.00 

1639.10 

2977.50 

1092.80 

1985.00 

819  678 

1488.75655.815 

1191.00 

34 

3279.19 

5956.  67  '1639.  66 

2978.33 

1093.18 

1985.56 

819.957 

1489.17 

656.039 

1191.33 

35 

3280.31 

5958.33:1640.22 

2979.17 

1093.55 

1986.11 

820.237 

1489.58 

656.262 

1191.67 

36 

3281.43 

5960.00;  1640.  77 

2980.00 

1093.92 

1936.67 

820.516 

1490.00 

656.486 

1192.00 

37 

3282.52 

5961.  67!  16  41.  32 

2980.83 

1094.28 

1987.22 

820.788 

1490.42 

656.704 

1192.33 

38 

3283.61 

5963.33  1641  86 

2981.67 

1094.65 

1987.78 

821.060 

1490.83 

656.922 

1192.67 

39 

3284.72 

5965.00 

1642.42 

2982.50 

1095.02 

1988.33 

821.340 

1491.25 

657.145 

1193.00 

4O 

3285.84 

5966.67 

1642.98 

2983.33 

1095.39 

1988.89 

821.619 

1491.67 

657.369 

1193.33 

41 

3286.93 

5968.331643.52 

2984.17 

1095.76 

1989.44 

821.891 

1492.08 

657.586 

1193.67 

42 

3288.02 

5970.00  1644.07 

2985.00 

1095:  12 

1990.00 

822.163 

1492.50 

657  .  804 

1194.00 

43 

3289.13 

5971.67  1644.63 

2985.83 

1096.49 

1990.56 

822.443 

1492.92 

658.028 

111)4.33 

44 

3290.25 

5913.33  1615.19 

2986.67 

1096  86 

1991.11 

822.722 

1493.33 

658.251 

1194.67 

45 

3291.37 

5975.001645.74 

2987.50 

1097.24 

1991.67 

823.002 

1493.75 

658.475 

1195.00 

46 

3292.  49|  597<i.67  1616.30 

2988.33 

1097.61 

1992.22 

823.281 

1494.17 

658.698 

1195.33 

47 

3293.  60  59  78.  33  161(5  86 

2989.17 

1097.98 

199-2.78 

823.5601494.58 

658.92-2 

1195.67 

48 

3294.72  5980.00  1647.42 

2990.00 

1098.35 

1993.33 

823.  840  11495.  00 

659.145 

1196.00 

49 

3295.  81  15981.  67^647.  97 

2990.83 

1098.72 

1993.89 

824.112 

1495.42 

659.363 

1196.33 

5O 

3298.90 

:>9:  v3.  33  1648.51 

2991.67 

1099.08 

1994.44 

824.384 

1495.83 

659.581 

1196.67 

51 

3298.02 

5985.00  1649.07 

2992.50 

1099  45 

1  995.  00  j  824  664  1496.25 

659.804 

1197.00 

52 

3299.13 

5986.67  1649.63 

2993.33 

1099.82 

1995.56824.943  1496.67 

660.028 

1197.33. 

53 

3:300.2.-) 

5988.33  1650.19 

2994.17 

1100.20 

1996.11!825.222  1497.08 

660.252 

1197.67 

54 

3301.37 

5990.00  1650.74 

2995.00 

1100.57 

1  996  .  67  i  825  .  502  1  497  .  50  660  .  475 

1198.00 

55 

3302.46 

5991.671651.29 

2995.83 

1100.93 

1997.22825.774 

1497.92660.693 

1198.33 

56 

3303.51 

.-)993.3i  1651.83 

2996.67 

1101.29 

1997.7882(5.046 

1498.33660.911  1198.67 

57 

3304.  (Hi 

51195.00  1652  39 

2997.50 

1101  67 

1  998  .  33  8-26  .  325  1  498  .  75  66  1  .  1  34 

1199.00 

58 

3305.  78 

5996.67  1652.95  2998.  33 

1102.04 

1998.  89  820.  (105  1499.  17  661.  35S 

1199.33 

59 

3306.  IX) 

5998.33  1653.51  2999.17 

1102.41 

1999.44  826.884'14G9.58  6(51  .581 

1199.67 

164 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


0°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

59° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
405.533 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 
590.000 

M7 

540.520983.333 

463.377  842  857 

737.500 

360.548 

655.556324.577 

o 

540.706983.611 

463.537  843.095 

405.672737.7'08 

360.672 

655.741  324.  688 

590.167 

1 

540.89-2 

983.889 

463.696843.333 

405.812737.917 

360.797 

655.920324.800 

590.333 

2 

541.074984.167 

463.852 

843.571 

405.948 

738.12.-) 

360.918 

050.111  324.909 

590.500 

3 

541.255 

984.444 

464.008 

843.810 

406.084 

738.333 

361.039 

056.290325.018 

590.667 

4 

541.442984.722 

464.167 

8  44.048 

406.224 

738.542 

361.163  656.481  325.130  590.833 

5 

541.628 

986.000 

464.327 

844.286 

406.364 

138.750 

301  287  656.667 

325.242591.000 

6 

541.809985.278 

464.483 

844.524 

406.  SOU 

738.958 

361.409656.852 

325.351  591.167 

7 

541.991 

985.556 

464.638 

844.762 

406.636 

739.167 

361.530 

657.037 

325.460 

591.333 

8 

542.172 

985.833 

464.794 

845.000 

406.773739.375 

361.651 

657.222 

325.569 

591.500 

9 

542.354 

986.111 

464.949 

845.238 

406.909739.583 

361.772 

657.407 

325.678 

591.667 

1O 

542.540 

986.389 

405.  109 

845.  47G 

407.049739.792 

361.896 

657.593 

325.790 

591.833 

11 

542.727 

986.667 

465.269 

845.714 

407.188740.000 

362.020 

657.778 

325.902 

592.000 

12 

542.908 

986.944 

465.424 

845.952 

407.325740.208 

362.141 

657.963 

326.011 

592.167 

13 

543.090987.222 

465.580 

846.190 

407.461  740.417 

362.262 

658.148 

326.120 

592.333 

14 

543.276 

987.500 

465.740 

846.429 

407.600740.625 

362.387 

658.333 

326.232 

592.500 

15 

543.4621987.778 

465.899 

846.667 

407.740740.833 

362  511 

658.519 

326.344 

592.667 

16 

543.644 

988.  05C 

466.055 

846.905 

407.876741.042 

362.632 

658.704 

326.453 

592.833 

17 

543.  825  i  988.3:33 

466.211 

847.143 

408.013741.250 

362.753 

658.889 

326.562 

593.000 

18 

544.012988.611 

466.370 

847.381 

408.152 

741.458 

362.877 

659.074 

326.673 

593.167 

19 

544.198988.889 

466.530 

847.619 

408.292741.667 

363.002 

659.259 

326.785 

593.333 

30 

544.379989.167 

466.686 

847.857 

408.  428  1741.  875 

363.123 

659.444 

326.894 

593.500 

21 

544.561 

989.444 

466.841 

848.095 

408.565742.083 

363.244 

659.630 

327.003 

593.667 

22 

544.747 

989.722 

467.001 

848.333 

408.704  742.292 

303.368 

659.815 

327.115 

593.833 

23 

544.933 

990.000 

467.161 

848.571 

•408.844  742.500 

363.492 

660.000 

327.227 

594.000 

24 

545.120 

990.27'8 

467.320 

848.810 

408.984  742.  70S 

363.617 

660.185 

327.3:39 

594.167 

25 

545.  306  1990.  55(3 

467.480 

849.  04b 

409.124  742.917 

363.741 

060.370 

327.451 

594.  333 

26 

545.488 

990.833 

467  636 

849.286 

409.  260  743.125 

363.862 

660.556 

327.560 

594.500 

27 

545.669 

991.111 

467.791 

849.524 

409.396  743.333 

363.983 

660.741 

327.669 

594.667 

28 

545.855 

991.389 

467.951 

849.762 

409.536 

743.542 

364.107 

660.926 

327,781 

594.833 

29 

546.042 

991.667 

468.111 

850.000 

409.676 

743.750 

364.232 

661.111 

327.892 

595.000 

30 

546.223 

991.944 

468.266 

850.  2S8 

409.812 

743.958 

364.353 

661.296 

328.001 

595.167 

31 

546.405 

992.222 

468.422 

850.476 

409.948 

744.167 

364.474 

661.481 

328.110 

595.333 

32 

546.591 

992.500 

468  582 

850.714 

410.088 

744.375 

364.598 

661.667 

328.222 

595.500 

33 

546.777 

992.778 

468.741 

850.952 

410.227 

744.583 

364.722 

661.852 

328.334 

595.667 

34 

546.964 

993.056 

468.901 

851.190 

410  367 

744.792 

364.847 

662.037 

328.446 

595.833 

35 

547.  150  993.  333 
547.331  993.611 

469  061 
469.217 

851.429 
851.667 

410.507  745.000 
410.643J745.208 

364.971 
365.092 

662.222 
662.407 

328.558 
328.667 

596.000 
596.167 

36 
37 

547.513 

993.889 

469.372 

851.905 

410  779  745.417 

365.213 

662.593 

328.776 

596.333 

38 

547.699 

994.167 

469.532 

852.143 

410.919 

745.625 

365.337 

662.778 

328.888 

596.500 

39 

547.886 

994.444 

469.692 

852.381 

411.059 

745.88? 

865.462 

662.963 

329.000 

596.667 

40 

548.067 

994.722 

469.847 

852.619 

411.195 

746.04^ 

365.583 

663.148 

329.109 

596.833 

41 

548.249 

995.000 

470.003 

852.857 

411.331  746.250 

365.704 

663.333 

329.218 

597.000 

42 

548.435 

995.278 

470.162 

853.095 

411.471S746.458 

365.828 

663.519329.330 

597.167 

43 

548.  62  i|  995.  556 

470.322 

853.333 

411.611  746.667 

365.952 

663.  7'04  1329.441 

597.333 

44 

5  48.  807  1995.  833 

470.482853.571 

411.751 

7'46.875 

366.077 

663.889 

329.553 

597.500 

45 

548.994 

996.111 

470.642853.810 

411.890747.088 

366.201 

664.074 

329.665 

597.667 

46 

549.180  996.389 

470.801  854.048 

412.030 

747.292 

366.325 

664.259 

329.777 

597.833 

47 

549.366 

996.667 

470.961 

854.286 

412.170 

747.500 

366.449 

664.444 

329.889 

598.000 

48 

549.548 

996.944 

471.117 

854.524 

412.306 

747.708 

366.570 

664.630 

329.998 

598.  167 

49 

549.729997.222 

471.272 

854.762 

412.442 

747.917 

366.691 

664.815 

330.107 

598.333 

50 

549.916 

997.500 

471.432 

855.000 

412.582 

748.125 

366.816 

665.000 

330.219 

598.500 

51 

550.102 

997.778 

471.592 

855.238 

412.722 

748.333 

366.940 

665.185330.331 

598.607 

52 

550.288998.056 

471.751 

855.476 

412.862 

748.542 

367.064 

605.  370  1  330.  443 

598.833 

53 

550.475998.333 

471.911 

855.714 

413.001  748.750 

367,189 

665.556330.554 

599.000 

54 

550.656 

998.611 

472.067 

855.958 

41  3.  138!  748.  958 

367.310 

665.  741  1330.  663 

599.167 

55 

550.838 

998.889 

472.222 

806.  190 

413.274 

749.167 

367.431 

665.  926330.  772 

599.33:3 

56 

551.024999.167 

472.  382  1856.429 

413.414 

749.375 

367.555 

6C6.111  330.884 

599.500 

57 

551.210 

999.444 

472.  542:  856.  (JO  7 

413.553 

749.583 

367.679666.296330.996 

599.607 

58 

551.39? 

999.  75k 

472.701:85G.90f 

413.693749.792 

367.804 

666.  481  J331.  108  599.  833 

59 

165 


TABLE   XIV.— ACTUAL  TANGENTS,    ETC. 


60° 

"SET 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

~~o" 

3308.01 

6000.00 

1654.07 

3000.00 

1102.78 

2000.00 

827.164 

1500.00 

661.805 

1200.00 

i 

3309.13 

6001.67 

1654.63 

3000.83 

1103.16 

2000.56 

827.443  1500.42 

662.028 

1200.33 

2 

3310.25 

6003.33 

1655.18 

3001.67 

1103.53 

20U1.11 

827.723  1500.83 

662.252 

1200.67 

3 

3311.37 

6005.00 

1655.74 

3002.50 

1103.90 

2001.67 

828.002 

1501.25 

662.475 

1201.00 

4 

3312.48 

6006.67 

1656.30 

3003.33 

1104.27 

2002.22 

828.281 

1501.67 

662  .  699 

1201.33 

5 

3313.57 

6008.33 

1656.85 

3004.17 

1104.64 

2002.78 

828.5531502.08 

662.917 

1201.67 

6 

3314.66 

6010.00 

1657.39 

3005.00 

1105.00 

2003  33 

828.8*5 

1502.50 

663.134 

1202.00 

7 

3315.7816011.67 

1657.95 

3005.83 

1105  37 

2003.81) 

-S29.105 

1502.92 

663.358 

1202.33 

8 

331  6.  89!  G013.  33 

1658.51 

3006.67 

1105.7:; 

2004.44 

829.384 

1503.33 

663.581 

1202.67 

9 

3318.01 

6015.00 

1659.07 

3007.50 

1106.12 

2005.00 

829.664 

15U3.75 

663.805 

1203.00 

10 

3319.13 

6016.67 

1659.63 

3008.33 

1*>6.49 

2005.56 

829.943 

1504.17 

664.029 

1203.33 

11 

3320.25 

6018.33 

1660.18 

3009.17 

1106.86 

2006.11 

S30.222 

1504.58 

664.252 

1003.67 

12 

3321.36 

6020.00 

1660.74 

3010.00 

1107.24 

2006.67 

830.502 

1505.00 

664.476 

1204.00 

13 

3322.48 

6021.67 

1661.30 

3010.83 

1107.61 

2007.22 

830.781 

1505.42 

664.699 

1204.33 

14 

3223.60 

6023.33 

1661.86 

3011.67 

1107.98 

2007.78 

831.060 

1505.83 

664.923 

1204.67 

15 

8324.72 

6025.00 

1662.42 

3012.50 

1108.35 

2008.33 

831.340 

1506.25 

665.146 

1205.00 

16 

3325.83 

6026.67 

1662.98 

3013.33 

1108.73 

2008.89 

831.619 

1506.67 

665.370 

1205.33 

17 

3326.95 

6028.33 

1663.54 

3014.17 

1109.10 

2009.44 

831.899 

1507.  OS 

665.593 

1205.67 

18 

3328.07 

6030.00 

1664.09 

3015.00 

1109.47 

2010.00 

832.178 

1507.50 

665.817 

1206.00 

19 

3329.18 

(5031.67 

1664.65 

3015.83 

1109.  M 

2010.56 

832.457 

1507.92 

606.040 

1206.33 

2O 

3330.30 

6033.33 

1665.21 

3016.67 

1110.21 

2011.11 

832.737 

1508.33 

666.264 

1206.67 

21 

3331.39 

6035.00 

1605.  70 

3017.50 

1110  58 

2011.67 

833.009 

1508.75 

666.482 

1207.00 

22 

3332.48 

6036.67 

1666.30 

3018.33 

1110.94 

2012.22 

833.281 

1509.17 

666.699 

1207.33 

23 

3333.60 

6038.33 

1666.86 

3019.17 

1111.31 

2012.78 

838.561 

1509.58 

666.923 

1207.67 

24 

3334.71 

6040.00 

1667.42 

3020.00 

1111.69 

2013.33 

833.840 

1510.00 

667.146 

1208.00 

25 

3335.83 

6041.67 

1667.98 

3020.83 

1112.06 

2013.89 

834.119 

1510.42 

667.370 

1208.33 

26 

3336.95 

6043.  33 

1668.54 

3021.67 

1112.43 

2014.44 

834.399 

1510.83 

667.593 

1208.67 

27 

3338.07 

6045.00 

1669.09 

3022.50 

1112.80 

2015.00 

834.678 

1511.25 

607.817 

1209.00 

28 

3339.18 

6016.67 

1669.65 

3023.33 

1113.18 

2015.56 

834.957 

1511.67 

668.041 

1209.33 

29 

3340.30 

6048.33 

1670.21 

3024.17 

1113.55 

2016.11 

835.237 

1512.08 

668.264 

1209.67 

30 

3341.42 

6050.00 

1670.77 

3025.00 

1113.92 

2016.67 

835.516 

1512.50 

668.488 

1210.00 

31 

3342.53 

6051.67 

1671.33 

3025.83 

1114.29 

2017.22 

835.796 

1512.92 

668.711 

1210.33 

32 

3343  65 

6053.33 

1671.89 

3026.67 

1114.67 

2017.78 

836.075 

1513.33 

668.935 

1210.67 

33 

3344.77 

6055.00 

1672.45 

3027.50 

1115.04 

2018.33 

836.354 

1513.75 

669.158 

1211.00 

34 

3345.89 

6056.6? 

1673.00 

3028.33 

1115.41 

2018.89 

836.634 

1514.17 

669.382 

1211.33 

35 

3347.00 

6058.33 

1673.56 

3029.17 

1115.78 

2019.44 

836.913 

1514.58 

669.605 

1211.67 

36 

3348.12 

6060.00 

1674.12 

3030.00 

1116.16 

2020.00 

837.192 

1515.00 

669.829 

1212.00 

37 

3349  24 

6061.67 

1674.68 

3030.83 

1116.53 

2020.56 

837.472 

1515.42 

670.052 

1212.33 

38 

3350.36 

6063.33 

1675.24 

3031.67 

1116.90 

2021.11 

837.751 

1515.83 

670.276 

1212.67 

39 

3351.47 

6065.00 

1675.80 

3032.50 

1117.27 

2021.67 

838.031 

1516.25 

670.499 

1213.00 

40 

3352.59 

6066.67 

1676.36 

3033.33 

1117.65 

2022.22 

838.310 

1516.67 

670.723 

1213.33 

41 

3353.71 

6068.33 

1676.92 

3034.17 

1118.0212022.  78 

838.589 

1517.08 

670.946  1213.67 

42 

3354.82 

6070.00 

1677.47 

3035.00 

1118  39:2023.33 

838.869 

1517.50 

671.1701214.00 

43 

3355.94 

6071.67 

1678.03 

3035.83 

1118.76!2023.89 

839.148 

1517.92 

671.393 

1214.33 

44 

3357.06 

0073.33 

1678.59 

3036.67 

1119.132024.44 

839.427 

1518.33 

671.617 

1214.67 

45 

3358.21 

6075.00 

1679.16 

3037.50 

1119.522025.00 

839.714 

1518.75 

671.846 

1215.00 

46 

3359.35 

6076.67 

1679.74 

3038.33 

1119  902025.56 

840.000 

1519.17 

672.075 

1215.33 

47 

3300.47 

6078.33 

1680.30 

3039.17 

1120.272026.11 

840.280 

1519.58 

672.299 

1215.67 

48 

3361.59 

6080.00 

1680.85 

3040.00 

1120.64  2026.67 

840.559 

1520.00 

072.522 

1216.00 

49 

3362.70 

6081.67 

1681.41 

3040.83 

1121.02 

2027.22 

840.839 

1520.42 

672.746 

1216.33 

50 

3363.82 

6083.33 

1681.97 

3041.67 

1121.39 

2027.78 

841.118 

1520.83 

672.970 

1216.67 

51 

3364.94 

6085.00 

1682.53 

3042.50 

1121.76 

2028.33 

841.397 

1521.25 

073  .103 

1217.00 

52 

3366.05 

6086.67 

1683.09 

30-13.33 

1122.13 

2028.89 

841.677 

1521.67 

673.417 

1217.33 

53 

3367.17 

6088.33 

1683.65 

3044.17 

1122.51 

2029.44 

841.956 

152,  '.08 

673.640 

2  1  7  .  67 

54  13368.29 

6090.00 

1684.21 

3045.00 

1122.882030.00 

842.235 

1522.50 

673.864 

1218.00 

55  3369.41 

6091.67 

1684.77 

3045.83 

1123.252030.56 

842.515 

1522.92 

074.087 

1318.33 

56  3370.52 

6093.  33 

1685.32 

3046.67 

1123.622031.11 

842.794 

1523.33 

674.311 

1218.67 

57  13371.64 

6095.00 

1685.88 

3047.50 

1124.002031.67 

843.074 

1523.75 

674.584 

1219.00 

58 

3372.76 

6096.67 

1686.44 

3048.33 

1124.372032.22 

813.353 

1524.17 

674.758 

1219.33 

59 

3373.90 

6098.33 

1687.01 

3049.17 

1124.75  2032.78 

843  640 

1524.58 

074.987 

1219.67 

166 


TABLE   XIV. — ACTUAL    TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

6O° 

,     Ta  n  . 

Arc. 

Tan.  |   Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

55  1  .  58:5  1  000  .  00  4  72  .  80  1  857  .143 

413.833 

750.000  367.928 

666.667 

331.220 

600.000 

~O~ 

55  1  .  760  1  000  .  28  473  .  021  i  857  .  381 

413.973 

750.208i368.052 

666.852 

331.332 

600.167 

1 

551.955  100J.  50  473.181  857.619 

414.112 

750.  41  7  1368.1  76 

667.037 

331.444 

600.333 

3 

552.142!  1000.  83  473.340 

857.857 

414.252 

750.  625  !  368.  301 

667.222 

331.555 

600.500 

3 

552.328 

1001.11  473.500 

858.095 

414.392 

750.833368.425 

667.407 

331.667 

600.667 

4 

552.510 

1001.39 

473.  6GO 

858.333 

414.528 

751.042 

368.546 

667.593 

331.776 

600.833 

5 

55-3.09] 

1001.67 

473.819 

858.571 

414.664 

751.250 

368.667 

667.778 

331.885 

601.000 

6 

552.877 

1001.94 

473.975 

858.810 

414.804 

751.458 

368.791 

667.963 

331.997 

601.167 

7 

553.064 

1002.22 

474.131 

859.048 

414.944 

751.667 

368.916 

668.148 

332.109 

601.333 

8 

553.250 

1002.50 

474.290 

859.286 

415.084 

751.875 

369.040 

668.333 

332.221 

601.500 

9 

553.436 

1002.78 

474.450 

859.524 

415.223 

752.083 

369.164 

668.519 

332.  a33 

601.667 

1O 

553.623 

1003.06 

474.610 

859.762 

415.363 

752.292 

369.288 

668.704 

332.445 

601.833 

11 

553.809 
553.995 

1003.33474.769 
1003.61  474.929 

860.000 
860.238 

415.503 
415.643 

752.500 
752.708 

369.413 
369.537 

668.889 
669.074 

332.557 
332.668 

602.000 
602.167 

13 
13 

554.181 

1003.89 

475.089 

860.476 

415.783 

752.917)369.661 

669.259 

333.780 

602.333 

14 

554.  3U8 

1004.17 

475.249 

860.714 

415.922 

753.125 

369.785 

669.444 

332.892 

602.500 

15 

554.554 

1004.44 

475.408 

860.952 

416.062 

753.833 

369.910 

669.630 

333.004 

602.667 

16 

564.740 

1004.72 

475.568 

861.190 

416.202 

753.542370.034 

669.815 

333  116 

602.833 

17 

554.927 

1005.00 

475.728 

861.429 

416.342 

753.750370.158 

670.000 

333.228 

603.000 

18 

555.113 

1005.28 

475.887 

861.667 

416.481 

753.958 

370.282 

670.185 

333.340 

603.167 

19 

555.299 

1005.56 

476.047 

861.905 

416.621 

754.167 

370.407 

670.370 

333.452 

603.333 

20 

555.481 

1005.83 

476.203 

862.343 

416.757 

754.375370.528 

670.556 

333.561 

603.500 

31 

555.662 

1006.11 

476.358 

862.381 

416  894 

754.583370.649 

670.741 

333.670 

603.667 

33 

555.849 

1006.39 

476.518 

862  619 

417.033 

754.792370.773 

670.926 

333.781 

603.833 

33 

556.035 

1(106.67 

476.678 

862.857 

417.173 

755.000370.897 

671.111 

333.893 

604.000 

34 

556.22! 

1006.94 

476.837 

863.095 

417.313 

755.208 

371.022 

671.296 

334.005 

604.167 

35 

556.407 

1007.22 

47-6.097 

863.333 

417.453 

755.417 

371.146 

671.481 

334.117 

604.333 

36 

556.594 

1007.50 

477.157 

803.571 

417.592 

755.625 

371.270 

671  CG7 

334.229 

604.500 

37 

556.780 

1007.78 

477.317 

863.810 

417.732 

755.833371.395 

671.852 

334.341 

604.667 

38 

556.966 

1008.06 

477.476 

864.048 

417.872 

756.042 

371.519 

672.037 

334.453 

604.833 

39 

557.153 

1008.33 

477.636 

864.286 

418.012 

756.250 

371  .643 

672  222 

334.564 

605.000 

30 

557.339 

1008.61 

477.796 

864.524 

418.151 

758.4581371  767 

672.407 

334.676 

605.167 

31 

557.525 

1008.89 

477.955 

864.762 

418.291 

756.667 

371.892 

672.593 

334.788 

605.333 

33 

557.712 

1009.17 

478.115 

865.000 

418.431 

756.875 

372.016 

672.778 

334.900 

605.500 

33 

557.898 

1009.44 

478.275 

865.238 

418.571 

757.083  372.  140 

67'2.963 

335.012 

605.667 

34 

558.084 

1009.72 

478.435 

865.476 

418.711  757.292 

372.264 

673.148 

335.124 

605.833 

35 

558.270 

1010.00 

478.594 

865.714 

418.850 

757.500372.389 

673.333 

335.236 

606.000 

36 

558  457 

1010.28 

478.754 

865.952 

418.990 

757.708 

372.513 

673.519 

335.348 

606.167 

37 

558.643 

1010.56 

478.914 

866.190 

419.130 

757.917 

372.637 

673.704 

335.459 

606.333 

38 

558.829 

1010.83 

479.073 

866.429 

419.270 

758.125 

372.761 

673.889 

335.571 

606.500 

39 

559.016 

1011.11 

479.233 

866.667 

419.409 

758.333 

372.886 

674.074 

335.683 

G06.667 

4O 

559.202 

1011.39 

479.393 

866.905 

419.549 

758.542 

373.010 

674.259 

1335.795 

606  833 

41 

559.388 

1011.67 

479.553 

867.143 

419.689 

758.750 

373.134 

674.444 

335  907 

607.000 

43 

559.574 

1011.94 

479.712 

867.381 

419.829 

758  958 

373.259 

674.630 

336  019 

607.167 

43 

559.761 

1012.22 

479.872 

867.619 

419.969 

759.167 

373.383 

674.815 

336.131 

607.333 

44 

559.952 

1012.50 

480  036 

867.857 

420.112 

759.375 

373.510 

675.000 

336.245 

607.500 

45 

560.143 

1012.78 

480.200 

868.095 

420.255 

759.583 

373.638 

675.185 

336.360 

607.667 

46 

560.329 

1013.06 

480.359 

868.333 

420  395 

759.792 

373.762 

675.370 

336.472 

607.833 

47 

560.516 

1013.33 

480.519 

868.571 

420.535 

760.000 

373.886 

675.556 

336.584 

608.000 

48 

560.702 

1013.61 

480.679 

868.810 

420.675 

760.208 

374.011 

675.741 

336.  69f 

608.167 

49 

560.888 

1013.89 

480.838 

869.048 

420.814 

7G0.417 

37'4.135 

675.926 

336.808 

608.333 

50 

561.074 

1014.17 

480.998 

809  286 

420.954 

760.625 

374.259 

676.111 

336.919 

608.500 

51 

561.261 

1014.44 

481.158 

869.524 

421.094 

760.  833 

374.383 

676.296 

337.031 

608.667 

53 

561.447 

1014.72 

481.318 

869.762 

421.234 

761.042 

374.508 

676.481 

337.143 

608.833 

53 

561.633 

1015.00 

481.477 

870.000 

421.373 

761.250(374.632 

676.667 

337.255 

609.000 

54 

561.820 

1015.28 

181.637 

870.  23S 

421.513 

761.458374.756 

676.852 

337.367 

609.167 

55 

563.006 

1015.56 

481  .  797 

870.476 

421.653 

761.6671374.880 

677.037 

337.479 

609.333 

56 

562.192 

1015.83 

481.956 

870.714 

421.793 

761.875375.005 

677.222 

337.591 

609.500 

57 

562.379  1016.11 

482.116 

870.952 

421.932 

762.  083  :  37  5.  129 

677.407 

337.703 

609.667 

58 

502.  570  11016.39 

-183.280 

871.190 

422.076 

7'62.  292  1375.256 

677.593 

337.817 

609.833 

59 

167 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


61" 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tun.       Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

3375.05  0100.00 

1087.59 

3050.00 

1125.1320.-J3.33 

S  tt  .  '.)->6 

1525.00 

675.210 

1220.00 

1 

3376.  176101.  67 

1088.15 

3050.83 

1125.51 

2033.89 

844.205 

1525.42 

675.440 

1220.33 

2 

•3377.2816103.83 

1088.70 

3051  .  07 

1125.88 

2034.4} 

844.485 

1525.88 

675.663 

1220.67 

3 

3378.406105.00 

1689.26 

3052.50 

1126.25 

2035.00 

844  764 

1526.25 

675.887 

1221.00 

4 

3379.55 

6106.07 

1689.82 

3053.33 

1120.02 

2035.50 

845  .  0  14 

1520.07 

076.110 

1221.33 

5 

3380.64 

6108.33 

1690.38 

3054.17 

1120.99 

2030.11 

845.323 

1527.08 

676.334 

1221.07 

6 

3381.75 

6110.00 

16J0.94 

3055.00 

1127.37 

2030.07 

845.002 

1527.50 

676.557 

1222.00 

7 

3382.87 

6111.67 

1691.50 

3055.83 

1127.7*4 

2037.22 

845.882 

1527.92 

676.781 

1222.33 

8 

3383.99 

6113.33 

1092.06 

3050.67 

1128.11 

2037.78 

846.161 

1528.33 

677.004 

1222.67 

9 

3385.13 

6115.00 

1692.63 

3057.50 

1128.49 

2038.33 

846.448 

1528.75 

677.234 

1223.00 

10 

3386.28 

6116.67 

1693.20 

3058.33 

1128.88 

2038.89 

846.734 

1529.17 

677.463 

1223.  as 

11 

3387.40 

0118.33 

1093.76 

3059.17 

1129.25 

2039.44 

847.013 

1529.58 

677.686 

1223.67 

12 

3388.  M 

0120.00 

1694.32 

3060.00 

1129.02 

2040.00 

847.293 

1530.00 

677.910 

122400 

13 

3389.63 

6121.67 

1694.88 

3060.83 

1129.99 

2040.50 

S47.572 

1530.42 

678.134 

1224.33 

14 

3390.75 

6123.33 

1695.44 

3001.67 

1130.37 

2041.11 

847.852 

1530.83 

678.357 

1224.67 

15 

3391.87 

6125.00 

1696.00 

3062.50 

1130.74 

2041.07 

848.131 

1531.25 

678.581 

1225.00 

16 

3392.98 

6126.67 

1690.55 

3003.33 

1131.11 

2042.22 

848.410 

1531.67 

078.804 

1225.33 

17 

3394.13 

0128.33 

1697.13 

3064.17 

1131.49 

2042.78 

848.697 

1532.08 

679.033 

1225.67 

18 

3395.28 

6130.  OU 

16^7.70 

3065.00 

1131.88 

2043.33 

848.983 

1532.50 

679.263 

1226.00 

19 

339o.39 

6131.67 

1698.26 

3065.83 

1132.25 

2043.89 

849.263 

1532.92 

679.  4SO 

1226.33 

30 

3397.51 

6133.33 

1698.82 

3066.67 

1132.62 

2044.44 

849.542 

1533.33 

679.710 

1226.67 

21 

3398.03 

6135.0U 

1099.38 

3067.50 

1132.99 

2045.00 

849.822 

1533.75 

679.933 

1227.00 

33 

3339.  15 

6136.0; 

1099.93 

3068.33 

1133.37 

2045.50 

850.101 

1534.17 

080.157 

1227.33 

23 

3400.89 

6138.33 

1700.51 

3069.17 

1133.75 

2040.11 

850.387 

1534.58 

080  380 

1227.67 

24 

3402.04 

6140.00 

1701.08 

3070.00 

1134.13 

2046.07 

850.674 

1535.00 

080.015 

1228.00 

25 

3403.15 

0141.67 

1701.04 

3070.83 

1134.50 

2047.22 

850.953 

1535.42 

080.839 

1228.33 

20 

3404.27 

6143.33 

1702.20 

3071.67 

1134.87 

2047.78 

851.233 

1535.83 

681.062 

1228.67 

27 

.'3405.39 

6145.00 

1702.70 

3072.50 

11  3o.  25 

2048.33 

851.512 

1536.25 

681.286 

1229.00 

28 

3406  51 

6146.67 

1703.32 

3073.33 

1135.62 

2048.89 

851.792 

1536  67 

081.509 

1229.33 

29 

3407.05 

6148.33 

1703.89 

3074.17 

1136.00 

2049.44 

852.078 

1537.08 

081.  7'39 

1229.67 

30 

3408.80 

6150.00 

1704.46 

3075.00 

1136.38 

2050.00 

852.365 

1537.50 

081.968 

1230.00 

31 

3409.92 

6151.67 

1705.02 

3075.83 

1130.76 

2050.56 

852.044 

1537.92 

082.191 

1230.33 

32 

3  41  1.03 

6153.33 

1705.58 

3076.67 

1137.13 

2051.11 

852.923 

1538.33 

682.415 

1230.67 

33 

3412.16 

0155.00 

1706.15 

3077.50 

1137.51 

2051.67 

853.210 

1538.7'5 

682.644 

1231.00 

34 

3413.32 

6156.67 

1706.72 

3078.33 

1137.89 

2052.22 

853.490 

1539.17 

682  873 

1231.33 

35 

3414.44 

6158.33 

1707.28 

3079.17 

1138.20 

2052.78 

858.77* 

1539.58 

683.097 

1231.67 

30 

3415.56 

6160.00 

1707.84 

3080.00 

1138.64 

2053.33 

854.055 

1540.00 

683.320 

1232.00 

37 

3416.08 

6161.67 

1708.40 

3080.83 

1139.01 

2053.89 

854.335 

1540.42 

683.544 

1232.33 

38 

8  417.79 

6103.33 

1708.96 

3081.67 

1139.38 

2054.44 

854.614 

1540.83 

6N3  767 

1232.67 

39 

3118.94 

0105.00 

1709.53 

3082.50 

1139.70 

2055.00 

854.900 

1541.25 

083.997 

1233.00 

40 

3420.09 

6166.67 

1710.11 

3083.33 

1140.15 

2055.  56 

855.187 

1541.67 

684.236 

1233.33 

41 

3421.20 

6168.33 

1710.60 

3084.17 

1140.52 

2056.11 

855.460 

1542.08 

684.450 

1233.67 

42 

3422.32 

6170.00 

1711.22 

3085.00 

1140.892050.67 

855  746 

1542.50 

684.673 

1234.00 

43 

3423.47 

6171.07 

1711.80 

3085.83 

1141.272057.22 

856.032 

1542.92 

684.902 

1234.33 

44 

3424.01 

6173.33 

1712.373080.07 

1141.652057.78 

850.818 

1543.33 

685.132 

1234.07 

45 

3425.73 

0175.00 

1712.933087.50 

1142.032058.33 

856.598 

1543.75 

685.355 

1235  00 

46 

47 

3426.85 
3427  99 

0176.67 
617'8.33 

1713.493088.33 
1714.0G!3089.17 

1142.402058.89 
1142.782059.44 

856.878 
857.164 

1514.17 
1544.58 

685.579 
685  808 

1235.33 
1235.67 

48 

3129.14 

0180.00 

1714.  6313090.  00 

1143.162060.0' 

857  451 

1515.00 

686  037 

1236.00 

49 

343  J.  26 

6181.67 

1715.19 

3090.83 

1143.542060.56 

857.730 

1545.42 

686.261 

1236.33 

50 

3431.37 

6183.33 

1715.75 

3091.67 

1143.91 

2001.11 

858  009 

1545.83 

686.484 

1236.67 

51 

3132  52 

6185.00 

716.32 

3092.50 

1144.29 

2001.67 

858.296 

1546.25 

686.713 

1237.00 

52 

3433.66 

6186.67 

716.90 

3093.33 

1144.07 

2062.22 

858.582 

1546.67 

686.943 

1237.33 

53 

3434  78 

6188.33 

717.45 

3094.17 

1145.05 

2002.78 

858.862 

1517.08 

687.160 

1237.07 

54 

3435.90 

6190.00 

718.01 

3095.00 

1145.42 

2003.33 

859.111 

1547.50 

687.390 

1238.00 

55 

3437.05 

0191.67 

718.59 

3095.83 

1145.80 

2003.89 

859.428 

1547.92 

687.019 

1238.33 

56 

3138.19 

6193.33 

719.16 

3096.07 

1146.18 

2004.44 

859.714 

1548.33 

687.848 

1238.67 

57 

3439.31 

6195.00 

719.72 

3097.50 

1140.55 

2005.00 

859.994 

1548.75 

688.072 

1239.00 

58 

3440.43 

6196.07 

1720  28 

3098.33 

1146  93 

2065.56860.273 

1549.17 

688.295 

1239.33 

59 

3441.57 

0198.33 

1720.85 

3099.17 

1147.31 

2066.  11  i860.  560 

1549.581688.525 

1239.67 

168 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

61° 

1ST 

Tan. 

Arc. 

Tan. 

Arc.      Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

562.761 

1016.67 

482.444871.429422.219 

762.500 

375.384 

677.778 

337.932 

610.000 

0 

562.947 

1016.94 

482.  003  871.  667  422.  3f>9 

762.708 

37  5  .  508 

677.963 

338.044 

610.167 

i 

663.138 

1017.22 

482.763 

871.905422.499 

762.917 

375.632 

678.148 

338.156 

610.  333 

3 

563.320 

1017.50 

482.923 

872.143 

422.639 

703.125 

375.757 

678.333 

338.268 

610.500 

3 

563.506 

1017.78 

483.083 

872.381 

422.778 

763.333 

375.881 

678.519 

338,380 

610.667 

4 

563.692 

1018.06 

483.242 

872.619 

422.918 

763.542 

376.005 

678.704 

338.491 

610.833 

5 

563.878 

1018.33 

483.402 

872.857 

423.058 

763.7'50 

376.129 

67S.889 

338.603 

611.000 

6 

564.065 

1018.61 

483.562 

873.095 

423.198 

763.958 

376.254 

679.074 

338  715 

611.167 

7 

564.251 

1018.89 

483.721 

873.333 

423.337 

764.167 

376.378 

679.259 

338.827 

611.333 

8 

564.442 

1019.17 

483.885 

873.571 

423.481 

764.375 

376.505 

679.444 

338.942 

611.500 

9 

564.633 

1019.44 

484.049 

873.810 

423.624 

764.583 

376.633 

679.630 

339.056 

611  667 

10 

564.819 

1019.72 

484.209 

874.048 

423.764 

764.792 

376.757 

679.815 

339.168 

611.833 

11 

565.006 

1020.00 

484.368 

874.286 

423  904 

765  000 

376.881 

680.000 

339.280 

612.000 

12 

565.192 

1020.28 

484.528 

874.524 

424.043 

765.208 

377.006 

680.185 

339.392 

612.167 

13 

565.378 

1020.56 

484.688 

874.762 

424.183 

765.417 

377.130 

680.370 

339.504 

612.333 

14 

565.565 

1020.83 

484.847 

875.000 

424.323 

765.625 

377.254 

680.556 

339.616 

612.500 

15 

565.751 

1021.11 

485.007 

875.238 

424.463 

765.833 

377.378 

680.741 

339.728 

612.007 

16 

565.942 

1021.39 

485.171 

875.476 

424.606 

766.042 

377.506 

680.926 

339.842 

612.833 

17 

566.133 

1021.67 

485.  335 

875.714 

424.749 

766.250 

377.633 

681.111 

339.957 

613.000 

18 

566.319 

1021.94 

485.495 

875.952 

424.889 

766.458 

377.758 

681.296 

340.069 

613.167 

19 

566.506 

1022.22 

485.654 

876.190 

425.029 

766.667 

377.882 

681.481 

340.181 

613.333 

20 

566.692 

1022.50 

485.814 

876.429 

425.169 

766.875 

378.006 

681.667 

340.293 

613.500 

31 

566.878 

1022.78 

485.974 

876.667 

425.309 

767.083 

378.130 

681.852 

340.405 

613.607 

22 

567.069 

1023.06 

486.137 

876.905 

425,452 

767.292 

378  258 

682.037 

340.519 

613.833 

23 

567.200 

1023.33 

486.301 

877.143 

425.595 

767.500 

318.385 

682.222 

340.634 

614.000 

24 

567.447 

1023.61 

486.461 

877.381 

425.735 

767.708 

378.510 

682.407 

340.746 

614.167 

25 

567.633 

1023.89 

486.621 

877.619 

425.875 

767.917 

378.634 

682.593 

340.858 

614.333 

26 

507  819 

1024.17 

486.780 

877.857 

426.015 

768.125 

378.758 

682.778 

340.970 

614.500 

21 

568.006 

1024.44 

486.940 

878.095 

426.154 

768.333 

378.882 

682.963 

341.082 

614.667 

2% 

568.197 

1021.72 

487.104 

878.333 

426.298 

768.542 

379.010 

683.148 

341.196 

614.833 

2<J 

568.388 

1025.00 

487.268 

878.571 

426.441 

768.750 

379.137 

683.333 

341.311 

615.000 

3O 

568.574 

1025.28 

487.427 

878.810 

426.581 

768.958 

379.262 

683.519 

341.423 

615.167 

31 

608.760 

1025.56 

487  587 

879.048 

426.721 

769.167 

379.386 

683.704 

341  .  535 

615.333 

'32 

568.951 

1025.83 

487.751 

879.286 

426.864 

769.375 

379.513 

683  889 

341.650 

615.500 

33 

569.143 

1026.11 

487.915 

879.524 

427.007 

769.583 

379.641 

684.074 

341.764 

615.667 

34 

569.329 

1026.39 

488.074 

879.762 

427.147 

769.792 

379.765 

684.259 

341.876 

615.833 

35 

569.515 

1026.67 

488.234 

880.000 

427.287 

770.000 

379.889 

684.444 

341.988 

616.000 

30 

569.701 

1026.94 

488.394 

880.238 

427.427 

770.208 

380.014 

684  630 

342.100 

616.167 

37 

569.888 

1027.22 

488.554 

^80.476 

427.566 

770.417 

380.138 

684.815 

342.212 

616.333 

38 

570.079 

1027.50 

488.717 

880.714 

427.710 

770.625 

380.265 

685.000 

342.327 

616.500 

39 

570.270 

1027.78 

488.881 

880.952 

427.853 

770.833 

380.393 

685.185 

342.441 

616.667 

40 

570.456 

1028.06 

489.041 

881.190 

427.993 

771.042 

380.517 

685.370 

342.553 

616.833 

41 

570.642 

1028.33 

489.201 

881.42H 

428.133 

771.250 

380.641 

685.556 

342  665 

617.000 

43 

570.834 

1028.61 

489.364 

881.667 

428.276 

771.458 

380.769 

685.741 

342.780 

617.167 

43 

57  .025 

1028.89 

489.528^881.905 

428.419 

771.667 

380.896685.926 

342.894 

617.333 

44 

57  .211 

1029.17 

489.688 

882.143 

428.559 

771.875 

381.020686.111 

343.006 

617.500 

45 

57  .397 

1029.44 

489.848 

882.381 

428.699 

772.083 

381.145686.296 

343.118 

617.667 

46 

57  .58> 

1029.72 

490.011 

882.619 

428.  H42 

772.292 

381.  272  1  686.  481 

343.233 

617.833 

47 

57  .779 

1030.00 

490.175 

882.857 

428.986 

772.500 

381  .400 

686.667 

343.348 

618.000 

48 

57  .966 

1030.28 

490.335 

883.095 

429.125 

772.708 

381.524 

686.852 

343.460 

618.167 

49 

572.152 

1030.56 

490.495 

883.333 

429.2f>5 

772.917 

381.648 

687.037 

343.571 

618.333 

5O 

572.343 

1030.83 

490.658 

883.571 

429.409 

773.125 

381.776 

687.222 

343.686 

618.500 

51 

572.534 

1031.11 

490.822 

883.810 

429.552 

773.333 

381.903 

687.407 

343.801 

618.667 

53 

572.720 

1031.39 

490.982 

884.048 

429.692 

773.542 

382.027 

687.593 

343.913 

618.833 

53 

572.907 

1031.67 

491.142 

884.286429.831 

773.750 

382.152 

687.778 

344.025 

619.000 

54 

573.098 

1031.9-1 

491.305 

884.524429.975 

773.95S 

382.279 

687.963 

344.139 

019.167 

55 

573.289 

1032.22 

491.469 

884.762430.118 

774.167 

382.407 

688.148 

344.254 

619.333 

56 

573.475 

1032.50 

491.629 

885.000430.258 

774.375 

382  531 

688.  333 

344.366 

519.500 

57 

573.661 

1032.78 

41)1.  7  89  885.  238  430.  398 

774.583 

382.655 

688.519 

344.478 

619.667 

58 

573.852 

1033.  C6 

491.953885.476430.541 

774.792 

382.783 

688.704 

344.593 

619.833 

59 

169 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


62° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc 

~~~O~ 

3442.72 

6200.  i;0  1721.42 

3100.00  1147.69 

8066.  ($7 

860  846 

1550.00 

688.754 

1240.00 

1 

H43.86 

6  JO  1.67  1721.  99 

3100.83  1148.07 

2067.22 

861.133 

1550.4- 

688.988 

1240.33 

2 

-544").  0! 

6203.33 

1722.57 

3101.67 

1148.45 

2067.78 

861.419 

1550.83 

689.212 

1240.67 

3 

3146.13 

6205.00 

1723.13 

3102.50 

1148.83 

2068.33 

861.699 

1551.25 

689.436 

1241.00 

4 

3147.24 

6206.67 

1723.69 

3103.33 

1149.20 

2068.89 

861.978 

1551.67 

689.659 

1241.33 

5 

3148.39 

6.208.  :J3 

1724.26 

3104.17 

1149.58 

2069.44 

862.264 

1552.08 

689.889 

1241  67 

6 

3149.54 

6210.00 

1724.83 

3105.00 

1149.96 

2070.00 

862.551 

1552.50 

690.118 

1242.00 

7 

3150.68 

6211.67 

1725.40 

3105.83 

1150.35 

2070.56 

862.838 

1552.92 

690.347 

1242.33 

8 

MM.  88 

6213.33 

1725.98 

3106.67 

1150.73 

2071.11 

863.124 

1553.33 

690.576 

1242.67 

9 

3453.94 

6215.00 

1726.54 

3107.50 

1151.10 

2071.67 

863.403 

1553.75 

690.800 

1243.00 

10 

3454.08 

6216.67 

1727.09 

3108.33 

1151.47 

2072.22 

863.683 

1554.17 

691.023 

1243.33 

11 

3455.21 

6.  '18.  33 

1727.68 

3109.17 

1151.85 

2072.78 

863.969 

1554.58 

691.253 

1243.67 

13 

3(56.35 

62-30.00 

1728.24 

3110.00 

1152.24 

3073.88 

864.256 

1555.00 

691.482 

1244.00 

13 

3457.50 

6221.67 

172S.81 

3110.83 

1152.62 

2073.89 

864.542 

1555.42 

691.711 

1244.33 

14 

3158.65 

6223.33 

1729.39 

3111.67 

1153.00 

2074.44 

864.829 

1555.83 

691.940 

1244.67 

15 

3459.76 

6225.00 

1729.95 

3112.50 

1153.37 

2075.00 

865.108 

1556.25 

692.164 

1245.00 

10 

3460.88 

6226.67 

1730.50 

3113.33 

1153.75 

2075.56 

865.388 

1556.67 

692.  38S 

1245.33 

17 

3462.03 

6228.33 

1731.08 

3114.17 

1154.13 

2076.11 

865.674 

1557.08 

692.617 

1245.67 

18 

3463.17 

6230.00 

1731.65 

3115.00 

1154.51 

2076.67 

865  961 

1557.50 

692.846 

1246.00 

19 

3464.32 

6231.67 

1733.22 

3115.83 

1154.89 

2077.22 

866.247 

1557.92 

693  075 

1246.  33 

20 

3465.46 

6233.33 

1732.80 

3116.67 

1155.27 

2077.78 

866.534 

1558.33 

693.305 

1246.67 

21 

8466.68 

6235.00 

1733.35 

3117.50 

1155.65 

2078.33 

866.803 

1558.75 

693.528 

1247.00 

22 

3467.70 

6236.67 

1788.91 

3118.83 

1156.02 

2078.89 

867.093 

1559.17 

693.752 

1247.33 

23 

3468.84 

623S.33 

734.49 

3119.17 

1156.40 

2079.44 

867.369 

1559.58 

693.981 

1247.67 

24 

3469.99 

6240.00 

735.06 

3120.00 

1156.78 

2080.00 

867.666 

1560.00 

694.210 

1248.00 

25 

3471.14 

6241.67 

735.63 

3120.83 

1157.16 

2080.56 

867  952 

1560.42 

694.431) 

1248.33 

26 

3472.28 

6243.33 

736.20 

3121.67 

1157.55 

2081.11 

868.239 

1560.83 

694.669 

1248.67 

27 

3473.43 

6245.00 

736.78 

3122.50 

1157.93 

2081.6? 

868.535 

1561.25 

694.898 

1249.00 

28 

3474.57 

6246.67 

737.35 

3123.33 

1158.31 

2082.22 

868.812 

1561.67 

695.127 

1249.33 

29 

3475.69 

6248.33 

737.91 

3124.17 

1158.68 

2082.78 

869.091 

1562.08 

695.351 

1249.67 

30 

3476.81 

6250.00 

738.47 

3125.00 

1159.06 

2083.33 

860.371 

1562.50 

695.574 

1250.00 

31 

3477.95 

6251.67 

739.04 

3125.83 

1159.44 

2083.89 

869.657 

1562.92 

695.803 

1250.33 

32 

3479.10 

6253.33 

739.61 

3126.67 

1159.82 

2084.44 

869.944 

1563.33 

696.033 

1250.67 

33 

3480.25 

6255.00 

740.19 

3127.50 

1160.20 

2085.00 

870.230 

1563.75 

696.262 

1251.00 

34 

3181.39 

6256.67 

740.76 

3128.33 

1160.58 

2085.56 

870.517 

1564.17 

696.491 

1-351.33 

35 
36 

34S3.54 
3483.68 

6258.33 
6260.00 

741.33 
741.91 

3129.17  1160.97 
3130.  OO1  11  61.  35 

2086.11 
2086.67 

870.803 
871.090 

1564.58 
1565.00 

696.720 
696.950 

1251.67 
1252.00 

37 

3184.83 

6261.67 

742.48 

3130.83  1161.73 

2087.23 

871.376 

1565.4.' 

697.179 

1252.33 

38 

3485.03 

6263.33 

743.0J 

3131.67  1162.11 

2087.78 

8?  1.6(53 

1565.83 

607.408 

1252.67 

39 

3437.12 

6265.00 

743.63 

3133.501162.49 

2088.33 

871.919 

1566.25 

697.637 

1253.00 

40 

348S.27 

6266.67 

744.20 

3133.33  1162.88 

2088.89 

872.236 

1566.67 

697.867 

1253.33 

41 

3489.41 

6368.33 

744.77 

3134.17  1163.26 

2089.44 

872  523 

1567.06 

698.096 

1253.67 

42 

3490.56 

6270.00 

745.34 

3135.00  1163.64 

2090.00 

872.809 

1567.50 

698.325 

1254.00 

43 

3491.68 

6371.67 

745.90 

3135.83  1164.01 

2090.56 

873.088 

1567.92 

698.549 

1254.33 

44 

3192.79 

6373.33 

746.46 

3136.67  1164.38 

2091.11 

873.368 

1568.33 

698.772 

1254.67 

45 

3493.94 

6J75.00 

747.033137.50  1164.77 

3091.67 

873.654 

1568.75 

699.003 

1255.00 

46 

3495.01) 

6276.67 

1747.  6113138.  33!  1165.  15 

2092.22 

873.941 

1569.17 

699.231 

1255.33 

47 

3496.23 

6278.33 

748.183139.17  1165.53 

2092.78 

874.227 

1569.58 

699.460 

1255.67 

48 
49 

3497.38 
3498.52 

6280.00 
6281.67 

748  75  3140.00 
1749.333140.83 

1165.91 
1166.29 

2093.33 
2093.89 

874.514 
874.801 

1570.00 
1570.42 

699.689  1256.00 
699.9191256.33 

50 

3499.67 

6283.33 

1749.90 

3141.67 

1166.68 

2094.44 

875.  087  '  1570.  83 

700.1481256.67 

51 

3500.82 

6285.00  1750.47 

3142.50  1167.06 

2095.00 

875  374  1571.25 

700.377  1257.00 

52 

3501.96 

6286.67  1751.05 

3143.33  1167.44 

2095.56 

875.6601571.67 

700.606  1257.33 

53 

3503.1! 

6288.331751.63 

3144.171167.82 

2096.11 

875.947  1572.08 

700.  836  11257.  67 

54 

3504.25 

6290.00  1752.19 

3145.00  1168.20 

2096.67 

876  283  1572.50 

701.065  1258.00 

55 

3505.40 

6291.67  1752.76 

3145.83  1168.59 

2097.22 

876.520  1572.92 

7'0  1.294  1258.  33 

56 

3506.55 

6293.33  1753.34 

3146.671168.97 

2097.78 

876.806  1573.33 

701.523  1258.67 

57 

3507.6!) 

6295.00  1753.91 

3147.50  1169.35 

2098.33 

877.093  1573.75 

701.7531259.00 

58 

3508.84 

6296.67  1754.48 

3148.331169.73 

2098.89 

877.379  1574.17 

701.982  1259.33 

59 

3509.98 

6298.33  1755.06 

3149.17  1170.12 

2099.44877.6661574  58 

70-3.211  1259.67 

170 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

63° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

574.044 

1033.33 

492.116885.714 

430.684 

775.000 

382.910 

688.889 

344.707 

620.000 

0 

574.235  1033.01 

492.  280  '885.  952 

430.828 

775.208 

383.037689.074 

314.822 

620.167 

I 

574.420  1033.89 

492.444886.190 

430.971 

775.417 

383.165689.259 

344.937 

620.333 

2 

574  012 

1034.17 

492.604886.429 

431.111 

775.625 

383.  28S 

689.444 

345.049 

620.500 

3 

674.798 

1034.44 

492.703886.667 

431.251 

775.833 

383.413 

089.630 

345.161 

620.667 

4 

574.989 

1034.72 

492.927 

880.905 

431.394 

776.042 

383.541 

689.815 

315.275 

620.833 

5 

575.180 

1035.00 

493.091 

887.143 

431.537 

776.250 

383.608 

690.000 

345.390 

621.000 

6 

575.372 

1035.28 

493.255 

887.381 

431.681 

776.458 

3S3.79G 

690.185 

345.505 

621.167 

7 

575.503 

1035.50 

493.419 

887.619 

431.824 

776.607 

3S3.923 

690.370 

345.619 

621.333 

8 

575.749 

1035.83 

493.578 

887.857 

431.964 

776.875 

384.048 

090.556 

345.731 

621.500 

9 

575.935 

1036.11 

493.738 

888.095 

432.104 

77".  083 

384.172 

690.741 

345.843 

621.667 

10 

570.120 

1030.39 

493  902 

888.333 

482.247 

77".  292 

384.299 

090.926 

345.958 

621.833 

11 

570.317 

1030.67 

494.060 

888.571 

432.390 

77".  500 

384.427 

691  .111 

346.073 

622.000 

13 

570.508 

1036.94 

494.229 

888.810 

432.534 

77".  708 

384.664 

691.290 

346.187 

622.167 

13 

570.699 

1037.22 

494.393 

889  048 

432  677 

77".  917 

334.082 

691.481 

346.302 

622.333 

14 

570.880 

1037.50 

494.553 

889.280 

432  817 

778.125 

384.800 

691.067 

340.414 

622.500 

15 

577.072 

1037.78 

494.713 

889.524 

432.957 

778.333 

384.930 

091.852 

346.526 

622.667 

16 

577.203 

1038.06 

494.870 

889.702 

433.100 

778.542 

385.058i  092.  037 

346.641 

622.833 

17 

577.454 

1038.33 

495.040 

890.000 

433  243 

778.750 

385.185 

692.222 

346.755 

623.000 

18 

577.645 

1038.61 

495.204 

890.238 

433.387 

778.958 

385.313 

692.407 

346.870 

623.167 

19 

577.836 

1038.89 

495.368 

890.470 

433.530 

779.167 

385.440 

692.593 

346.985 

623.333 

20 

578.023 

1039.17 

495.528 

890.714 

433.670 

779.375 

385.504 

692.778 

347.097 

623.500 

21 

578.209 

1039.44 

495.087 

890.952 

433  810 

779.583 

385.088 

092.903 

347.209 

623.  667 

22 

578.400 

1039.72 

495.851 

891.190 

433.953 

779.792 

385.  8161693.  148 

347.323 

6243.  833 

23 

578.591 

1040.00 

490.015 

891.429 

434.090 

780.000 

385.943 

093.333 

347.438 

624.000 

24 

578.782 

1040.28 

490.179 

891.667 

434.240 

780.208 

386.071 

093.519 

347.553 

624.167 

25 

578.973 

1040.50 

490.342 

891.905 

434.383 

780.417 

386.198 

093.704 

347.668 

624.333 

26 

579.104 

1040.83 

490.500 

892.143 

434.526 

780.625 

386.326 

693.88!) 

347.782 

624.500 

27 

579.355 

1041.11 

490.  6iO 

892.381 

484.6ft) 

780.833 

386.453 

694.074 

347.897 

624.667 

28 

579.542 

1041.39 

490.830 

892.019 

434.809 

781.042 

386.577 

694.259 

348.009 

624.833 

29 

579.728 

1041.67 

496.989 

892.857 

434.949 

781.250 

386.702 

694.444 

348.121 

625.000 

30 

579.919 

1041.94 

497.153 

893.095 

435.093 

781.458 

386.829 

094.630 

248.236 

625.167 

31 

580.110 

1042.22 

497.317 

893.333 

435.236 

781.007 

386.957 

694.815 

348.350 

625.333 

32 

580.301 

1042.50 

497.481 

893.571 

435.379 

781.875 

387.084 

695.000 

348.465 

625.500 

33 

580  492 

1012.78 

497.045 

893.810 

435.523 

782.083 

387.212 

095.185 

348.580 

625.667 

34 

580  083 

1043.06 

497.808 

894.048 

435.000 

782.292 

387.339 

095.370 

348.694 

625.833 

35 

580.874 

1043.33 

497.972 

894.286 

435.809 

782.500 

387.466 

095.556 

348.809 

626.000 

36 

581.000 

1043.01 

498.130 

894.524 

435.953 

782.708 

387.594095.741 

348.924 

626.167 

37 

581.257 

1043.89 

498.300 

894.762 

430.090 

788.917 

387.721 

695.926 

349.039 

626.  333 

38 

581.448 

1044.17 

498.464 

895.000 

436.239 

783.125 

387.849 

096.111 

349.153 

020.500 

39 

581.639 

1044.44 

498.628 

895.238 

436.383 

783.333 

387.976 

696.296 

349.268 

626.667 

40 

581.830 

1044.72 

498.791 

895.476 

430.520 

783.542 

388.104 

696.481 

349.3*3 

626.833 

41 

582.021 

1045.00 

498.955 

895.714 

436.669 

783.750 

388.231 

696.  (567 

349.498 

627.000 

42 

582.207 

1045.28 

499.115895.952 

436.809 

783.958 

388.355 

096.852 

349.610 

627.167 

43 

582.394 

1045.50 

499.275896.190 

436.949 

784.107 

388.480 

697.037 

349.721 

627.333 

44 

582.585 

1045.83 

499.438896.429 

437.092 

784.375 

388.607 

697.222 

349.836 

627.500 

45 

582.776 

1046.11 

499.602896.607 

437.236 

784.583 

388.735 

697.407 

349.951 

627.007 

46 

582.907 

1046.39 

499.706890.905 

437.379 

784.792 

388.862 

697.593 

350.006627.833 

47 

583.158 

1046.07 

199.930  897.  143 

437.522 

785.000 

388.990 

697.778 

350.180628.000 

48 

583.349 

1040.94 

500.094897.381 

437.666 

785.208 

389.117 

697.963 

350.295 

028.107 

49 

583.540 

1047.22 

500.257897.619 

437.809 

785.417 

389.244 

698.148 

350.410 

628.333 

50 

583.731 

1047.50 

500.421 

897.857 

437.953 

785.625 

389.372698.333 

350.525628.500 

51 

583.922 

1047.78 

500.585 

89S.095 

438.090 

785.833 

389.499 

698.519 

350.639628.667 

52 

584.113 

1048.00 

500.7491898.333 

438.239 

786.042389.627 

698.704 

350.754 

028.833 

53 

584.304 

1048.33 

5D0.913898.571 

438  383 

786.250389.754 

698.889 

350  809 

629.000 

54 

584.495 

1048.01 

501.  070  S9S.  810 

438.520 

786.458389.882 

699.074 

350.983 

0->9.167 

55 

584  .  080 

1048.89 

501.-J40  8SW.048 

438.669 

780.007390.009 

699.259 

351.098 

029.333 

56 

584.877 

1049,17 

501.404  899.280 

438.813 

780.875390.137 

699.444 

351.213 

029.500 

57 

685.061) 

1049  44 

501.  508;  899.  524 

438.950787.083390.264 

699.630 

351.328 

029.007 

58 

585.200 

1049.72 

501.732]  899.  702 

439.099  787.292  390.  392  1  699.  815 

351.442029.833 

59 

171 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


63° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 
~O~ 

Tan. 
3511.13 

Arc. 

Tan.      Arc. 

Tan. 

Arc. 

2100.00 

Tan. 

877.952 

Arc. 

Tan. 

Arc. 

1260.00 

16300.00  1755.633150.00 

1170.50 

1575.00  702.440 

1 

35  1  2  .  28  630  1  .  07  1  756  .  20  31  50  .  83 

1170.8Sl2100.5ti  878.  23U  1575.42  702.  (570  1260.33 

•> 

3513.42 

6303.33  1756.783151.67 

1  1  71  .  20  2  1  (  )  1  .  1  1  ;  8  ,  8  .  520  1  575  .  s:j  702  .  899 

1260.67 

3 

3514.57 

6305  .  00  1  757  .  35  i  3  1  52  .  50 

1171.64:2101.07  878.812  157(5.25  703.128 

1261.00 

4 

3515.71 

6308  .  67  1  757  .  92  \  31  53  .  33 

1172.03  2102.22 

819.  09ti 

1576.07703.357 

1261.33 

5 

3510.86  6308.33  1758.4913154.  1? 

1172.41 

2102.78 

879.385 

1577.08  7'03.587 

1261.07 

6 

3518.01 

6310.00  1759.07,3155.00 

1172.79 

2103.33 

879.672 

1577.  50:703.  816 

1262.00 

7 

3519.15 

6311.67  1759.64  3155.83 

1173.17 

2103.89 

879.958 

1577.  92  1704.  045 

1262.33 

8 

3520.30 

6313.33  1760.21  3156.67 

1173.55 

2104.44 

880.245 

1578.33704.274 

1262.07 

9 

3521.44 

6315.00 

1760.79 

3157.50 

1173.94 

2105.00 

880.531 

1578.75 

704.504 

1263.00 

10 

3522.59 

6316.67 

1761.36 

3158.33 

1174.32 

2105.50 

880.818 

1579.17 

704.733 

1263.33 

11 

3523  73 

6318.33 

1761.93 

3159.17 

1174.70 

2106  11 

881.104 

1579.58704.902 

1263.67 

12 

3584.88 

6320.00 

1762.50 

3160.00 

1175.08 

2106.67 

881.391 

1580.00705.191 

1264.00 

13 

3526.06 

6321.67 

1763.09 

3160.83 

1175.47 

2107.22 

881.685 

1580.42705.426 

1264.33 

14 

3527.23 

6323.33 

1763.68 

3161.67 

1175.86J2107.78 

881.978  1580.831705.661 

1264.07 

15 

3528.38 

6325.00 

1764.25 

3162.50 

1176.  2512108.  33 

882.205  1581.  25  7'05.  891 

1205.00 

16 

3529.52 

63-36.67 

1761  83 

3163.33 

1176.632108.89 

882.551  1581.07  700.120 

1205.33 

17 

3530.  G7 

6328.33 

1765.40 

31(54.17 

1177.01 

2109.44 

882  .  838  1  582  .  (  >8  ,  7  00  .  349 

1205.07 

18 

3531.81 

6330.00 

1765.97 

3165.00 

1177.39 

2110  00 

883  .12411  582  .  50  7'00  .  578 

1200.00 

19 

3532.96 

6331.67 

1766.54 

3165.83 

1177.77 

2110.56 

883.41111582.92700.808 

1266.33 

20 

3534  11 

6333.33 

1767.12 

3166.67 

1178.16 

2111.11 

883.008 

1583.33 

707.037 

1266.67 

21 

3535.25 

6335.00 

1767.69 

3167.50 

1178.54 

2111.67 

883.984  1583.75707.260 

1207.00 

22 

3536.40 

6336.67 

1768.26 

3168.33 

1178.92 

2112.22 

884.  271  j  1  581.  17:  7t  '7.  4  95 

1207.33 

23 

3537.54 

633S.33 

1768.84 

3169.17 

1179.30 

2112.78 

884.557  1584.58  707.725 

1207.07 

24 

3538.69 

6310.00 

1769.41 

3170.00 

1179.68 

2113.33 

884.814 

1585.  00  707.  954 

1268.00 

25 

3539.84 

6341.67 

1769.98 

3170.83 

1180.07 

2113.89 

885.130 

1585.42708.183 

1268.33 

26 

3540.98 

6343.33 

1770.56 

3171.67 

118J.45 

2114.44 

885.417 

1585.  83  1708.41  3 

1268.67 

27 

3542.16 

6345.00 

1771.14 

3172.50 

1180.81 

2115.00 

885.710 

158(5.  25  17  OS.  04  7 

1269.00 

28 

3543.33 

6346.67 

1771.73 

3173.33 

1181.23 

2115.5(5 

880.001 

1586  67708.882 

1269.33 

29 

3544.48 

6348.33 

1772.30 

3174.17 

1181.61 

2116.11 

880.291 

1587.08 

709.112 

1269.67 

30 

3545.62 

6350.00 

1772.88 

3175.00 

1182.00 

2110.67 

883  .  577 

1587.50 

7'09.341 

1270.00 

31 

3546.77 

6351.67 

1773.45 

3175.83 

1182.38 

2117.22 

880  804 

1587.92 

709.570 

1270.33 

32 

3547.91 

6353.33 

1774.0:3 

3176.67 

1182.76 

2117.78 

887.150 

1588.33 

7'09.800 

1270.07 

33 

8649.06 

6355.00 

1774.59 

3177.50 

1183.14 

2118.33 

887.437 

1588.75 

710.029 

1271.00 

34 

3550.21 

6356.67 

1775.17 

3178.33 

1183.52 

2118.8!) 

887.723 

1589.17 

710.258 

1271.33 

35 

3551.38 

6358.33 

1775.76 

3179.17 

1183.92 

2119.44 

888.017 

158!).  58 

710.493 

1271.67 

36 

3552.55 

6360.00 

1776.34 

3180.00 

1184.31 

2120.  OU 

888.311 

1590.00 

710.728 

1272.00 

37 

3553.70 

6361.67 

1776.92 

3180.83 

1184.69 

2120.56 

888.597 

1590.42 

710.957 

1272.33 

38 

3554.85 

6363.33 

1777.49 

3181.67 

1185.07 

2121.11 

888.884 

1590.83 

711.187 

1272.07 

39 

3555.99 

6365.00 

1778.06 

3182.50 

1185.45 

2121.67 

889.170 

1591.25 

711.410 

1273.00 

40 

3557.14 

6366.67 

1778.63 

3183.33 

1185.83 

2122.22 

889.457 

1591.67 

711.645 

1273.33 

41 

3558.31 

6368.33 

1779.22 

3184.17 

1186  23 

2122.78 

889.751 

1592.08 

711.880 

1273.07 

42 

3559.49 

6370.00 

1779.81 

3185.00 

1186.02 

2123.33 

890.044 

1592.50 

712.115 

1274.00 

43 

3560.63 

6371.67 

1780.38 

3185.83 

1187.00 

2123.89 

890.331 

1592.92 

712.344 

1274.33 

44 

3561.78 

6373.33 

1780.96 

3186.67 

1187.38 

2124.44 

<90.G17 

1593  33  712.573 

1274.07 

45 

3562.93 

6375.00 

1781.53 

3187.50 

1187.76 

2125.00 

890.904 

1593.75  712.803 

1275.00 

46 

3564.07 

6376.67 

1782.10 

3188.33 

1188.15 

2125.56 

891.190 

1594.  17;  71  3.  032 

1275.33 

47 

3565.25 

6378.33 

1782.69 

3189.17 

1188.54 

2126.11 

891.484 

1594.58713.267 

1275.67 

48 

3566.42 

6380.00 

1783.28 

3190.00 

1188.93 

2126.C.7 

891.778 

1595.00  713.502 

1276.00 

49 

3567.57 

6381.67 

1783.85 

3190.83 

118J.31 

2127.22 

892.064 

1595.  42!  713.  731 

1276.33 

50 

3568.71 

6383.33 

1784.42 

3191.67 

1189.69 

2127  78 

892.351 

1595.83 

713.960 

1270.07 

51 

3569.86 

6385.00 

1781.99 

3192.50 

1190  08 

2128.33 

892.638 

1596.25  714.190 

1277.00 

52 

3571.00 

6386.67 

1785.57 

3193.33 

1190.46 

2128.89 

892.924 

1596.67:714.419 

1277.33 

53 

3572.18 

6388.33 

1786.15 

3194.17 

.190.85 

2129.41 

893.218 

1597.08714.654 

1277.07 

54 

3573.35 

6390.00 

1786.74 

3195.00 

1191.24 

2130.00 

893.511 

597.50  714.889 

1278.00 

55 

3574.50 

6391.67 

1787.32  3195.83 

1191.62 

2130.56 

893.798 

1597.92715.118 

1278.33 

56 

8575.65 

8393.88 

1787.893196.67 

1192.00 

2131.11 

894  085 

1598.33715.347 

1278.07 

57 

3576.79 

6395.00 

1788.46 

3197.50 

1192.39 

2131.67 

8!)4  371 

1598.75:715.577 

1279.00 

58 

3577.94 

6396.67 

1789  03 

3198.33 

1192.77 

2132  22 

894.658 

1599.  17!  715.  806 

1279.33 

59 

3579.11 

6398.33 

1789.62 

3199.17 

1193.16 

2132!  78 

894.951 

1599.  58  171  6.  041  1279.67 

TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

63° 
M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |  Arc. 

585.451 

1050.001501.895 

900.000 

439.243,787.500 

390  .519  700  .  000  351  .  557  630  .  000 

O 

585.642 

1050.  28  1502.  059 

900.238 

439.386 

787.708 

390  646  700  .  1  85  351  .  672  630  .  1  67 

1 

585.832 

1050.56  502.223 

900.470 

439.529 

787.917 

390  .  7  74  700  .  370  35  1  .  787  630  333 

586.024 

1050.83 

502.387 

900.71- 

439.673 

788.125 

390.901 

700.556351.901  630.500 

3 

586.215 

1051  .  1  1 

502.551 

439.816 

788.333 

391.029 

700.  741;  352.  01  6  630.  667 

4 

586.406  1051.39 

502.7I4'901.190 

439.960 

788.542 

391.150 

700.926352.131  630.833 

5 

586.597  1051.67 

502.878  901.429 

440.103 

788.750 

391.284 

701.111  352.246  631.000 

6 

586.7881051.94 

503  042  901.  667 

440.246 

788.958 

391.411 

701.296352.360631.167 

7 

586.979  1052.22 

503.206901.905 

440.390 

789.167 

391.539 

701.  481  1&52.  475  631.  333 

8 

587.170 

1052.50 

503.370 

902.143 

440.5:33789.375 

391.660 

701.667 

352.590 

631.500 

9 

587.361 

1052.78 

503.533 

902.381 

440.676789.583 

391.794 

701.852 

352.705 

631.667 

1O 

587.553:1053  06 

503.697902.619 

440.820789.792 

391.921 

702.037 

352.819631.833 

11 

587.744  1053.33 

503.861 

902.857 

440.963790.000 

392  048 

702.222 

352.934632.000 

13 

587.939  1053:61 

504.029 

903.095 

441.110790.208 

392.179 

702.407353.052  632.167 

13 

588.135  1053.S9 

504.197 

903.333 

441.257 

790.417 

392.310 

702.593353  169632.333 

14 

588.326 

1054.17 

504.361 

903.571 

441.400 

790:625 

392.437 

702.778 

353.284  632.f,00 

15 

588.517 

1054.44 

504.524 

903.810 

441.544 

790.833 

392.565 

702.963 

353.399632.667 

16 

588.7081054.72 

504.688 

904.048 

441.687 

791.042 

392.692 

703.148 

353.513632.833 

17 

588.900  I055.ni 

504.852 

904.  28( 

441.830 

791.250 

392.820 

703.333 

353.628633.000 

18 

589.091 

1055.28 

505.016 

904.524 

411.974 

791.458 

392.947 

703  519 

353.743 

633.167 

19 

589.282 

1055.56 

505.180 

904.762 

442.117 

791.667 

393.074 

703.704 

353.858 

633  333 

2O 

589.473 

1055.83 

505.343 

905.000 

442.260 

791.875 

393  202 

703.889 

353.972  633  500 

21 

589.664 

1056  .  1  1 

505.507 

905.238 

442.404 

792.083 

393.329 

704  074 

354.087 

633.667 

589.855 

1056.39 

505.671 

905.476 

442.547 

792.292 

393.457 

704.259 

354.202 

633.833 

23 

590.046 

1056.67 

505.8:35 

905.714 

442.  69( 

792.500 

393.584 

704  444 

354.317 

634.000 

24 

590.237 

1056.94 

505.999 

905.952 

442.834 

792.708 

393.712 

704.630 

354.431 

634.167 

25 

590.428 

1057  22 

506.163 

906.190 

442.977 

792.917 

393.839 

704.815 

354.546 

6:34.333 

26 

590.624 

1057.50 

506.330 

906.429 

443.124 

793.125 

393.970 

705.000 

351.  (164 

634.500 

27 

590.820 

1057.78 

506.498 

906.667 

443.271 

793.333 

394.100 

705.185 

354.781 

634.667 

28 

591.011 

1058.06 

506.662 

906.905 

443.414 

793.542 

394.228 

705.370 

354.896 

634.833 

29 

591.202 

1058.33 

5C6.826 

907.143 

443.558 

793.750 

394.355 

705.556 

355.011 

635.000 

30 

591.393 

1058.61 

506.990 

907.381 

443.701 

793.958 

394.483 

705.741 

355.126 

635.167 

31 

591.584 

1058.89 

507.15-i 

907.619 

443.844 

794.167 

394.610 

705.926 

355  240 

635.333 

32 

591.775 

1059.17 

507.317 

907.857 

443.988 

794.375 

394.738 

706.111 

355.355 

635.500 

33 

591  .  966 

1059.44 

507.481 

908.095 

444.131 

794.583 

394.865 

706.296 

355.470 

635.667 

34 

592.162 

1059.72 

507.649 

908.333 

444.278 

794.792 

394.996 

706.481 

355.587 

635  833 

35 

592.358  1060.00 

507.817 

908.571 

444.425 

795.000 

395.126 

706.667 

355.705 

636.000 

36 

592.549  1060.28 

507.  9S1 

908.810 

444.568 

795.208 

395.254 

706.852 

355.820 

636.167 

37 

592.740 

1060.50 

508.145 

909.  (-48 

444.712 

795.417 

395.381 

707.037 

355.9:34 

636.333 

38 

592.931 

1060.83 

508.308 

909.286 

444.855 

795.625 

395.509 

707.222 

356.049 

636.500 

39 

593.122 

1061.11 

508.472 

909.524 

444.998 

795.833 

395.636 

707.407 

356.164 

636.667 

40 

5U8.318 

1061.39 

508.640 

909.76-.' 

445  145 

796.042 

395.767 

707.593 

356.282 

636.833 

41 

593.514 

1061.67 

508.808 

910.000 

445.292 

796.250 

395.898 

707.778 

356.399 

637.000 

42 

593.705 

1061.94 

508.972 

910.238 

445.436 

796.458 

396.025 

707.963 

356.514 

637.167 

43 

593.896 

1062.22 

509.136 

910.476 

445.579 

796.667 

396.152 

708.148 

356.629 

637.833 

44 

594.087 

106:2.50 

509.299 

910.714 

445.722 

796.875 

396.280 

"08.333 

356.743 

637.500 

45 

594.278 

1062.78 

509.463 

910.952 

445.866 

797.083 

396.407 

"08.519 

356  858 

637.667 

46 

594.474 

1063.06 

509.631 

911.190 

446.013 

797.292 

396.538 

"08.704 

356.976 

637.833 

47 

594.670 

1063.33 

509.799 

911.429 

446.160 

797.500 

396.669 

"08.S89 

357.093 

638.000 

48 

594.861 

1063.61 

509.963 

911.887 

446.303 

797.708 

396.796 

"09.074 

357.Ji08 

638.167 

49 

595.052 

1063.89 

510.127 

911.905 

416.446 

797.917 

396.924 

'09.259 

357.323 

638.333 

5O 

595.243 

1064.17 

510.290 

912.143 

446.590 

798.125 

397.051 

"09.444 

357.438 

638.500 

51 

595  434 

1064.44 

510.454 

912.381 

446.733 

798.333 

397.178 

"09.630 

357.  flf* 

i38.G67 

52 

595.630 

1084.72 

510.622 

912.619 

446.880 

798.542 

397.309 

"09.815 

357.670638.833 

53 

595.826 

1065.00 

510.790 

912.857 

447.027 

798.  7'50 

397.440 

"10.000 

357.  7>7  639  000 

54 

596.017 

1065.28 

510.954 

913.095 

447.170 

798.958 

397.567 

"10.185 

357.902639.167 

55 

596.208 

1065.56 

511.118 

913.333 

447.314 

799.167 

397.695 

"10.370 

358.017639.333 

56 

596  399 

1065.83 

511.281 

913.571 

447.457 

799.375 

307.822 

"10.556 

358.132639.500 

57 

596.590 

1066.11 

511.445 

913.810 

4(7.600 

799.583 

397.950 

-"10.741 

358.246639  667 

58 

596.786 

1066.39 

511.613 

914.048 

447.747 

1*99  792 

398.080 

"10.926 

358.364639.833 

59 

173 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


64° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

^7 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
1193.55 

Arc. 
2133733 

Tan. 

Arc. 

Tan. 

Arc. 

o 

3580.29 

6400.00 

1790.21 

3200.00 

895.245 

1600.00 

716.276 

1280.00 

i 

8581.43 

6401.67 

1790.78 

3200.83 

1193.93 

2133.8'J8J)5.532 

1600.42 

716.505 

1280.33 

3 

3582.58 

6403  33 

1791.35 

3201.67 

1194.32 

2134.44895.818 

1600.83 

716.734 

1280.  (57 

3 

3583.75 

6405.00 

1791.94 

3202.50 

1194.71 

2135.00896.112 

1601.25 

716.969 

1281.00 

4 

3584.93 

6406.67 

1792.53 

3203.33 

1195.10 

2135.56896.405 

1601.67 

717.204 

1281.33 

5 

3586.  OT 

6408.33 

1793.10 

3204.17 

1195.48 

2136.11 

896.692 

1602.08 

717.434 

1281.67 

6 

3587.22 

6410.00 

1793.6!^ 

3205.0D 

1195.86 

2136.67 

896.979 

1602.50 

717.663 

1282.00 

7 

3588.39 

6411.67 

1794.26 

3205.83 

1196  25 

2137.22 

897.272 

1602.92 

717.898 

1282.33 

8 

3589.5? 

6413.33 

1794.85 

3206.67 

1196.65 

2137.78897.566 

16d3.33 

718.133 

1*82.67 

9 

3590.71 

6415.00 

1795.4-2 

3207  50 

1197.03 

2138.33 

897.852 

1603.75 

718.362 

1283.00 

1O 
11 

3591.86 
3593.03 

6416.67 
6418.33 

1796.00 
1796.58 

3208.33 
3209.17 

1197.41 
1197.80 

213S.89 
2139.44 

898.139 
898.433 

1604.17 
1604.58 

718.591 

7  IS.  82(5 

1283.33 
1283.67 

13 

3594.21 

6420.00 

1797.17 

3210.00 

1198.19 

2140.00 

898.726 

1605.00 

7  19..  061 

1284.00 

13 

3595.36 

6421.67 

1797.74 

3210.83 

1198.58 

2140.56 

899.013 

1605.42 

719.291 

1284.33 

14 

3596.50 

6423.33 

1798.32 

3211.67 

119S.96 

2141.11 

899.300 

1605.83 

719.520 

1284.67 

15 

3597.68 

6425.00 

179S.90 

3212.50 

1199.35 

2141.67 

899.593 

1606.25 

719.755 

1285.00 

16 

3598.85 

6426.67 

1799.49 

3213.33 

1199.74 

2142.22 

899.887 

1606.67 

719.990 

1285  33 

17 

3600.03 

6428  33 

1800.08 

3214.17 

1200.13 

2142.78 

900.181 

1607.08 

720.225 

1285.67 

18 

3601.20 

6430.00 

1800.67 

3215.00 

1200.52 

2143.33 

900.474 

1607.50 

720.460 

1286.00 

19 

3602.35 

6431.67 

1801.24 

3215.83 

1200.91 

2143.89 

900.761 

1607.92 

720.689 

1286.33 

2O 

3603.49 

6433.33 

1801.81 

3216.67 

1201.29 

2144.44 

901.047 

1608.33 

720.918 

1286.67 

31 

3604.07 

6435.00 

1802.40 

3217.50 

1201.68 

2145.00 

901.341 

1608.75 

721.153 

1287.00 

22 

3(505.84 

6436.67 

1802.99 

3218.33 

1202.07 

2145  53 

901.635 

1609.17 

721  .388 

1287.33 

23 

3606.99 

6438.33 

1803.56 

3219.17 

1202.45 

2146.11 

901.921 

1609.5S 

721.618 

1287.67 

24 

3608.13 

6440.00 

1804.13 

3220.  OJ 

1202.83 

2146.67 

902.208 

1610.00 

721.847 

1288.00 

25 

3609.31 

6441  .  67 

1801.72 

3220.85 

1203.23 

2147.22 

9">2.502 

1H10.42 

722.082 

1288.33 

26 

3610.48 

6443.33 

1805.31 

3221.67 

1203.62 

2147.78 

902.795 

1610.83 

722.31? 

1288.67 

21 

3611.66 

6445.00 

1805.89 

3222.50 

1204.01 

2148.33 

903.089 

1611  25 

722.552 

1289.00 

28 

3612.83 

6446.67 

1806.48 

3223.33 

1204.40 

2148.89 

903.383 

1611.67 

722.78? 

1289.33 

29 

3613.98 

6448.33 

1807.05 

3224.17 

1204.78 

2149.44 

903.669 

1612.08 

723.016 

1289.67 

30 

3615.12 

6450.00 

1807.63 

3225.00 

1205.16 

2150.00 

903.956 

1612.50 

723.245 

1290.00 

31 

3616.30 

6451.67 

1808.2! 

3225.83 

1205  56 

2150.56 

904.249 

1612.92 

723.480 

1290.33 

32 

3617.47 

6453.33 

1808.80 

3226.67 

1205.95 

2151.11 

904  543 

1613.33 

723.715 

1290.67 

33 

3618.65 

6455.00 

1809.39 

3227.50 

1206.34 

2151.67 

904.837 

1613.75 

723.950 

1291.00 

34 

3619.82 

(5456.67 

1809.9S 

3228.33 

1206.73 

2152.22 

905.131 

1614.17 

724.185 

1291.33 

35 

36-20.97 

6458.33 

1810.55 

3229.17 

1207.11 

2152.78 

905.417 

1614.58 

724.415 

1291.67 

36 

3622.11 

6460.00 

1811.12 

3230.00 

1207.50 

2153.33 

905.704 

1615.00 

724.644 

1292.00 

37 

3623  29 

6461.67 

1811.71 

3230.83 

1207.89 

2153.89 

905.997 

1615.42 

724.879 

1292.33 

38 

3621.46 

6463.33 

1812.30 

3231.67 

1208.28 

2154.44 

906.291 

1615.83 

725.114 

1292.67 

39 

3625.64 

6465.00 

1812.88 

3232.50 

1208.6? 

2155.00 

90,3.585 

1616.25 

725.349 

1293.00 

4O 

3626.81 

6466.67 

1813.47 

3233.33 

1209.06 

2155.56 

906.878 

1616.67 

725.584 

1293.33 

41 

3627.99 

6468.33 

1814.06 

3234.17 

1209.45 

2156.11 

907.172 

1617.08 

725.819 

1293.67 

43 

3629.16 

6470.00 

1814.65 

3235.00 

1209.84 

2156.67 

907.466 

1617.50 

726.054 

1294.00 

43 

3630.31 

6471.67 

1815,22 

3235.83 

1210.23 

2157.22 

907.752 

1617.92 

726.283 

1294.33 

44 

3631.45 

6473.33 

1815.79 

3236.67 

1210.61 

2157.78 

908.039 

1618.33 

726.512 

1294.67 

45 

3632.63 

6475.00 

1816.38 

3237.50 

1211.00 

2158.33 

908.333 

1618.75 

726.747 

1295.00 

46 

3633.80 

6476.67 

1816.97 

3238.33 

1211.39 

2158.89 

908.626 

1619.17 

726.982 

1295.33 

47 

3634.98 

6478.33 

1817.55 

3.  '39.  17 

1211.78 

2159.44 

908.920 

1619.58 

727.217 

1295.67 

48 

3636.15 

6480.00 

1818.14 

3240.00 

'212  17 

2160.00 

909.214 

1620.00 

727.452 

1296.00 

49 

3637.33 

6481.67 

1818.73 

3240.83 

1212.57 

2160.56 

909.507 

1620.42 

727.687 

1296.  33 

50 

3638.50 

6483  33 

1819.32 

3241  67 

1212.96 

8ttl.11 

909.801 

1620.83 

727.922 

1296.67 

51 

3639.67 

6485.00 

1819.90 

3242.50 

1213.35 

2161.67 

910.095 

1621.25 

728.157 

1297.00 

53 

3640.85 

6486  67 

1820.49 

3243.33 

1213.71 

2162.22 

910.  3S9 

1621.67 

728.392 

1297.33 

53 

3641.99 

6488.33 

1821.06 

3244.17 

1214.12 

2162.78 

910.675 

1622.08 

728.621 

1297.67 

54 

3643.14 

6490.00 

1821.64 

3245.00 

1214.51 

21  a<*.  83 

910.962 

1622.50 

728.851 

1298.00 

55 

3644.32 

6491.67 

1822.22 

3245.83 

1214.90 

2163.89911.255 

1622.92 

729.086 

1298.33 

56 

3645.49 

6493  33 

1822.81 

3246.67 

1215  29 

2164.44  911.549 

1623.33 

729.321 

1298.67 

57 

3646.66 

6495.00 

1823.40 

3247.50 

1215.68 

21  65.00!  91  1.843 

1623.75 

729.556 

1299  00 

58 

3647.84 

6496.67 

1823.99 

3248.33 

1216.07 

2165.56912.136 

1624.1? 

729  791 

1299.33 

59 

3649.  Olj  6498.  33 

1824.57 

3249.1? 

1216.  4612166.  11:912.  430 

1624.58 

730.026 

1299.67 

174 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Cnrve. 

1O°  Curve. 

64° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

596.982 

1066.67 

511.781  9H.28C) 

447.894 

800.000398.211 

711.111 

358.482 

640.000 

0 

597.173 

1066.94 

511.945914.524 

448.038 

800.208398.338 

711.296 

358.596 

640.167 

1 

597.364 

1067.22 

512.109914.762 

448.181 

800.417398.466 

711.481 

358.711 

640.333 

3 

597.560 

1067.50 

512.276915.000 

448.328 

800.  625  '398  596 

711.667 

358.829 

640.500 

3 

597.756 

1067.78 

512.444 

915.  23H 

448.475 

800.  833  '398.  727 

711.852 

358.946 

640.667 

4 

597.94; 

1068.06 

512.608 

915.476 

448.618 

801.042 

398.854 

712.037 

359.061 

640.833 

5 

598.138 

1068  .33 

512.772 

915.714 

448.762 

801.250 

39S.982 

712.222 

359.176 

641.000 

6 

598.334 

1068.61 

512.940 

915  952 

448.909 

801.458 

399.113 

712.407 

359.293 

641.167 

7 

598.530 

1068.89 

513.108 

916.190 

449.055 

801.667 

399  .  243 

712.593 

359.411 

641.333 

8 

598.721 

1069.17 

513.272 

916.429 

449.199 

801.875 

399.371  712.778 

359.526 

641.500 

9 

598.912 

1069.44 

513.435 

916.667 

449.342 

802.083 

399.498712.963 

359.640 

641.667 

1O 

599.108 

1069.72 

513.603 

916.905 

449.489802.292 

399.629713.148 

359.758 

641.833 

11 

599.304 

1070.00 

513.771 

917.143 

449  636802.500 

399.759713.333 

•359  876 

642.000 

13 

599.495 

1070.28 

513.935 

917.381 

449.779802.708 

399.887713.519 

359.990 

642.167 

13 

599.686 

1070.56 

514.099 

917.619 

449.923802.917 

400.014713.704 

300.105 

642.333 

14 

599.882 

1070.  as 

514.267 

917.85? 

450.  07  0803."  125 

400.145713.889 

360.223 

642.500 

15 

000.077 

1071.11 

514.435 

918.095 

450.217803.333 

400.27'6714.074 

360.340 

642.667 

16 

600.273 

1071.39 

514.603 

918.333 

450.364803.542 

400.406714.259 

360.458 

642.833 

17 

600.469 

1071.67 

514.770 

918.571 

450.511  803.750 

400.537714.444 

360.576 

643.000 

18 

600.660 

1071.94 

514.934 

918.810 

450.654 

803.958 

400.664 

714.630 

360.690 

643.167 

19 

600.851 

1072.2v 

515.098 

919.048 

450  797 

804.167 

400.792 

714.815 

360.805 

643.333 

30 

601.047 

1072.50 

515.266 

919.286 

450.944 

804.375 

400.922 

715.000 

360  923 

643.500 

31 

601.243 

1072.78 

515  434 

919.524 

451.091 

804.583 

401.053 

715.185 

361.040 

643.667 

33 

601.434 

1073.06 

515.598 

919.762 

451.234 

804.792 

401.181 

715.370 

361.155 

643.833 

33 

601.625 

1073.33 

515.761 

920.000 

451  378 

805.000 

401.308 

715.556 

361.270 

644.000 

34 

601.821 

1073.61 

515.929 

920.238 

451.525 

805  208 

401.439 

715.741 

361.387 

644.167 

35 

602.017 

1073.89 

516.097 

920.476 

451.672 

805.417 

401.569 

715.926 

361.505 

644.333 

36 

602.213 

1074.17 

516.265 

920.714 

451.819 

805.625 

401.700 

716.111 

361.623 

644.500 

37 

602.408 

1074.44 

516.433 

920.952 

451.966 

805.833 

401.831 

716.296 

361.740 

644.667 

38 

602.600 

1074.72 

516.597 

921  190 

452.109 

806.042 

401.958 

716.481 

361.855 

644.833 

39 

602.791 

1075.00 

516.761 

921.429 

452.252 

806.250 

402.085 

716.667 

361.970 

645.000 

3O 

602.987 

1075.28 

516.929 

921.607 

452.399 

806.458 

402.216 

716.852 

362.087 

645.167 

31 

603.182 

1075.56 

517.096 

921  905 

452.546 

806.667 

402.347 

71  \037 

362.205 

645.333 

33 

603.378 

1075.83 

517.264 

922.143 

452.693 

806.875 

402.477 

7r.222 

362.322 

645.500 

33 

603.574 

1076.11 

517.43V1 

922.381 

452.840 

807.083 

402.  60H 

7r.407 

362.440 

645.067 

34 

603.765 

1076.39 

517.596 

922.619 

452.983 

807.292 

402.735 

7r.593 

362.555 

645.833 

35 

603.956 

1076.67 

517.700 

922.857 

453.127 

807.500 

402.863 

717.778 

362.670 

646.000 

36 

604.152 

1076.94 

517.928 

923.095 

453.274 

807.708 

402.994 

717.963 

362.787 

646.167 

37 

604.348 

1077.22 

518.096 

923.333 

453.421 

807.917 

403.124 

718.148 

362.905 

646.333 

38 

604.544 

1077.50 

518.264 

923.571 

453.568 

808.125 

4U3.255 

718.333 

363.022 

646.500 

39 

604.740 

1077.78 

518.431 

923.810 

453.715 

808  333 

403.385 

718.519 

363.140 

646.667 

4O 

604.935 

1078.06 

518.599 

924.048 

453.861 

808.542 

403.516 

718  704 

363.258 

646.833 

41 

605.131 

1078.33 

518.767 

924.280 

454.008 

808.750 

403.647 

718.889 

363.375 

647.000 

43 

605.322 

1078.61 

518.931 

924.524 

454.152 

808.958 

403.774 

719.074 

363.490 

647.167 

43 

605.513 

1078  89 

519.095 

924.762 

454.295 

809.167 

403.902 

719.259 

363.605 

647.333 

44 

605.709 

1079.17 

519.263 

925.000 

454.442 

809  375 

404.032 

719.444 

363.722 

647.500 

45 

605.905 

1079.44 

519.431 

925.238 

454.589 

809.583 

404.163 

719.630 

363.840 

647.667 

46 

606.101 

1079.72 

519  599 

925.476 

454.736 

809.792 

404.294 

719.815 

•3G3.957 

647.833 

47 

606.297 

1080.00 

519.766 

925.714 

454.883 

810.000 

404.424 

720.000 

364.075 

648.000 

48 

606.493 

1080.28 

519.934 

925.952 

455.030 

810.208 

404.555 

720.185 

364.193 

648.167 

49 

| 

606.689 

1080.56 

520.102926.190 

455.177 

810  417 

404.686 

720.370 

-564.310 

648.333 

5O 

606.884 

1080.83 

520.270926.429 

455.324 

810.625 

404.816 

720.556 

364.428 

648  500 

51 

607.080 

1081.11 

520.438926.667 

455.471 

810.833 

404.947 

720  741 

364.546 

648.607 

53 

607.271 

1081.39 

520.  602  '926.  905 

455.614 

811.042 

405.074 

720.926 

364.660 

648.833 

53 

607.462 

1081.67 

520.766 

927.143 

455.757 

811.250 

405.202 

721.111 

364.775 

649.00( 

54 

607.658 

1081.9) 

520.934 

927.381 

455.904 

811.458 

405.332 

721.296 

364.893 

649  107 

55 

607.854 

1082.2-,' 

521.101 

927.619 

456.05! 

811.007 

405.463 

721.481 

305.010 

049.333 

56 

608.050 

1082.50 

521.269 

927.857 

456.198 

811.875 

405.594 

721.667 

365.128 

649  500 

57 

608.246 

1082.78 

521.437 

928.095 

456.345 

812.083 

405.724 

721.852 

365.245 

649.667 

58 

608.442 

1083.06 

521.605 

928.333 

456.492 

812.29.' 

405.855 

722.  037 

365.363  649.833 

59 

175 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


65° 

1°  Carve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

IST 
~~o 

Tittt. 

3~050~l9 

Arc. 

Tan. 

A  re. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

6500.03 

1825.163250.00 

1216.85 

2160.67 

912.724 

1625.00 

730.261 

1300.00 

i 

8051.8(3 

0501  .  67 

18^5.75'3250.H3 

1217.25 

2307.22 

913.018:1025.42 

730.496 

1300.33 

2 

805:3.54 

05U3  .  33 

1826.  34  '325  1.07 

1217.64 

2107.78 

913.311  1025.83 

730.  731  i  1300.  67 

3 

305:3.71 

0505.00 

1826.923252  50 

1218.03 

2168.33 

913.005  1020.25 

730.966 

1301.00 

4 

3054.89 

6500  07 

1827.51  3253.33 

1218.42 

2168.89 

913.899  1020.07 

731.201 

1301.33 

5 

3056.06 

6508.33 

1828.10 

3254.17 

1218.81 

2169.44 

914.192  1027.08 

731.436 

1301.67 

6 

3057.24 

6510.00 

1828.68 

3255.00 

1219.20 

2170.00 

914.480  1027.50 

731.671 

1302.00 

7 

3058.41 

6511.67 

1829.27 

3255.83 

1219.00 

2  70.56 

914.780 

1027.92 

731.906 

1302.33 

8 

3059.58 

6513  33 

1829.86 

3256.67 

1219.99 

2  71.11 

915.073 

1028.33 

732.140 

1302.67 

9 

3060.76 

6515.00 

1830.45 

3257.50 

1220.38 

2  71.67 

915.307 

1628.75 

732.375 

1303.0J 

1O 

3661.93 

6516.67 

1831.03 

3258.33 

1220.77 

2  72.22 

915.661 

1629.17 

732.010 

1303  33 

11 

3603.11 

6518.33 

1831.62 

3259.17 

1221.16 

2  72.78 

915.955 

1629.58 

7'32.845 

1303  07 

12 

3664.28 

6520.00 

1832.21 

3200.00 

1221.55 

2  73.33 

916.248 

1030.00 

733.080 

130400 

13 

3605.40 

6521.67 

1832.80 

3260.83 

1221.95 

2  73.89 

916.542 

1030.42 

733.315 

1304.33 

14 

3000.63 

6523.33 

1833.38 

3261.67 

1222.31 

2  74.44 

916.830 

1030.83 

733.530 

1304.67 

15 

3007.81 

6525.00 

1833.97 

3262.50 

1222.73 

2  75.00 

917.129 

1031.25 

7'33.785 

1305.00 

16 

3668.98 

6526.67 

1834.50 

3263.33 

1223.12 

2  75.56 

917.  423|  1031.  07 

734.020 

1305.33 

17 

3670.16 

6528.33 

1835.15 

3264.17 

1223.51 

2176.11 

817.717 

1032  08 

734.255 

1305.6? 

18 

3671.33 

6530.00 

1835.73 

3265.00 

1223.90 

2176.67 

918.010 

1632.50 

734.490 

1306.00 

19 

3672.51 

6531.67 

1830.32 

3265.83 

1224.29 

2177.22 

918.304 

1632.92 

734.725 

1306.33 

20 

3673.68 

6533.33 

1836.91 

3268.67 

1224.69 

2177.78 

918.598 

1033.33 

734.960 

1306.67 

21 

3674.85 

6535.00 

18:57.49 

3267.50 

1225.08 

2178.33 

918.892 

1033.75 

735.195 

1307.00 

22 

3676.03 

6530.6; 

1838.08 

3268.33 

1225.47 

2178.89 

919.185 

1034.  n 

735.430 

1307.33 

23 

3677.20 

6538.33 

1838/07 

3209.17 

12-25.80 

2179.44 

919.479 

1034.58 

735.005 

1307.67 

24 

3678.38 

0540.00 

1839  20 

327'0.00 

1220.25 

2180.00 

919.773 

1035.00 

735.900 

1308  00 

25 

3679.55 

6541.67 

1839.84 

3270.83 

1220  64 

2180.56 

920.000 

1035.42 

730.135 

1308.33 

26 

1880.73 

0543.33 

1840.43 

3271.07 

1227.01 

2181.11 

920.360 

1035.83 

730.370 

1308.67 

27 

3081.90 

6545.00 

1841.02 

3272.50 

1227.43 

2181.07 

920  654 

1030.25 

730  005 

1309.00 

28 

3683.08 

6546.67 

1841.61 

3273.33 

1227.82 

21M2.22 

920.947 

1630.07 

730.840 

1309.33 

29 

3081.25 

6548.33 

1842.19 

3274.17 

1228.21 

2182.78 

921.241 

1037.08 

737.075 

1309.67 

3O 

3685.43 

6550.00 

1842.78 

3275.00 

1228.60 

2183.33 

921.535 

1037.50 

737.310 

1310.00 

31 

36,%.0'J 

0551  .  67 

18J3.37 

3275.83 

1228.9'.) 

21S3.S9 

921.829 

1037  92 

737.545 

1310.33 

3  2 

3087.77 

6553.33 

1843.95 

3276.67 

1229.3S 

2184.44 

922.122 

1038.33 

737.780 

1310.67 

33 

3088.95 

0555.00 

1844.54 

3-277.50 

1229.78 

2185.00 

922.410 

1038.75 

738.015 

1311.00 

34 

3090.12 

0550.67 

1845.13 

3278.33 

1230.17 

2  1  85  .  56 

922.710 

1639.17 

738.250 

1311.33 

35 

3091.3'} 

6558.33 

1845.73 

3-279.17 

1230.57 

2180.11 

923.011 

1639.58 

738.491 

1311.67 

36 

9602.58 

0560.00 

1846.33 

328J  00 

1230.01 

2180.07 

923.311 

1040.00 

738.732 

1312.00 

37 

3693.70 

6561.67 

1846.92 

3280.83 

1231.36 

2187.22 

923.005 

1640.42 

738.907 

1312.33 

38 

3094.88 

6503.33 

1847.51 

3281.67 

1231.75 

2187.78 

923.899 

1640.83 

739.202 

1312.67 

39 

3696.05 

0565.00 

1848.09 

3282.50 

1232.14 

2188.33 

924.193 

1641.25 

739.437 

1313.00 

40 

3697.23 

6566.67 

1848.68 

3283.33 

1232.54 

2188.89 

924.486 

1641.67 

739.672 

1313.33 

41 

3688.40 

6508.33 

1849.27 

3284.17 

1232.93 

2189.44 

924  .  780 

1642.08 

739.907 

1313.67 

42 

3699.58 

6570.00 

1849.86 

3285.00 

1233.32 

2190  00 

925.074 

1642  50 

740.142 

1314.00 

43 

3700.75 

6571.67 

1850.44 

3285.83 

1233.71 

2190.56 

925.307 

1642.92 

740.377 

1314.33 

44 

3701  93 

6573.33 

1851.03 

3286.07 

1234.10 

2191.11 

925.661 

1643.33 

740.012 

1314.67 

45 

3703.13 

6575.00 

1851.63 

3287.50 

1234.50 

2191.67 

925.962 

1643.75 

740.852 

1315.00 

46 

3704.33 

0570.67 

1852.23 

3288  33 

1234  90 

2  192.2  J 

926.263 

1644.17 

741.093 

1315.33 

47 

3705.51 

6578.3:; 

1852.823289.17 

1235.30 

2192  78 

926.556 

1644.58 

741.328 

1315.67 

48 

8706.68 

6580.00 

1853.41  3290.00 

1235.69 

2193.33 

926.850 

1645.00 

741.563 

1316.00 

49 

3707.80 

6581.07 

1854.00 

3290.83 

1236.08 

2193  89 

927.144 

1645.42 

741.798 

1316.33 

5O 

3709.03 

6583.33 

1854.58 

3291.67 

1236.47 

2194.44 

927.438 

1645.83 

742.033 

1316  67 

51 

3710.21 

6585.00 

1855.17 

3292.50 

1230.80 

2195.00 

927.731 

1646.25 

742.  208  11317.  00 

52 

3711.38 

6586.67 

1855.76 

3293.33 

1237.25 

2195.56 

928.025  1646.07 

742.  503  '13  17.  33 

53 

3712.58 

6588.33 

1856.36 

3294  17 

1237.66 

2196.11 

928.320:1047.08 

742.744 

1317.07 

54 

3713  79 

6590.00 

1856.96 

3295.00 

1238.00 

2196.67 

928.  027  i  1047.  50 

742.984 

1318.00 

55 

3714.96 

6591.67 

1857.55 

3295.83  1238.45 

2197.22 

928.  920  '104  7.  92 

743.219 

1318.33 

56 

3716.14 

6593.33 

1858.14 

3296.  67  !  1238.  84 

3197.78 

929.214  1648.33 

743.4.=v4 

1318.07 

57 

3717.31 

6595.00 

1858.72 

3297.  50  11239.  23  21  98.  33 

929.508  1048''.  75 

7  43.089 

1319.00 

58 

3718.49 

6596.67 

1859.31 

3298.33  12:i9.622l98.8J) 

929.80111049.17 

743.924 

1319.33 

59 

3719.69 

6598.33 

1859.91 

3299.17  1240.  0212199.44 

9:>,0.  102  1049.58 

744.105 

1319.07 

176 


TABLE   XTV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  C 

Tan. 

urve. 

65° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Arc. 

M. 

608.  638;  1083.  33 

521.773 

928.571 

456  639 

812.500 

405.986722.222365.481 

650.000 

~O~ 

608.833  1083.61 

521.941 

928.810456.786812.708 

406.  116  722.  40?  J365.  598 

050.167 

1 

609.059  1083.89 

522.109 

929.048456.933 

812.917 

406.247722.593365.716 

050.333 

2 

609.225  1084.1? 

522.277 

929.286457.080 

813.125 

406.377 

722.778 

365.833 

650.500 

3 

609.421 

1084.44 

522.445 

929.524457.227 

813.333 

406.508 

722.963 

365.951 

650.667 

4 

609.617 

1084.72 

522.613 

929.762457.374 

813.542 

406.639723.148 

366.069 

650.833 

5 

609.813 

1085.00 

522.780 

930.000457.521 

813.750 

406.769 

7*43.838 

366.186 

651.000 

6 

610.008 

1085.28 

522.948 

930.238 

457.668 

813.958 

406.900 

723.519 

366.304 

651  .  167 

610.204 

1085.56 

.123.116 

930.476 

457.815 

814.167 

407.031 

723.704 

366.421 

651.333 

8 

610.400 

1085.83 

523.284 

930.714 

457.961 

814.375 

407.161 

723.889 

366.539 

651.500 

9 

610.596 

1086.11 

523.452 

930.952 

458.108 

814.588 

407.292 

724.074 

366.65? 

651.66? 

10 

610.792 

1086.39 

523.  620 

931.190 

458.255 

814.792 

407.423 

724.259 

366.774 

651.833 

11 

610.988 

1086.67 

523.788 

931.429 

458.402 

815.000 

407.553 

724.444 

366.892 

652.000 

12 

611.184 

1086.94 

523.956 

931.66? 

458.549 

815.208 

407.684 

724.630 

367.010 

652.16? 

13 

611.379 

1087.22 

524.124 

931.905 

458.696 

815.417 

407.815 

724.815 

367.127 

652.333 

14 

611.575 

1087.50 

524.292 

932.143 

458.843 

815.625 

407.945 

725.000 

367.245 

652.500 

15 

811.  771  11087.  78 

524.459 

932.381 

458.990 

815.833 

408  076 

725.185 

367.362 

652.667 

16 

611.96?  1088.06 

524.627 

932.619 

459.13? 

816.042 

408.206 

725.370 

367.480 

652.833 

17 

612.16oild88.33 

524.795 

932.857 

459.284 

816.250 

408.337 

725.556 

367.598 

653.000 

18 

612.359 

1088.61 

524  .  963 

933.095 

459.431 

816.458 

408.468 

725.741 

367.715 

653.167 

19 

612.555 

1088.89 

525.131 

933.333 

459.578 

816.66? 

408.598 

725.926 

367.833 

653.333 

2O 

612.750 

1089.17 

525.299 

933.571 

459.725 

816.875 

408.729 

726.111 

367.950 

653.500 

21 

612.940 

1089.44 

525.46? 

933.810 

459.872 

817.083 

408.860 

726.296 

368.068 

653.667 

22 

613.  142 

1089.72 

525.635 

934.048 

460  019 

817.292 

408  990 

726.481 

368.186 

653.833 

23 

613.338 

1090.00 

525.803 

934.286 

460.166 

817.500 

409.121 

7*6.667 

368.303 

654.000 

24 

613.534 

1090.28 

525.970 

934.524 

460.312 

817.7'08 

409.252 

726.852 

368.421 

654.167 

25 

613.730 

1090.50 

526.  138 

1)34.762 

460.459 

817.917 

409.382 

727.037 

368.538 

654.333 

2G 

613.925 

1090.83 

526.  300 

935.000 

460.606 

818.125 

409.513 

727.222 

368.656 

654.500 

27 

614.121 

1091.11 

526.474 

935.238 

460.753 

818.333 

409.643 

727.407 

368.77'4 

654  .  66? 

28 

614.317 

1091.39 

526.642 

935.476 

460.900 

818.542 

409.774 

727.593 

368.891 

654.833 

29 

614.513 

1091  67 

526.810 

935.714 

461.047 

818.750 

109.905 

727.778 

369.009 

655.000 

30 

614.709 

1091.94 

526.978 

935.952 

461.194 

818.958 

410.035 

727.963 

369.126 

655.16? 

31 

614.905 

1092.22 

527.140 

1)30.190 

461.341 

819.167 

410.160 

728.148 

369.244 

655.333 

32 

615.101 

1092.50 

527.314 

936.429 

461.488 

819.375 

410.297 

728.333 

369  362 

655.500 

33 

615.290 

1092.78 

527.482 

936.667 

461.635 

819.583 

410.42? 

728.519 

369.479 

655.667 

34 

(515.497 

1093  06 

527.654 

936.905 

461.785 

819.792 

410.561 

728.704 

369.600 

655.833 

35 

015.0'.)HH>93.33 

527.826 

1)37.143 

461.936 

820.000 

410.695 

728.889 

369.720 

656.000 

36 

015  <S!)4 

1093.61 

527.993 

937.381 

462.083 

820.208 

410.826 

729.07'4 

369.838 

656.16V 

37 

616.089 

1093.89 

528.161 

937.619 

462.230 

820.417 

1  10.  956 

729.259 

369.955 

656.333 

38 

616.285 

1094.17 

528.329 

937.85? 

462.377 

820.625 

'411.08? 

729.444 

370.073 

656.500 

39 

616.481 

1094.44 

528.497 

938.095 

462.524 

820.833 

411.218 

729.630 

370.191 

656.667 

40 

616.677 

1094.72 

528.665 

938.333 

462.671 

821.042 

411.348 

729.815 

370.  80S 

656.833 

41 

616.873 

1095.00 

528.833 

938.571 

462.818 

821.250 

411.479 

730.000 

370.426 

657.000 

42 

617.069 

1095.28 

529.001 

938.810 

462.965 

821.458 

411.609 

730.185 

370.543 

657.167 

43 

617.265 

1095.56 

529.169 

939.048 

463.112 

821.667 

411.740 

7;  0.370 

370.661 

657.333 

44 

617.465 

1095.83 

529.341 

939.286 

463.262 

821.875 

411.874 

730.556 

370.782 

657.500 

45 

617.660 

109(5.11 

529.513 

939.524 

463.413 

822.083 

412.008 

730.741 

370.902 

657.667 

46 

617.862 

1096.39 

529.681 

939.762 

463.559 

822.292 

412.138 

730.926 

371.020 

657.833 

47 

618.057 

1096.6? 

529.849 

940.000 

463.70*1 

822-.  500 

412.269 

731.111 

371  13? 

658.000 

48 

618.253 

1096.94 

530.016 

940.238 

463.853 

822.708 

412.400 

731.296 

371.255 

658.107 

49 

618.449 

1097.22 

530.184 

940.476 

464.000 

822.91? 

412.580 

731.481 

371.372 

658.333 

50 

618.645 

1097.50 

530.352 

940.714 

464.14? 

823.125 

412  661  731.66? 

371.490658.500 

51 

618.841 

1097.78 

530.520 

940.952 

464-294 

823.333 

412.792:731.852 

371.  608  J658.66? 

52 

619.041 

1098.06 

530.692 

941.190 

464  445 

823.542 

412.925  7'32.037 

371.728 

658.833 

53 

619.242 

1098.33 

530.864 

941.429 

464.595 

823.75' 

413.059732.222 

371.849 

659.000 

54 

619.438 

1098.61 

531.032 

941.667 

464.742 

823.  95S 

413.190732.407 

371.966 

659.167 

55 

619.634 

1098.89 

531.200 

941  905 

464  889 

824.167 

413.321  732.593 

372.081 

059.333 

56 

619.830 

1099.1? 

531.36H 

942.143 

465.036 

824.375 

413.451 

732.778 

372.201 

059.500 

57 

620.026 

1099.44 

531.536 

942.381 

465.183 

824  5S3 

413.582 

732.963 

372.319 

659.667 

58 

620.226 

1099.72 

531.708 

942.619 

465.334 

824.792 

413.716 

733.148 

372.439 

659.833 

59 

177 


TABLE   XIV. — ACTUAL  TANGENTS,    ETC. 


63° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

3720.89  0000.  OU  1800.51 

3300.00 

1240.43 

2200  .  00 

930.403  1650.00 

744.400  1320.00 

1 

3722.076601.07  1801.10 

3300.83 

1240.82 

2200  .  50 

930.  097  |  1050.  42 

744.  641  '1320.33 

2 

3723.240003.33  1801.09 

3301.07 

1241.21 

2201  .  1  1 

930.991  1650.83 

744.876  1320.07 

3 

3724  .  44  0005  .  00  '  1  802  .29 

3302.50 

1241.0 

2201  07  931.291 

1051.25 

745.110  1321.00 

4 

3725.  05  0000.07  [1802.  89 

3303.  3  i 

1242.01 

2202.22931.592 

1051  07 

745.3571321.33 

5 

3720.820008.331803.48 

3304.17 

1242.40 

2202  781931.880 

1052.08 

745.592  1321.07 

6 

3728.000010.00  1804.07 

3305.00 

1242.79 

2203.3393-2.180 

1052.50 

745.8271322.00 

7 

3729.17  0011.07  1804.05 

3305  .  83 

1243.19 

2203.89 

932.473 

1652.92 

746  062  1322.33 

8 

3;  30.  3o  GO  13.  33  1805.24 

3300.07 

1243.58 

2-204.44 

932.707 

1053.33 

746.2971322.67 

9 

3731.55 

6615.00 

1865.84 

3307.50 

1243.98 

2205.00 

933.008 

1653.75 

740.538  1323.00 

1O 

3732.75 

6616.67 

1866.44 

3308.33 

1244.38 

•£205.50 

933.309 

1654  17 

74G.77'S1323.33 

I  i 

3733.93  0018.33  1807.03 

3309.17 

1244.77 

2206.11 

933.  003  |1054.  58 

747.013  1323.67 

12 

3735.100020.00,1807.02 

3310.00 

124;;.lti  2200.07 

933.950  1055.00 

747.2481324.00 

13 

3730.30 

0621.67  1868.22 

3310.83 

1245.50  2207.22 

934.257  1055.42 

747  489!  1324.  33 

14 

3737.51 

6623.33  1808.82 

3311.07 

1245.90  2207.78 

934.5581055.83 

747.7301324.67 

15 

3738.08 

0025  00 

1869.41 

3312.50 

1240.3(52208.33 

934.852  1050.25 

747.96511325.00 

16 

3739.80 

002(5.07 

1870.00 

3313.33 

1240.752208.89 

935.145  1650.07 

748.200:1325.33 

17 

3741.00 

0028.33 

1870.60 

3314.17 

1247.15  2209.44 

935.446  1057.08 

748.441  1325.67 

18 

3742.2(5 

0030.00 

1871.20 

3315.00 

1247.55  2210.00 

935.747,1657.50 

748.681 

1320.00 

19 

3743.44 

(5031.07 

1871.79 

3315.83 

1247  942210.56 

936.  041  ^057.  92 

748.916 

1320.33 

20 

3744.01 

0633  33 

1872.38 

3316.67 

1248  332211.11 

930.335 

1658.33 

749.151 

1326  67 

21 

3745.82 

0035  00 

1872.9S 

3317.50 

1248.732211.67 

930.035  165S.75 

749.392 

1327.00 

22 

3747.02 

0030  (57 

1873.58 

3318  33 

1249.142212.22 

936.930  1059.17 

749.633 

1327.33 

23 

3748.19 

0038.33 

1874.17 

3319.17 

1249.532212.78 

937.230  1059.58 

749.868 

1327  67 

24 

3749.37 

0040.00 

1874.75 

3320.00 

1249.922213.33 

937.524 

1600.00 

750.103  1328.00 

25 

3750.57 

0041.07 

1875.35 

3320.83 

1250.3-2  2213  89 

937.825 

1060.4-2 

750.343  1328.33 

26 

3751.77 

0043.33 

1875.90 

3321.07 

1250.722214.44 

938.125 

1000.83 

750.584 

1328.67 

27 

3752.95 

0045.00 

1876.54 

3322.50 

1251.11  2215.00 

938.419 

1001.25 

750.819 

1329.00 

28 

3754.12 

0040.07 

1877.13 

3323.33 

1251.502215.50 

938.713 

1001.07 

751.054 

1329.33 

29 

3755.33 

0048.33 

1877.73 

3324.17 

1251.90 

2216.11 

939.014 

1002.08 

751.295 

1329.07 

30 

3756.53 

0650.00 

1878.33 

3325.00 

1252.31 

2216.67 

939.315 

1662.50 

751.536 

1330.00 

3i 

3757.71 

0051  .  07 

1878.92 

3325.83 

1252  70:2217.22 

939.  60S 

1062.92 

751.771  1330.33 

32 

3758.88 

(5053  33 

1879.51 

3326.67 

1253.09  2217.78 

939.902 

1663.33 

752.  000  !  1330.  07 

33 

3700  08 

(5055.00 

1880.11 

3327.50 

1253.49  2218.33 

940.203 

1003.75 

752.240  1331.00 

34 

3761.29 

0050.67 

1880.71 

3328.33 

1253.892218.89 

940.504 

1004.17 

752  487  1331.33 

35 

3702.49 

0058.33 

1881.31 

3329.17 

1254.29-J219.44 

940.805 

1604.58 

752.728 

1331.67 

36 

3703.09 

6000.00 

1881.92 

3330.00 

1251.092220.00 

941.105 

1065  00 

752.968 

1332  00 

37 

3704  87 

(5001.07 

18S2.50 

33:30.83 

12.-)5.08 

2220.56 

941.399 

1005.42 

753.203 

1332.33 

38 

3700.04 

0003.33 

1883.09 

3331.67 

1255.482221.11 

941.693 

1005.83 

753  438 

1332.67 

39 

3767.24 

0005.00 

1883.69 

3332.50 

1255.882221.07 

941.994 

1060.25 

753.679 

1333.00 

4O 

3768.45 

6006.67 

1884.29 

3333.33 

1256.28 

2222.22 

942.295 

1666.67 

753.920 

1333.33 

41 

3769.65 

6668.33 

1884.89 

3334  .17 

1256.68 

2222.78 

942.595 

1007.  OS 

754.161 

1333.07 

42 
43 

3770.85 
3772.03 

0070.00 
6071.67 

1885.50 
1886  OS 

3335.00 
3335.83 

1  257.  08  j  2223.  33 
1257.472223.89 

942.896 
943.190 

1007.50 
1067.92 

754.401 
754.636 

1334  00 
1331.33 

44 

3773.20 

(5673.33 

1880.67 

3330  07 

1257.86 

2224.44 

913.484 

1008.33 

754.871 

1334  67 

45 

3774.41 

6675.00 

1887.27 

3337.50 

1258  27 

2225.00 

943.785 

1008.75 

755.112  1335.00 

46 

3775.61 

0676.67 

18S7.S7 

3338.33 

1258.67 

2225.50 

944.085 

16(59.17 

755.  353  ;1335.  33 

47 

3776.81 

6078.83 

1888  4s 

3339.17 

1259.07 

2226.11 

944.386 

1009.58 

755.5931335.07 

48 

3778.02 

0080.00 

1889.08 

3340.00 

1259.47 

2226.67 

944.687 

1670.00 

755.834  1336.00 

49 

3779.22 

0681.67 

1889.0" 

3340.83 

1259.87 

2227.22 

944.988 

1070.42 

750.075  1336.33 

5O 

3780.42 

6683.33 

1890.28 

3341.67 

1260.27 

2227.78 

945.289 

1670.83 

756.316  1336  67 

51 

3781.00 

0685.00 

1890.87 

3342.50 

1200.60 

2-228.33 

915.583 

1(571.25 

756  551!  1337.  00 

52 

3782  77 

6686.67 

1891.40 

3343.33 

12(51.05 

2228.89 

945.870 

1071.07 

756.780  1337.33 

53 

3783.98 

6088  33 

1892.00 

3314.17 

1261.46 

2-229.44 

940.177 

1072.  OS 

757.026  1337.67 

54 

3785.18 

(5090.00 

1892.06 

3345.00 

1261.80l2-J30.00 

946.478 

1672.50 

757.267  1338.00 

55 

3786  38 

0091.07 

1S93.20 

3345.83 

1202.20  2230.56 

946.779 

1072.92  757.508  1338.:-  3 

56 

3787.59 

0693  33 

1893.80 

3346.67 

1202.0(5:2231.11 

947.080 

1073.33:757.748    3.^8.07 

57 

3788.79 

6695.00 

1894.40 

3347.50 

1203.  06!  2231.  07 

947.381 

1073  7T)!757.9S9  1339.00 

58 

3789.99 

(5096  67 

1895.07 

3348.33 

1263.40 

2232.22 

947.681 

1074.  17^58.  230  1339.33 

59 

3791.19 

6098.33 

1895.67 

3349.17 

1203.802232.78 

947.982  1674.58  758.471  1339.07 

178 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

66° 

Tau. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

6:20.4:27 

1100.00 

531.880j942.857 

465.484 

825.000413  849733.333 

372.560 

660.000 

O 

620  .  623  1  1  00  .  28  532  .048  943  .  095 

465.631 

825.208413.980 

733.519 

372.678 

660.167 

1 

620.818  1100.56 

532.2161943.333 

465.778 

825.417414.111 

733.704 

372.795 

660.333 

2 

621.  019  1100.83 

532.388 

943.571 

465.928 

825.625414.245 

733.889 

372.916 

660.500 

3 

621.220  1101.11 

532.560 

943.810 

466.079 

825.833414.378 

734.074 

373.036 

660.667 

4 

621.416 

1101.39 

532.727 

944.048 

466.226 

826.042414.509 

734.259 

373.154 

660.833 

5 

621.611 

1101.67 

532.895 

944.286 

466.373 

826.250414.640 

734.444 

373.271 

661.000 

6 

621.807 

1101.94 

533.063 

944.524 

466.520 

826.458414.770 

734.630 

3:3.389 

661.167 

7 

622.003 

1102.22 

533.231 

944.762 

466.667 

826.667414.901 

734.815 

373.507 

661.333 

8 

622.204 

1102.50 

533.403 

945.000 

466.817 

826.875 

415.035 

735.000 

373.627 

661.500 

9 

622.404 

1102.78 

533.575 

945.238 

466.968 

827.083 

415.169 

735.185 

373.748 

661.667 

10 

622.600 

1103.06 

533.743 

945.476 

467.115 

827.292415.299 

735.370 

878.865 

661.833 

11 

6  J2.  796;  1103.  33 

533.911 

945.714 

467.262 

827.500i415.430 

735.556 

373.983662.000 

12 

622.9971103.61 

534.083 

945.952 

467.412 

827.  708!  41  5.  564 

735.741 

374.103:662.167 

13 

623.197 

1103.89 

534.255 

946.190 

467.563 

827.917415.698 

735.926 

374.224  662.333 

14 

623.393 

1104.17 

534.423 

946.429 

467.710 

828.125415.828 

736.111 

374.341 

662.500 

15 

623.589 

1104.44 

534.591 

946.667 

467.857 

828  333415.959 

736.296 

374.459 

662.667 

16 

623.790 

1104.72 

534.763 

946.905 

468.007 

828.542416.093 

736.481 

374.579 

662.833 

17 

623.990 

1105.00 

534.935 

947.143 

468.158 

828.750 

416.226 

736.667 

374.700 

663.000 

18 

624.186 

1105.28 

535.103 

947.381 

468.305 

828.958 

416.357 

736.852 

374.817 

663.167 

19 

624.382 

1105.56 

535.270 

947.619 

468.452 

829.167 

416.488 

737.037 

374.935 

663.333 

20 

624.583 

1105  83 

535.442 

947.857 

4G8.602 

829.375 

416  622 

737.222 

375.056 

663.500 

21 

624.783 

1106.11 

535.614 

948.095 

468.753 

829.583 

416.755 

737.407 

375.176 

663.667 

22 

624.979 

1106.39 

535.782 

948.  333 

468.900 

829.792 

416.886 

737.593 

375.294 

663.833 

23 

625.175 

1106.67 

535.950 

948.571 

469.046 

830.000 

417.017 

737.778 

375.411 

664.000 

24 

625.376 

1106.94 

536.122 

948.810 

469.197 

830.208 

417.151 

737  .  963 

375.532 

664.167 

25 

625.576 

1107.22 

536.294 

949.048 

469  347 

830.417 

417.284 

738.148 

375.652 

664.333 

26 

625  .  772 

1107.50 

536.462 

949.286 

469.494 

830.625 

417.415 

738.333 

375.770 

664.500 

27 

625.968 

1107.78 

536.630 

949.524 

469.641 

830.833 

417.546 

738.519 

375.887 

664.667 

28 

626.169 

1108.06 

536.802 

949.762 

469.792 

831.042 

417.679 

738.704 

376.008 

664.833 

29 

626  369 

1108.33 

536.974 

950.000 

469.942 

831.250 

417.813 

738.889 

376.128 

665.000 

30 

626.565 

1108.61 

537.142 

950.238 

470.089 

831.458 

417.944 

739.074 

376.246 

665.167 

31 

626.761 

1108.89 

537.310 

950.476 

470.236 

831.667 

418.075 

739.259 

376.364 

665.  .333 

32 

626.962 

1109.17 

537.482 

950.714 

470.387 

831  875 

418.208 

739.444 

37(5.484 

665.500 

33 

627.162 

1109.44 

537.654 

950.952 

470.537 

832.083418.342 

739.630 

376.604 

665.667 

34 

627.363 

1109.72 

537.826 

951.190 

470.688 

832  292 

418.476 

739  815 

376.725 

665.833 

35 

627.563 

1110.00 

537.  99* 

951.429 

470.838 

S32.500 

418.610 

740.000 

376.845 

666.000 

36 

627.759 

1110.28 

538.166 

951.66? 

470.985 

832.708 

418.741 

740.185 

376.963 

666.167 

37 

627.955 

1110.56 

538.334 

951.905 

471.132 

832.917 

418.871 

740.370 

377.081 

666.333 

38 

628.156 

1110.83 

538.506 

952.143 

471.283 

833.125 

419.005 

740  556 

377.201 

666.500 

39 

628.356 

1111.11 

538.678 

952.381 

471.433 

833.333 

419.139 

740.741 

377.322 

666.667 

40 

628.557 

1111.39 

538.850 

952.619 

471.584 

833.542 

419.273 

740.926 

377.442 

666.833 

41 

628.758 

1111.67 

539.022 

952.857 

471.734 

833.750 

419.406 

741.111 

377.563 

667.000 

42 

628.953 

1111.94 

539.189 

953.095 

471.881 

833.958 

419.537 

741.296 

377.680 

667.167 

43 

629.149 

1112.22 

539.357 

953.33-1 

472.028 

834.167 

419.668 

741.481 

377.798 

667.33-5 

44 

629.350 

1112.50 

539.529 

953.571 

472.179 

834.375 

419.802 

741.667 

377.918 

667.500 

45 

629.551 

1112.78 

539.701 

953.810 

472.329 

834.583 

419.935 

741.852 

378.039 

667.667 

46 

629.751 

1113.06 

539.873 

954.048 

472.480 

834.792 

420.069 

742.037 

378.159 

667.833 

47 

629.952 

1113.33 

540.045 

954.286 

472.630 

835.000 

420.203 

742.222 

378.280 

668.000 

48 

630.152 

1113.61 

540.217 

954.524 

472.781 

835.208 

420.33? 

742.407 

378.400 

668.167 

49 

630.353 

1113.89 

540.389 

954.762 

472.931 

835.417 

420.471 

742.593 

378.521 

668.333 

5O 

630.5-19 

1114.17 

540.557 

955.000 

473.078 

835.625 

420.601 

742.778 

378  638 

668.500 

51 

630.745 

1114.44 

540.725 

955.238 

473  225 

835.833420.732 

742.963 

378.756 

668.667 

52 

630.945 

1114.72 

540.897 

955.476 

473.376 

836.042420.866 

743.148 

378.876 

668  833 

53 

631.146 

1115.00 

541.069 

955.714 

473.526 

836.250421.000 

743.333 

879.897 

669.000 

54 

631.347 

1115.28 

541.241  955  952 

473.677 

836.458421.133 

743.519 

379.117 

669.167 

55 

631  547 

1115.56 

541.413956.190 

473  827 

836.667421.26? 

743.704 

379.238 

669.333  56 

631  .  748 

ni5.  as 

541.585 

956.429 

473.978 

836.875421.401 

743.889 

379.358 

669  500  57 

631.949 

1116.11 

541  .  757 

956.667 

474.128 

837.  G83  421.  535 

744.074 

379.479 

(569  667  58 

632.149  1116.39 

541.929 

956.905 

474.279 

837.292421.669 

744.259 

379.599 

669.833  59 

179 


TABLE  XIV.— ACTUAL   TANGENTS,    ETC. 


67° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

~o" 

Tan. 
3793.40 

Arc. 
6700.00 

Tan. 

1896.27 

Arc. 
3350700 

Tan. 
F264726 

Arc. 

Tan. 

Arc. 
1675.00 

Tan. 

758.711 

Arc. 

22.i3.33 

948.283 

1340.00 

1  379  i.  57  670  1.67 

1896.86 

3350.83 

1264.65 

2233.89 

948.577  1675.42 

758.946  1340.33 

3  3194.75 

6703.33 

1897.44 

3351  67 

1265.05 

2234.44 

948.871  1675.83 

759.  18111340.  67 

3  3795.95 

6705.00 

1898.04 

3352.50 

1265.45 

2235.00 

949.171  1676.25 

759.422  1341.00 

4!  3797.  15 

6706  67 

1898.65 

3353.33 

1265.85 

2235.56 

949.472  1676.67 

759.663 

1341.33 

5  '3798.366708.33 

1899.253354.17 

1266.252236.11 

949.773  1677.08 

759.903 

1341.67 

6  371)9.566710.00 

1893.853355.00 

1266.652236.6? 

950.074 

1677.50 

760.144 

1342.00 

7  |3800.  76  671  1.67 

1900.  45  '3355.  83 

1267.052237.22 

950.375 

1677.92 

760.385 

1342.33 

8 

3801.976713.33 

1901.053356.67 

1267.45 

2237.78 

950.676  1678.33 

?'60.626 

1342.67 

9 

3803.176715.00 

1901.65 

3357.50 

1267.85 

2238.33 

950.977 

1678.75 

760.866 

1343.00 

10 

3804.376716.67 

1902  26 

3358.33 

1268.25 

2238.89 

951.278 

1679.17 

761.107 

1343.33 

1.1 

3805.586718.33 

1902.86 

3359.17 

1268.66 

2239.44 

951.5781679.58 

761.348 

1343.67 

13 

3806.786720.00 

1903.4633(30.00 

1269.06 

2240.00 

951.879  1680.00 

761.588 

1344.00 

13 

3807.98:6731.67 

1904.063360.83 

1269.46 

2240.56 

952.180  1680.42 

761.829 

1344.33 

14 

3809.  19,  6723.  33 

1904.66 

3361.67 

1269.86 

2241.11 

952.481  1680.83 

762.070 

1344.67 

15 

3810.3916725.00 

1905.26 

3362.50 

1270.26 

2241  .  67 

952.782  1681.25 

762.311 

1345.00 

16 

3811.596726.67 

1905.87 

3363.33 

1270.66 

2242.22 

953.083  1681.67 

762.551 

1345.33 

17 

38  12.  80  6728.  33 

1906.47 

3364.17 

1271.06 

2242.78 

953.384  1682.08 

?'62.792 

1345.67 

18 

3814.00 

6730.00 

1907.07 

3365.00 

1271.46 

2243.33 

953.684  1682.50 

763  033 

1346.00 

19 

3815.20 

6731.67 

1907.67 

3365.83 

1271.86 

2243.89 

953.985 

1682.92 

763.273 

1346.33 

2O 

3816.41 

6733.33 

1908.27 

3386.67 

1272.27 

2244.44 

95  t.  286 

1683.33 

763.514 

1346.67 

31 

3817.61 

6733.00 

1908.87 

3367.50 

1272.67 

2245.00 

954.587  1683.75 

763  .  755 

1347.00 

33 

3S18.81 

6736.67 

1909.48 

33(58.33 

1273.07 

2245  56 

954.8881684.17 

763.996 

1347.33 

33 

3820.01 

6738.33 

1910.08 

3369.17 

1273.47 

2246.11 

955.189  1684.58 

764.236 

1347.67 

34 

3821.22 

6740.00 

1910.68 

3370.00 

1273.87 

2246.67 

955.490  1685.00 

764.477 

1348.00 

35 

3822.42 

6741.67 

1911.28 

3370.83 

1274.27 

2247.22 

95").  790  11  685.  42 

764.718 

1348.33 

36 

3823.62 

6743.33 

1911.88 

3371.67 

1274.67 

2247.78 

956.091  1685.83 

764.958 

1348.67 

37 

3824.83 

6745.00 

1912.48 

3372.50 

1275.07 

2248.33 

9>6.  392  1  1686.  25 

765.199 

1349.00 

38 

3826.03 

6746.67 

1913.09 

3373.33 

1275  48 

2248.89 

956.6931686.67 

765.440 

1349.33 

39 

3827.23 

6748.33 

1913.69 

3374.17 

1275.88 

2249.44 

956.994 

1687.08 

765.681 

1349.67 

30 

3S28.4J 

6750.00 

1914.29 

3375.00 

1276.28 

2250.00 

957.295 

1687.50 

765.921 

1350.00 

31 

3829.64 

6751.67 

1914.89 

3375.83 

1276.68 

2250.56 

957.596 

1687.92 

766.162 

1350.33 

33 

3830.84 

6753.33 

1915.49 

3376.67 

1277.08 

2251  .  1  1 

957.897 

1688.33 

766.403 

1350.67 

33 

3832.05 

6755.00 

1916.09 

3377.50 

1277.48 

2251.67 

958.197 

1688.75 

766.644 

1351.00 

34 

3833.25 

6756.67 

1916.70 

3378.33 

1277.88 

2252.22 

958.498 

1689.17 

766.884 

1351.33 

35 

3834.45 

6758.33 

1917.30 

3379.17 

1278.28 

2252.78 

958.799 

1689.58 

767.125 

1351.67 

36 

3835.66 

6760.00 

1917.90 

3380.00 

1278.68 

2253.33 

959.100 

1690.00 

767.366 

1352.00 

37 
38 

3836.80 
3838.06 

6761.67 
6763.33 

1918.50 
1919.10 

3380.83 
3381.67 

1279.09 
1279.49 

2253.89 
2254.44 

959.  401  j  161)0.  42 
959.702  1690.83 

767.606 
767.847 

1352.33 

1352.67 

39 

3839.27 

6765.00 

1919.70 

3332.50 

1279.89 

2253.0' 

1)60.003 

1691.25 

768.088 

1353.00 

40 

3840.47 

6766.67 

1920.31 

3383.33 

1280.29 

2255.56 

960.303 

1691.67 

768.329 

1353.33 

41 

3841.70 

6768.33 

1920.92 

3384.17 

1280.70 

2256.11 

960.61111692.08 

768.575 

1353.67 

43 

3842.93 

6710.00 

1921  54 

3385.00 

1281.11 

2256.67 

960.920 

1692.50 

768.821 

1354.00 

43 

3844.14 

6771.67 

1922.14 

3385.83 

1281.51 

2257.22 

901  .  220 

1692.92 

7(59.062 

1354.33 

44 

3845.34 

6773.33 

1922.74 

3336.67 

1281.91 

2257.78 

961.521 

1693.33 

769.303 

1354.67 

45 

3846  54 

6775.00 

1923  34 

33S7.5P 

1282.31 

2258.  .33 

961.822 

1693.75 

769.544 

1355.00 

46 

3847.75 

6776.67 

1923.94 

3388.33 

1282  71 

2258.89 

962.123 

1694.1? 

769.784 

1355.33 

47 

3848.95 

6778.33 

1924.55 

3389.17 

1283.12 

2259.44 

962.424 

1694.58 

770.025 

1355.67 

48 

3850.15 

6780.00 

1925.15 

3390.00 

1283.52 

2260.00 

962.725 

1695.00 

770.266 

1356.00 

49 

3851.36 

6781.67 

1925.75 

3390.83 

1283.92 

2260.56 

963.026 

1695.42 

770.506 

1356.33 

50 

3852.56 

6783.33 

1926.35 

3391.67 

1284.32 

•226  1.11 

968.898 

1695.83 

770.747 

1356.67 

51 
53 

3853.79 
3855.02 

6785.00 
6786.67 

1926.97 
1927.58 

3392.50 
3393.33 

1284.73 
1285.14 

2261.67 
2262.22 

963.634 
963.942 

1696.25 
1696.67 

770.994 
771.240 

1357.00 
1357.33 

53 

3856.23 

6788.33 

1928.18 

3394.17 

1285.54 

2262.78 

9(14.243 

1697.08 

771.481 

1357.67 

54 

3857.43 

6790.00 

1928  79 

3395.00 

1285.94 

2263.33 

964.544 

1697.50 

771.722 

1358.00 

55  3858.63 

6791.67 

1929.39 

3395.83 

1286.34 

2263.89 

964.845 

1697.92 

?  71.  962  1358.33 

56i3859.84  6793.33 
57  380  1.07  1  6795.  00 

1929.99 
1930.60 

3396.67 
3397.50 

1280.74 
1287.16 

2264.44 
2265.00 

965.146 
965.454 

1698.33 
1698.75 

772.203  1358.67 
772.4491359.00 

58  3863.30  6796.67 

1931.22 

3398.33 

1287.57 

2265.56 

965.7621699.17 

772.696  1359.33 

59  3863.50,6798.33 

1931.82 

3399.17 

1287.97 

2266.11 

96ft.  063!  1699.58 

772.937il359.67 

180 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

67° 

Tan. 

Arc. 

Tan.  I   Arc. 

Tan. 

Arc. 

837.500 

Tan. 

4217803 

Arc. 

Tan. 

Arc. 

M. 

632.  350;  11  16.  67 

542.101  957.143 

474.429 

744.444 

379.720 

670.000 

O 

632.546  1116.94 

542.209957.381 

474.576 

837.708421.9:33 

744.630 

379.83? 

670.167 

1 

632  .  742  !  1  1  1  7  .  22  542  .  437  957  .  619 

474.723 

837.917422.064 

744.815 

379.955 

670.333 

2 

632.942  1117.50 

542.609957.857 

474.874 

838.125 

422.198 

745.000 

380.075 

670.500 

3 

633.143  1117.78542.781 

958.095 

475.024 

838.333 

422.332 

745.185 

380.196 

670.607 

4 

633.343  1118.06 

542.953 

958.333 

475.175 

838.542 

422.465 

745.370 

380.316 

670.833 

5 

633.544 

1118.33543.125 

958  571 

475.325 

838.750 

422.599 

745.556 

380.43? 

671.000 

6 

633.745 

1118.61 

543.297 

958.810 

475.476 

838.958 

422.733 

745.741 

380.55? 

671.16? 

7 

633.945 

1118.89 

543.469 

959.048 

475.626 

839.167 

422.867 

745.926 

380.678 

671.333 

8 

6:34  .  146 

1119.17 

5  43.  641 

959.286 

475.77? 

839.375 

423.001 

746.111 

380.798 

671.500 

9 

634.347 

1119.  44'543.  813 

959.524 

475.928 

839.583 

423.134 

746.296 

380.919 

671.66? 

1O 

634.547 

1119.72 

543.  985  1959.762 

476.078 

839.792 

423.268 

746.481 

381.039 

671.833 

11 

6:34.748 

1120.00 

544.157 

960.000 

476.229 

840.000 

423.402 

746.66? 

381.160 

672.000 

13 

634.948 

1120.28544.329 

960.238 

476.379 

840.208 

423.536 

746.  852 

381.280 

672.16? 

13 

635.149 

1120.56 

544.501 

960.476 

476.530840.417J423.670 

747.03? 

381  401  672.333 

14 

635.  3501  11  20.  83:54  4.  673 

960.714 

476.680 

840  .625  '423.  804 

747.222 

381.521  672.500 

15 

635.550  1121.11 

544.845 

960.952 

476.831 

840.833423.937 

747.407 

381.641  672.66? 

16 

635.751 

1121.39545.017 

.mi.  190 

476.981 

841.042 

424.071 

747.593 

381.762672.833 

17 

635.953 

1121.67 

545.189 

J6  1.429 

477.132 

841.250 

424.205 

747.778 

381.882 

673.000 

18 

636.152 

1121.94 

545.361 

961.667 

477.282 

841.458 

424.339 

747.963 

382.003 

673.16? 

19 

636.353 

1122.22 

545.533 

961.905 

477.433 

841.66? 

424.473 

748.148 

382.123 

673.333 

30 

636.553 

1122.50 

545.705 

962.143 

477.583 

841.875 

424  607 

748.1333 

382  244 

673.500 

31 

636.754 

1122.781545.877 

962.381 

477.734 

842.083 

424.740 

748.519 

382.364 

673.667 

636.955 

1123.06546.049 

962.619 

477.884 

842.292 

424.874 

748.704 

382  485 

673.833 

33 

637.155 

1123.33 

546.221 

962  857 

478.035 

842.500 

425.008 

748.889 

382.605 

674.000 

24 

637.356 

1123.61 

546.393 

963.095 

478.185 

842.708 

425.142 

749.074 

382.726 

674.16? 

25 

637.557 

1123.89 

546.565 

903.333 

478.336 

842  917 

425.276 

749.259 

382.846 

674.333 

26 

637.757 

1124.  17|546.  737 

963.571 

478.486 

843.125 

425.410 

749.444 

382.967 

674.500 

27 

637.958 

1124.44 

546.909 

963.810 

478.637 

843  .  333 

425.543 

749.630 

383.087 

674.66? 

28 

638.158 

1124.72 

547.081 

964.048 

478.787 

843.542 

425.677 

749.815 

383.208 

674.833 

39 

638.359 

1125.00 

547.253 

964.286 

478.938 

843.750 

425  811 

750.000 

383.328 

675.000 

30 

638.560 

1125.28547.425 

964.524 

479.089 

843.958 

425.945 

750.185 

383.449 

675.16? 

31 

638.760 

1125.56 

547.597 

964.762 

479.239 

844.16? 

426.079 

750.370 

383.569 

075.333 

33 

638.961 

1125.83:547.769 

965.000 

479.390 

844.375 

426.212 

750.556 

383.690 

675.500 

33 

639.162 

1126.11 

547.941 

965.238 

479.540 

844.583 

426.346 

750.741 

383.810 

075.667 

34 

639.362 

1126.39 

548.113 

965.476 

479.691 

844.792 

426.480 

750.926 

383.931 

675.833 

35 

639.563 

1126.67 

548.285 

965.714 

479.841 

845.000 

426.614 

751.111 

384.051 

676.000 

36 

639.763 

1126.94 

548.457 

965.952 

479.992 

845.208 

426  .  748 

751.296 

384.171 

676.167 

37 

639.964 

1127.2.' 

548.629 

966.190 

480.142 

845.417 

426.882 

751.481 

384.292 

676.333 

38 

640  165 

1127.50 

548.801 

966.429 

480.293 

&4S.625 

427.015 

751.667 

384.412 

676.500 

39 

610.365 

1127.78 

548.973 

966.66? 

480.443 

845.8:33 

427.149 

751.852 

384.533 

676.667 

4O 

640.571 

1128.06 

549.149966.905 

480  597 

846.042  427.286 

7*2.08? 

384.050 

076.833 

41 

640.770 

1128.33 

549.325967.143 

480.751 

846.  250!  427.  423 

752.222 

384.780 

677.000 

43 

640.977 

112-'.  61  !549.  497  907.  381 

480.902 

846.458427.55? 

752.407 

884.9011 

077.16? 

43 

641.177 

1128.89 

549.609 

967.619 

481.053 

846.667 

427.691 

5*2.598 

385.021 

077.333 

44 

641.378  1129.17i549.841 

967.85? 

481.203 

846.875427.825 

752.778 

385.141 

077.500 

45 

641.579  1129.44 

550.013 

908.095 

481.  354 

847.083427.959 

752.963 

385.201 

677.667 

46 

641.7791129.72 

550  185 

968.333 

481.504 

847.292428.092 

753.148 

385.382 

677.833 

47 

641.980J1130.00 

550.35? 

908.571 

481.655 

847.500428.226 

753.333 

385.502 

678.000 

48 

642.181 

1130.28 

550.529 

968.810 

481.805 

847.708428.360 

753  519 

385.623 

678.16? 

49 

612.381 

1130.56 

550.701 

969.048 

481.956 

847.917 

428.494 

753.704 

385.743 

678.333 

5O 

642.587 

1130.83 

550.877 

969.286 

482.110 

848.125  428.631 

753.889 

385.86? 

678.500 

51 

642.792 

1131.11 

551.053 

969.524 

482.264 

848.333428.768 

754.074 

385.990 

678.66? 

53 

642.993  1131.39551.225 

909.762 

482.414 

848.542428.902 

754.259 

386.111 

678.833 

53 

643.193  1131.67551.397 
643.394sll31.94551.569 

970  000 
970.2:38 

482.565 
482.715 

848.750429.036 
848.958'429.169 

754.444 

754.630 

386.231 
380.351 

679.000 
679.16? 

54 
55 

643.595  1132.22 

551.741 

970.476 

482.866 

849.167429.303 

754.815386.472 

679.333 

56 

643.8001132.50.551.917 

970.714 

483.020 

849.375429.440 

755.000 

386.595 

679.500 

57 

644.005  1132.78 

552.093 

970.952 

483.174 

849.583429.577 

755.185 

386.719 

679.667 

58 

644.206  1133.06  552.265 

971.190 

483.325 

849.792429.711  755.370 

386.839 

679.833 

59 

181 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


68° 

1°  Curve, 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan  . 

Arc.      Tan. 

Arc. 

Tan. 

Arc. 

o 

3861.71 

6800.00 

1932.42 

3400.00 

1288.37 

J266.07960.364 

1700.00 

773.177 

1300.00 

1 

3865.91 

0801.07 

1933.03 

3400.83 

1288.77 

2207.22900.005 

1700.42 

773.418 

1300.33 

9 

3867.11 

6803.33 

1933.63 

3401.67 

1289.17 

22(57.78966.965 

1700.83 

773.659 

1360.67 

3 

3808.34 

6805.00 

1934.24 

3402.50 

1289.58 

2268.33907.273 

1701.25 

773.905 

1301.00 

4 

3869.58 

0806.67 

1934.86 

3403.33 

1289.99 

.'208.89907.582 

1701.67 

774.152 

1361.33 

5 

387-1.78 

6808.33 

1935.40 

3404.17 

1290.39 

2269.44967.882 

1702.08 

774.392 

1361.07 

6 

3871.98 

6810.00 

1936.06 

3405.00 

1290.79 

2270.00908.183 

1702.50 

774.633 

1362.00 

7 

3873.19 

6811.67 

1936.66 

3405.83 

1291.19 

2270.50968.484 

1702.92 

774.874 

1362.33 

8 

3874.39 

6813.33 

1937.27 

3406.67 

1291.60 

2271.11  968.785 

1703.33 

775.115 

1362.67 

9 

3875.62 

6815.00 

1937.88 

3407.50 

1292.01 

2271.67 

969.093 

1703.75 

775.361 

1363.00 

1O 

3876.85 

0816.67 

1938.50 

3408.33 

1292.42 

2272.22 

969.401 

1704.17 

775.607 

1363.33 

11 

3878.06 

6818.33 

1939.10 

3409.17 

1292.82 

2272.78969.702 

1704.58 

775.848 

1363.67 

12 

3879.26 

6820.00 

1939.70 

3410.00 

1293.22 

2273.33970.003 

1705.00 

776.089 

1364.00 

13 

3880.49 

6821.67 

1940.32 

3410.83 

1293.63 

2273.89970.311 

1705.42 

776.335 

1364.33 

14 

3881.72 

6823  33 

1940.93 

3411.67 

1294.04 

2274.44  970.619 

1705.83 

776.582 

1364.07 

15 

3882.93 

6825.00 

1941.53 

3412.50 

1294.44 

2275.00970.920 

1706.25 

776.822 

1365.00 

10 

3884.13 

6826.67 

1942.14 

3413.33 

1294.84 

2275.56971.221 

1706.67 

777.003 

1365.33 

17 

3885.33 

6828.33 

1912.74 

3414.17 

1295.24 

2276.11  971.521 

1707.08 

777.304 

1365.07 

18 

3886.54 

6830.00 

1943.34 

3415  00 

1295.65 

2276.67971.822 

1707.50 

777.545 

1366  00 

19 

3887.77 

6831.67 

1943.96 

3415.83 

1296.06 

2277.22 

972.130 

1707.92 

777.791 

1366.33 

20 

3889.00 

6833.33 

1944.57 

3416.67 

1296.47 

2277.78 

972.438 

1708.33 

778.038 

1366.67 

21 

3890.20 

6835.00 

1945.17 

3417.50 

1296.87 

2278.33972.739 

1708.75 

778.278 

1367.00 

22 

3891  41 

6836.67 

1945.77 

3418.33 

1297.27 

2278.89973.040 

1709.17 

778.519 

1367.33 

23 

3892.64 

6838.33 

1946.39 

3419.17 

1297.68 

2279.  44  !  973.  348 

1709.58 

778.765 

1367.67 

24 

3893  87 

6840.00 

1947.01 

3420.00 

1298.09 

2280.00973.656 

1710.00 

779.012 

1368.00 

25 

3895.07 

6841  67 

1947.61 

3420  83 

1298.49 

2280.56973.957 

1710.42 

779.253 

1368.33 

26. 

3896.28 

6843  33 

1948.21 

3421.67 

1298.89 

2281.11 

974.258 

1710.83 

779.493 

1308.67 

27 

3897.51 

6845.00 

1948.83 

3422.50 

1299.30 

2281.67 

974.566 

1711.25 

779.740 

1309.00 

28 

3898.74 

6846.67 

1949.44 

3423.33 

1299.71 

2282.  22  1  974.  874 

1711.67 

779.980 

1309.33 

29 

3899.97 

6848.33 

1950.06 

3424.17 

1300.12 

2282.78 

975.182 

1712.08 

780.233 

1369.67 

30 

3901.20 

6850.00 

1950  67 

3425.00 

1300.54 

2283.33 

975.490 

1712.50 

780.479 

1370.00 

31 

390-2.41 

6851.67 

1951.28 

3425.83 

1300.94 

J283.89i975.791 

1712.92 

780.720 

1370.33 

32 

3903.61 

6853.33 

1951.88 

3426.67 

1301.34 

2284.44 

976.092 

1713.33 

780.961 

1370.67 

33 

3904.84 

6855.00 

1952.49 

3427.50 

1301.75 

2285.00 

976.400 

1713.75 

781.207 

1371.00 

34 

3906.07 

6856.67 

1953.11 

3428.33 

1302.16 

2285.56 

976.708 

1714.17 

781.453 

1371.33 

35 

3907.28 

6858.33 

1953.71 

3429.17 

1302.56 

J286.ll 

977.009 

1714.58 

781.694 

1371.67 

36 

3908.48 

6860.00 

1954.31 

J430.00 

1302.96 

2286.67 

977.309 

1715.00 

781.935 

1372.00 

37 

3909.71 

6861.67 

1954.93 

3430.83 

1303.37 

2287.22 

9:7.618 

1715.42 

782.181 

1372.33 

38 

•3910.94 

6863.33 

1955.54 

3431.67 

1303.78 

J287.78 

977.926 

1715.83 

782.428 

1372.67 

39 

3912.18 

6865.00 

1956.16 

3432.50 

1304.19 

2288.33 

978.234 

1716.25 

782.674 

1373.00 

40 

3013.41 

6866.67 

1956.78 

3433.33 

1304.60 

2288.89 

978.542 

1716.67 

782.921 

1373.33 

41 

3914.61 

6868.33 

1957.38 

3434.17 

1305.00 

2289.44 

978.842 

1717.08 

783.161 

1373.67 

42 

3915.81 

6870.00 

1957.98 

3435.00 

1305.41 

J290.00 

979.143 

1717.50 

783.402 

1374.00 

43 

3917.05 

6871.67 

1958.60 

3435.83 

1305.8-,' 

2290.56 

979.451 

1717.92 

783.649 

1374.33 

44 

3918.28 

6873.33 

1959.21 

3436.67 

1306.23 

2291.11 

979.759 

1718.33 

783.895 

1374.07 

45 

3919.51 

6875.00 

1959.83 

3437.50 

1306.64 

2291.67 

980.067 

1718.75 

784.141 

1375.00 

46 

39  .'0.74 

0876.67 

1960.44 

3438.33 

1307.05 

2292  22 

980.375 

1719.17 

784.388 

1375.33 

47 

3921.95 

6878.33 

1961.04 

3439.17 

1307.45 

2292!  78 

980.676 

1719.58 

784.629 

1375.67 

48 

3923.15 

6880.00 

1961.65 

3440.00 

1307.85 

2293  .  33 

980.977 

17'20.00 

784.869 

1376.00 

49 

3924.38 

6881.67 

1962.26 

3440.83 

1308.26 

2293.89 

981.285 

1720.42 

785.116 

1376.33 

50 

3925.61 

6883.33 

1962.88 

3441.67 

1308.67 

2294.44 

981.593 

1720.83 

785.302 

1376.67 

51 

3926.84 

6885.00 

1963.49 

3442.50 

1309.08 

2295.00 

981.901 

1721.25 

785.609 

1377.00 

52 

3928.08 

6886.67 

1964.11 

3443.33 

1309.49 

2295.56 

982.209 

1721.67 

785.855 

1377.33 

53 

31)29.31 

0888.33 

1964.73 

3444.17 

1309.90 

2296.11 

982.517 

1722.08 

7'86.102 

1377.07 

54 

3930.54 

6890.00 

1965.34 

3445.00 

1310.31 

2296.67 

982.825 

1722.50 

786.348 

1378.00 

55 

3931.74 

0891.67 

1965.94 

3445.83 

1310.72 

2297.22 

983.126 

1722.92 

786.589 

1378.33 

56 

3932.95 

0893.  33 

1966.55 

3446.67 

1311.12 

2297.78 

983.427 

1723.33 

786.830 

1378.67 

57 

3934.18 

6895.00 

1967.16 

3447.50 

1311.53 

2298.33 

983.735 

1723.75 

787.070 

1379.00 

58 

3935.41 

0896.67 

1967.78 

3448.33 

1311.94 

2298.89 

984.043 

1724.17 

787.3-22  1379.33 

59 

3936.64 

6898.33 

1968.39 

3449.17 

1312.35 

2299.44 

984..  351 

1724.58 

787.509  1379.07 

182 


TABLE    XIV. — ACTUAL    TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

68° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
483.475 

Arc. 

Tan. 

Arc. 

Tan  . 

Arc. 

M. 

644.407 

1133.33 

552.437 

971.429 

850.000 

429.845 

755.556 

386.960680.000 

0 

644.607 

1133.61 

552.609 

971.667 

483.626^850.208 

429.979 

755.741 

387.080680.167 

1 

644.808 

1133.89 

552.781 

971.905 

483.776850.417 

430.113 

755.926 

387.201  680.333 

2 

645.013 

1134.17 

552.957 

972.143 

483.930850.625 

430.250 

756.111 

387.  324  680.1  f  -00 

3 

645.219 

1134.44 

553.133 

972.381 

484.  084  850.  833 

430.387 

756.296 

387.447  680.067 

4 

645.419 

1134.72 

553.305 

97'2.619 

484.235851.042 

430.520 

756.481 

387.  f  68  680.  833 

5 

645.620 

1135.00 

553  477 

972.857 

484.  386  '851.  250 

430.654 

756  667 

387.688681.000 

(> 

645.821 

1135.28 

553.649 

973.095 

484.536851.458 

430.788 

756.  85',' 

387.809681  167 

7 

646.021 

1135.56 

553.821  973.333 

484.687 

851.667 

430.922 

757.037 

387.929681.333 

8 

646.22? 

1135.83 

553.997 

973.571 

484.841 

851.875 

431.059 

757.222 

388.052 

681.500 

9 

646.432 

1136.11 

554.173 

973.810 

484.995 

852  083 

431.196 

757.407 

388.176 

681.667 

1O 

646.633 

1136.39 

554.345 

974.048 

485.  145  1852.  292 

431.  330  1  757.  593 

388.296:681.833 

11 

646.833 

1136.67 

554.517 

974.286 

485.296 

852.500 

431.  464  1  757.  778 

388.417682.000 

12 

647.039 

1136.94 

554.691 

974.524 

485.450 

852.708 

431.601 

757.963 

388.540 

682  167 

13 

647.244 

1137.22 

554.870 

974.762 

485.604 

852.917 

431  738 

758.148 

388.663 

682.333 

14 

647.445 

1137.50 

555  042 

975.000 

485.755 

853.125 

431.871 

758.333 

388.784 

682.  00 

15 

647.645 

1137.78 

555.214 

975.238 

485.905 

853:333 

432.005 

758.519 

388  904 

682  667 

16 

647.846 

1138.06 

555.386 

975.476 

486.056 

853.542 

432.139 

758.704 

389.025682.833 

17 

648.047 

1138.33 

555.558 

975.714 

486.206 

853.750 

432.2731758.889 

389.1451683.000 

18 

648.252 

1138.61 

555.734 

975.952 

486.360 

853.958 

432.410 

759.074 

389.269 

683.167 

19 

648.457 

113S.89 

555.910 

976.190 

486.514 

854.167 

432  547 

759.259 

389.392 

683.333 

20 

648.658 

1139.17 

556.082 

976.429 

486.665 

854.375 

432  681  1759.444 

389.513 

683.500 

21 

648.859 

1139.44 

556.254 

976.667 

486.815 

854.583 

432.815 

759  630 

389.633 

683.667 

22 

649.064 

1139.72 

556.430 

976.905 

486.970 

854.792 

432.952 

759.815 

389.756 

683.833 

23 

649.269 

1140.00 

556.606 

977.143 

487  124 

855.000 

433.089 

760.000 

389  880 

684.000 

24 

649.470 

1140.28 

556.778 

977.381 

487.274 

855.208 

433.222 

7'60.185 

390.000 

684  167 

25 

649.671 

1140.56 

556.950 

977.619 

487.425 

855.417 

433.356 

760.370 

390.121 

684.333 

26 

649.876 

1140.83 

557.126 

977.857 

487.579 

855.625 

433.493 

760.556 

390.244 

684.500 

27 

650.081 

1141.11 

557.302 

978.095 

487.733 

855.833 

433.630 

760.741 

390.367 

684.667 

28 

650.287 

1141.39 

557.478 

978.333 

487.887 

856.042 

433.767 

760.926 

390.491 

684.833 

29 

650.492 

1141.67 

557.654 

978.571 

488.041 

856  250 

433.904 

761.111 

390.614 

685.000 

30 

650.693 

1141.94 

557.826 

978.810 

488.192 

856  458 

434.038 

761.296 

390.734 

685.167 

31 

650.894 

1142.22 

557.998 

979.048 

488.342 

856.667 

434.  172 

761.481 

390.855 

685.333 

32 

651.099 

1142.50 

558.174 

979.286 

488.496 

856.875 

434.309 

761.667 

390.978 

685.500 

33 

651.304 

1142.78 

558.350 

979.524 

488.650 

857.083 

434.446 

761.852 

391.102 

685.667 

34 

651.505 

1143.06 

558.522 

979.762 

488.801 

857.292 

434.580 

762.037 

391.222 

685.833 

35 

651.706 

1143.33 

558.694 

980.000 

488.951 

857.500 

434.714 

762  222 

:/.)!.  343 

686.000 

36 

651.911 

1143.61 

558.871 

980.238 

489.106 

857.708 

434.851 

762.407 

391.466 

686.167 

37 

652.116 

1143.89 

559.017 

980.476 

489.260 

857.917 

434.988 

762.593 

391.589 

686.333 

:i8 

652.322 

1144.17 

559.223 

980.714 

489.414 

858.125 

435.125 

762.778 

391.713 

686.500 

39 

652.527 

1144.44 

559.399 

980.952 

489.568 

858.333 

435.262 

762.963 

391.836 

686.667 

40 

652.  72H 

1144.72 

559.571 

981.190 

489.718 

858.542 

435.396 

763.148 

391.956 

686.833 

41 

652.928 

1145.00 

569.748 

981.429 

489.869 

858.750 

435.529 

763.333 

392.077 

t  87.  000 

42 

653.134 

1145.28 

559.919 

981.667 

490.023 

858  958 

435.666 

763.519 

392.200 

687.167 

43 

653.339 

1145.56 

560.095 

981.905 

490.177 

H59.167 

435  803 

763.704 

392.324 

6S7.333 

44 

653.545 

1145.83 

560.271 

982.143 

490.331 

859.375 

435.940 

763.889 

392.447 

687.500 

45 

653.750 

1146.11 

560.447 

982.  3S1 

490.485 

859.583 

436.077 

764.074 

392.570 

687.667 

46 

653.951 

1146.39 

560.619 

982.619 

490.636 

859.792 

436.211 

764.259 

392.691 

687.833 

47 

654  .  151 

1146.67 

560.791 

982.857 

490.786 

860.000 

436.345 

764.444 

392.811 

688.000 

48 

654.357 

1146.94 

560.967 

983.095 

490.940 

860.208 

436.482 

764.630 

392.935 

688.167 

49 

654.562 

1147.22 

561.143 

983.333 

491.095 

860.417 

436.619 

764.815 

393.058 

688.333 

50 

654.788 

1147.50 

561.319 

983.571 

491.249 

K60.625 

436.756 

765.000 

393.181 

688.500 

51 

654.973 

1147.78 

561  495 

983.810 

491.403 

860.833 

436.893 

765.185 

393.305 

688.667 

52 

655.178 

1148.06 

561.672 

9S4.04S 

491.557 

861.042 

437.030 

765.370 

393.428 

688.833 

53 

655.384 

1148.33 

561.  848  '984.  286 

491.711 

861.250 

137.107 

765.556 

393.551 

689.000 

54 

655.584 

1148.61 

562.  020  '  984.  524 

491.862 

861.  45S 

437.301 

765.741 

393.672 

689.167 

55 

655.785 

1148.89 

562.  192  '984.  762 

492.012 

861.667 

437.435 

765.926 

393.792 

689.333 

56 

655.990 

1149.17J562.368985.000 

492.166 

861  ,H7T. 

437.572 

766.111 

893.916 

689.500 

57 

05(5.  190 

1149.44  562.  544  '985.  238 

492.320 

862.083 

437.709 

766.296 

394.039 

689.667 

58 

656  .  401  1  1  1  49  .  72  :  562  .  720  985  .  4  76 

492.474 

862.292 

437.846 

7G6.481 

394.162 

689.833 

59 

183 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


69" 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Are. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

3937.8? 

6900.00 

1969.01  3450.00 

1312.76 

2300.  OJ 

984.6.)9  1725.00 

787.815  1380.00 

1 

3939.11 

6901.67 

1969.633450.83 

1313.17 

2300.56 

984.967  1725.42 

788.062  1380.33 

2 

39  JO.  34 

6903.33 

1970.243451.67 

1313.58 

2301.11 

985.275 

1725.83 

788.3081380.67 

3 

3941.57 

6905.00 

1970  86  3452.50 

1313.99 

2301.67 

985.583 

1726.25 

788.5551381.00 

4 

3942.80 

6906.67 

1971.473453.33 

1314.40 

2302.22 

985.891  1726.67 

788.801  1381.33 

5 

3944.03 

6908.33 

1972.093454.17 

1314.81 

2302.78 

986.199  1727.  Oh 

789.048  1381.67 

6 

3945.27 

6910.00 

1972.703155.00 

1315.22 

2303.33 

986.507  1727.50 

789.294  1382.00 

7 

3946.50 

6911.67 

1973.323455.83 

1315.63 

2303.89 

986.815 

1727.92 

78^.540 

1382.33 

8 

3947  73 

6913.33 

1973.943456.67 

1316.05 

2304.44 

987.123 

1728.33 

789.78? 

1382.67 

9 

3948.93 

6915.00 

1974.54 

3457.50 

1316.45 

2305.00 

987.424 

1728.75 

790.028 

1383.00 

10 

3950.14 

6916.6? 

1975.14 

3458.33 

1316.85 

2305.56 

987.725 

1729.1? 

790.268 

1383.33 

11 

395  1.  3  r 

6918.33 

1975.76 

3459.17 

1317.26 

2306.11 

988.033 

1729.58 

790.515 

1383.67 

13 

3952.60 

6920.00 

1976.37 

3460.00 

1317.67 

2306.67 

988.341 

1730.00 

790.761 

1384.00 

13 

3'.)53.83 

6921.6? 

1976.99 

3460.83 

1318.08 

2307.22 

988.649 

1730.42 

791.008 

1384.33 

14 

3955.06 

6923.33 

1977.60 

3461.67 

1318.49 

2307.78 

988.95? 

1730.83 

791.254 

1384.67 

15 

3956.29 

6925.00 

1978.22 

3162.50 

1318.90 

230S.33 

989.265 

1731.25 

791.501 

1385.00 

16 

3957.53 

6926.67 

1978.84 

3463.33 

1319.31 

2308.89 

989.573 

1731.67 

791.74? 

1385.33 

17 

3958.76 

6928.33 

1979.45 

3464.1? 

1319.72 

2309.44 

989.881 

1732.08 

791.994 

1385.67 

18 

3959.99 

6930.00 

1980.0? 

3465.0) 

1320.13 

2310.00 

990.189 

1732.50 

792.240 

1386.00 

19 

3961.2-.* 

6931.67 

1980.68 

3465.83 

1320.54 

2310.56 

990.497 

1732.92 

792.486 

1386.33 

30 

396-2.45 

6933.33 

1981.33 

3466.67 

1320.95 

2311.11 

990.805 

1733.33 

792.733 

1386.67 

31 

3963.69 

6935.00 

1981.92 

1467.50 

1321.36 

2311.67 

991.113 

1733.75 

792.979 

1387.00 

33 

3964.92 

6936.6? 

1982.53 

3468.33 

1321.78- 

2312.22 

991  421 

1734.1? 

793.226 

1387.33 

33 

3966.15 

(5938.33 

1983.15 

3409.1? 

1322.19 

2312.78 

991.730 

1734.58 

793.472 

1387.67 

34 

S907.3H 

6940.00 

1983.76 

3  470.00 

1332.60 

2313.33 

992.038 

1735.00 

793.719 

1388.00 

35 

3968.61 

6941.67 

1984.3813470.  83 

1323  01 

2313.89 

992.346 

1735.42 

793.965 

1388.33 

36 

396'.).  85 

6913.33 

1985.00 

5471.6; 

1323.42 

2314.44 

992.654 

1785.88 

T94.212 

1388.67 

37 

3971.08 

6945.00 

1985.61 

1472.50 

1323.83 

2315.00 

992.962 

1736.25 

794.458 

1389.00 

38 

3972.31 

6946.67 

1986.  2i 

3173.33 

1324.24 

2315.56 

993.270 

1736.67 

794.704 

1389.33 

39 

3973.54 

6948.33 

1986.84 

3174.17 

13  -'4.  65 

2316.11 

993.578 

1737.08 

794.951 

1389.67 

3O 

3974.77 

(5950.00 

1987.46 

3475.03 

1335.06 

2316.6? 

993.886 

1737.50 

795.19? 

1390.00 

31 

3976.03 

6951.67 

1988.09 

3475.83 

1325.48 

2317.2-2 

994.201 

1737.92 

795.450 

1390.33 

33 

3977.29 

6953.33 

1988.72 

3476  67 

1325.90 

2317.78 

J94.516 

1738.33 

795.702 

1390.67 

33 

3978.53 

6955.00 

1989.31 

3477.50 

1326.31 

2318.33 

J94.824 

1738.75 

795.948 

1391.00 

34 

3979.  7t> 

6956.67 

1989.95 

3178.33 

1326.72 

2318.89 

995.132 

1739.17 

796.195 

1391.33 

35 

3980.99 

6958.33 

1990.57 

3179.17 

1327.13 

2319.44 

995.440 

1739.58 

796.441 

1391.67 

36 

3982.22 

6960.00 

1991.  IS 

3  HO.  00 

1327.54 

2320.00 

995.748 

1740.00 

796.688 

1392.00 

37 

3983.45 

6961  .  6? 

I  W  1.80 

3180.83 

1327.95 

2320.56 

996.056 

1740.42 

796.934 

1392.33 

38 

3984.69 

6963.33 

1992.42 

3481.67 

1328.37 

2*21.11 

996.364 

1740.83 

797.180 

1392.67 

39 

3985.92 

6965.00 

1993.03 

3182.50 

1328.78 

2321.67 

996.672 

1741.25 

797,427 

1393.00 

4O 

3987.15 

6966.67 

1903.65 

34S3.33 

1329.19 

2322.22 

996.980 

1741.6? 

797.673 

1393.33 

41 

3988.38 

6968.33 

1991.26 

3484.17 

1329.60 

232-2.78 

997.288 

1742.08 

797.920  1393.67 

43 

3989.61 

6970.00 

1994.88 

3485.00 

1330.01 

2323.33 

997.596 

1742.50 

798.166  1394.00 

43 

3990.87 

6971.6? 

1995.51 

3485.83 

1333.43 

2323.89 

997.912 

1742.92 

793.418  1394.33 

44 

3992.13 

6973.33 

1936.14 

34S6.6? 

133).  85 

2324.44 

998.227 

1713.33 

798.671  1394.67 

45 

3993.37 

6975.00 

1996.  76  1  3  487.  50 

1331.26 

2325.00 

998.535 

1713.75 

798.917  1395.00 

46 

3994.60 

6976.67 

1  997.  3  r  3488.33 

1331.67 

2325.56 

998.843 

1744.1? 

799.163  1395.33 

47 

3995.83 

6978.33 

1997.993489.1? 

1332.08 

2326.11 

9W.151 

1744.58 

799.410  1395.67 

48 

3997.06 

6980.00 

1998.60:3490.00 

1332.49 

2326.6? 

999.459 

1745.00 

799.656  1396.00 

49 

3998.29 

6981.67 

1999.22 

3490.83 

1332.90 

2327.22 

999.767 

1745.42 

799.903  1396.33 

5O 

3999.52 

6983.33 

1999.84 

3491.67 

1333.31 

2327.78 

1000.07 

1745.83  800.149 

1396.67 

51 

4000.76 

6985.00 

2000.45 

3492.50 

1333.72 

2328.33 

1000.38 

1746.25 

800  396  1397.00 

53 

4001.99 

6986.6? 

2001.07 

3493.33 

1334.13 

2328.89 

1000  69 

1746.67 

800.642  1397.33 

53 
54 

4003.25 
4004.51 

6988.33 
6990.00 

2001.70 
2002.33 

3491.17 
3495.00 

1334.55 
1334.97 

2329.44  1001.01 
2330.00  1001.32 

1747.08 
1747.50 

800  894  1397.67 
801.1471398.00 

55 

4005.74 

6991.67 

2002.94 

3495.83 

1335.38 

2340.56 

1001.63 

1747.92 

801.3931398.33 

58 

4006.97 

6993.33 

2003.56 

3496.67 

1335.80 

2331.11 

1001.94 

1748.33 

801.63!)  1398.67 

57 

4008.21 

6995.00 

2004.18 

3497.50 

1336.21 

2331.67 

1002.25 

1748.75 

801.8861399.00 

58 

4009.44 

6996.6? 

2004.79 

3498.33 

1336.62 

2332.22 

1002.55 

1749.17 

802.132  1399.33 

59 

4010.70 

6998.33 

2005.42 

3499.17 

1337.04 

2332.7811002.87 

1749.58 

802.385  1399.07 

184 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


o 

10°  Curve. 

Tan. 

Arc. 

Tan. 

Arc.      Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

656,607 

1150.00 

562.890 

985.7141492.629 

862.500 

437  983 

766.607 

894.286 

690.000 

O 

650.812 

1150.28 

563.072 

985.  952  492.  783 

802.708 

438.120 

766.852 

394.409690.167 

1 

05".  01  7  1150.56 

563.248 

986.190 

492.937 

802.917 

438.257 

767.037 

394.532 

690.333 

2 

657.223 

1150.83 

563.424 

986.429 

493.091 

863.125 

438.394 

767.222 

394.650 

090.500 

3 

657.428 

1151.11 

563.600980.607 

493.245 

863.333 

438.531 

707.407 

394.779 

090.667 

4 

65".  634 

1151.39 

563.  776  1980.905 

493.399 

803.542 

438.668 

767.593 

394.902 

690.833 

5 

657.839  1151.  67 

563.953987.143 

493.553 

803.750 

438.805 

767.778 

395  026 

691.000 

6 

658.044 

1151.94 

504.  129  1987.  381 

493  70; 

803.958 

438.942 

767.903 

395.149 

091.167 

7 

658.850 

1152.22 

564.305 

987.619 

493.861 

804.167 

439.079 

768.148 

395.272 

691.333 

8 

658.451 

1152.50 

564.477 

987.857 

494.012 

861.375 

439.213 

768.333 

395.393 

691.500 

9 

658.651 

1152.78 

564.649 

988.095 

494.162 

804.583 

439.347 

768.519 

395.513 

691.667 

1O 

658.857 

1153.00 

564.825 

988.333 

494  317 

804.792 

439.484 

768.704 

395.037 

691.833 

11 

659.062 

1153.33 

565.001 

988.571 

494.471 

805.000 

439.621 

768.889 

395.700 

692.000 

12 

659.267 

1153.61 

505.177 

988.810 

494.625 

865.208 

439.758 

769.074 

395.883 

692.167 

13 

659.473 

1153.89 

565.353 

989.048 

494.779 

865.417 

439.895 

769.259 

396.007 

692.333 

14 

659.678 

1154.17 

505.529 

989.280 

494.933 

865.625 

440.032 

769.444 

396.130 

692.500 

15 

659.884 

1154.44 

505.705 

989.524 

495.087 

865/833 

440.169 

769.630 

396.253 

692.667 

Hi 

660.089  1154.72 

505.881 

989.762 

495.241 

866.042 

440.306 

769.815 

396.377 

692.833 

17 

660.294 

1155.00 

506.057 

990.000 

495.395 

866.250 

440.443 

770.000 

896.500 

693.000 

18 

660.500 

1155.28 

566.234 

990.238 

495.549 

806.458 

440.580 

770.185 

390.023 

093.167 

19 

660.705 

1155.56 

566.410 

990.470 

495.703 

866.667 

440.717 

770.370 

396.747 

693  333 

20 

660.911 

1155.83 

566.586 

990.714 

495.858 

806.875 

440.854 

770.556 

396.870 

693.500 

21 

661.116 

1156.11 

566.762 

990.952 

496.012 

867.083 

440.991 

770.741 

396.993 

693.667 

22 

661.321 

1156.39 

566.938 

991.190 

496.166 

867.292 

441.128 

770.926 

397.117 

693.833 

23 

661.527 

1156.67 

567.114 

991.429 

496.320 

867.500 

441.265 

771.111 

397.240 

694.000 

24 

0(51.732 

1156.94 

567.290 

991.007 

496.474 

807.7'08 

441.402 

771.290 

897.MJ8 

694.167 

25 

601.938 

1157.22 

567.466 

991.905 

496.628 

867.917 

441.539 

771.481 

397.487 

094.333 

2G 

002.143 

1157.50 

567.642 

992.143 

496  .  782 

808.125 

441.070 

771.667 

397.610 

094.500 

27 

662.348 

1157.78 

507.818 

992.381 

496.936 

808.333 

441.813 

771  852 

397.733 

694.667 

28 

662.554 

1158.00 

567.994 

992.619 

497.090 

808.542 

441.950 

772.037 

397.857 

694.833 

29 

662.759 

1158.33 

568.171 

992.857 

497.245 

868.750 

442.087 

772  222 

397.980 

695.000 

30 

662  909 

1158.61 

508.351 

993.095 

497.402 

868.958 

442  227 

772.407 

398.106 

695.167 

31 

663.180 

1158.89 

508.531 

993.333 

497.560 

809.107 

442  367 

772  593 

398.233 

095.333 

32 

663.385 

1159.17 

568.70? 

993.571 

497.714 

809.375 

442.504 

772  '.778 

398  350 

695.500 

33 

663.590 

1159.44 

568.883 

993.810 

497.868 

869.583 

442.641 

772.963 

398.479 

695.667 

34 

063.790 

1159.72 

569.059 

994.048 

498.022 

809.792 

442.778 

773.148 

398.603 

695.833 

35 

664.001 

1160.00 

569.235 

991.286 

498.176 

870.000 

442.915 

773  333 

398.726 

696.000 

36 

664.207 

1100.28 

569.411 

994.524 

498.330 

870.208 

443.052 

773.519 

398.849 

696.167 

37 

664.412 

1160.56 

569.587 

994.762 

498.485 

870.417 

443  J89 

773.704 

398.973 

696.333 

38 

664.617 

1100.83 

569.763 

995.000 

498.639 

870.025 

443.320 

77'3.889 

399.096 

696.500 

39 

664.823 

1161.11 

569.940 

995.238 

498.793 

870.833 

443.463 

774.074 

399  219 

696.667 

40 

665.028  1161.39 

570.116 

995.470 

498.947 

871.042 

443.600 

77-4.259 

399.343 

696.833 

41 

605.234  1161.67 

570.292 

995.714 

499.101 

871.250 

443.737 

774.444 

399  466 

697.000 

42 

665.444lll61.94 

570.472 

995.952 

499.259 

871.458 

443.878 

774.630 

31)9.592 

697.167 

43 

665.654 

1162.22 

570.652 

996.190 

499.410 

871.667 

444.018 

774.815 

399.718 

697.833 

44 

665.859 

1162.50 

570.828 

996.429 

499.571 

871.875 

444.155 

775.000 

399  842 

697.500 

45 

666.  065  Si  162.  78 

571.004990.667 

499.725 

872.083 

444.292 

775  185 

399.965 

697.667 

46 

666.  270  ;  1163.  OH 

571.180:996.905 

499.879 

872.292 

444.429 

775.370 

400.088 

697.833 

47 

600.476 

1163.33 

571.350 

997.143 

500.033 

872.500 

444.566 

775.550 

400.212 

698.000 

48 

000.681 

1163.01 

571.533 

997.381 

500.187 

872.708 

444.703 

775.741 

400.335 

698.167  49 

666.886 

1163.89 

571.709 

997.619 

500.341 

872.917 

444.840 

775.926 

400.459 

698.333  50 

607.092 

1164.17 

571.885 

997  857 

500.495 

873.125 

444.977 

776.111 

400.582 

698.500 

51 

667.297 

1164.44 

572.061 

998.095 

500.049 

873.333 

445.114 

776.296 

400.705 

098.607 

52 

667.507 

1164.72 

572.241 

998.333 

500.807 

873.542 

445.254 

776.481 

400.831 

098.833 

53 

667.718 

1165.00 

572.421 

998.571 

500.965 

873.750 

445.394 

776.667 

400.958 

699.000 

54 

667.923 

1165.28 

572.597 

998.810 

501.119 

873.958 

445.531 

776.852 

401.081 

699.167 

55 

668.128 

1165.50 

572.773 

999.  04S 

501.273 

874.167 

445.668 

777.037 

401.204 

099.333 

56 

668.334 

1165.83 

572.949 

999.286J501.427 

874.375 

445  805 

777.222 

401.328 

699.500 

57 

668.539 

1166.11 

573.120 

999.524501.581 

874.583 

445.942 

777.407 

401.451 

699.667 

58 

668.749 

1166.39 

573.300 

999.702501  739 

874.792 

440.083 

777.593 

401.577 

699.833 

59 

185 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


70° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

7000.00 

Tan. 

Are. 

Tan. 

Arc. 

Tan. 

1603.18 

Arc. 

Tan. 

Arc. 

O 

4011.96 

2006.05 

3500.00 

1337.46 

2333  33 

1750.00 

802.637 

1400.00 

1 

-1013.19 

7001.672006.67 

3500.83 

1337.87 

•2333.89 

1003.49 

1750.42 

802.883 

1400.33 

2 

4014.42 

7003.332007.28 

3501.67 

1338.28 

•2334.44 

1003.80 

1750.83 

803.130 

1400.67 

3 

4015.65 

7005.  00  12007.  90 

3502.50 

1338.69 

2335.00 

1004.11 

1751.25 

803.376 

1401.00 

4 

4016.89 

7006.67)2008  52 

3503.33 

1339.10 

2335.56 

1004.42 

1751.67 

803.623 

1401.33 

5 

4018.15 

7008.332009.15 

3504.17 

1339.5-2 

2336.11 

1004.73 

1752.08 

803.875 

1401.67 

O 

4019  41 

7010.002009.78 

3505.00 

1339.94 

2336.67 

1005.05 

1752.50 

804.127 

1402.00 

7 

40-20.64 

7011.672010.39 

3505.83 

1340.35 

2337.22 

1005  35 

1752.92 

804.373 

1402.33 

8 

402  t.  87 

7013.  331201  1.01 

3506.67 

1340.76 

2337.78 

1005.66 

1753.33 

804.620 

1402.67 

9 

4023.13 

7015.00 

2011.64 

3507.50 

1341.18 

2338.33 

1005.98 

1753.75 

804.872 

1403.00 

1O 

1024.39 

7016.67 

2012.27 

3508.33 

1341.60 

2338.89 

1006.29 

1754.17 

805.124 

1403.33 

11 

4025.62 

7018.33 

2012.89 

3509.17 

1342.01 

2339.44 

1006.60 

1754.58 

805.371 

1403.67 

1  2 

1026.86 

7020.00 

2013.50 

3510.00 

1342.42 

2340.00 

1  U06.91 

1755.00 

805.617 

1404.00 

13 

4028.12 

7021.67 

2014.13 

3510.83 

1342.84 

2340  .  56 

1007.22 

1755.42 

805.869 

1404.33 

14 

4029.38 

7023.33 

2014.76 

3511.67 

1343.26 

2341.11 

1007.54 

1755.83 

806.121 

1404.67 

15 

4030.61 

7025.00 

2015.38 

3512.50 

1343.67 

2341.67 

1007.85 

1756.25 

806.368 

1405.00 

16 

4031.84 

7026.67 

2015.99 

3513.33 

1344.09 

2342.22 

1008.16 

1756.67 

806.614 

1405.33 

17 

4033.10 

7028.33 

2016.62 

3514.17 

1344.51 

2342.78 

1008.47 

1757.08 

806.866 

1405.67 

18 

4034.36 

7030.00 

2017.25 

3515.00 

1344.93 

2343.33 

1008.79 

1757.50 

807.119 

1406.00 

19 

4035.59 

7031.67 

2017.87 

3515.83 

1345.34 

2343.89 

1009.09 

1757.92 

807.365 

1406.33 

2O 

4036.82 

7033.33 

2018.49 

3516.67 

1345.75 

•2344.44 

1009.40 

1758.33 

807.612 

1406.67 

21 

4038.09 

7035.00 

2019.12 

3517.50 

1346.17 

2345.00 

1009.72 

758  .  75 

807.864 

1407.00 

22 

4039.35 

7036.67 

2019.75 

3518.33 

1346.59 

2345.56 

1010.03 

759.17 

808.116 

1407.33 

23 

4040.58 

7038.33 

2020.36 

3519.17 

1347.00 

2316.11 

1010.34 

759.58 

808.362 

1407.67 

24: 

4041.81 

7040.00 

2020.98 

3520.00 

1347.41 

2346.67 

1010.65 

760.00 

808.609 

1408.00 

25 

4043.07 

7041.67 

2021.61 

3520.83 

1347.83 

2347.22 

1010.96 

760.42 

808.861 

1408.33 

26 

4044.33 

7043.33 

2022.24 

3521.67 

1348.25 

2347.78 

1011.28 

760.83 

809.113 

1408  67 

27 

4045.56 

7045.00 

2022.86 

3522.50 

1348.66 

2348.33 

1011  59 

761.25 

809.3(50 

1409.00 

2$ 

4046.79 

7046.67 

2023.47 

3523.33 

1349.07 

2348.89 

1011.89 

761.67 

809.606 

1409.33 

29 

4048.06 

7048.33 

2024.10 

3524.17 

1349.49 

2349.44 

1012.21 

762.08 

809.858 

1409.67 

30 

4049.32 

7050.00 

2024.73 

3525.00 

1349.91 

2350.00 

1012.53 

762.50 

810.110 

1410.00 

31 

4050.58 

7051.67 

2025.36 

3525.83 

1350.33 

2350.56 

1012  84 

762.92 

810.363 

1410.33 

32 

4051.84 

7053.33 

2025.99 

3526.67 

1350.75 

23')1.  11 

1013.16 

763.33 

810.615 

1410.67 

33 

4053.07 

7055.00 

2026.61 

3527.50 

1351.16 

2351.67 

1013.46 

763.75 

810.861 

1411.00 

34 

4054.30 

7056.67 

2027.22 

3528.33 

1351.57 

2352.22 

1013.77 

764.17 

811.108 

1411.33 

35 

4055.56 

7058.33 

2027.85 

3529.17 

1351.99 

2352.78 

1014.09 

764.58 

811.360 

1411.67 

36 

4056.82 

7060.00 

2028.49 

3530.00 

1352.41 

2353.33 

1014.40 

765.00 

811.612 

1412.00 

37 

4058.08 

7061.67 

2029.12 

3530.83 

1352.83 

2353.89 

1014.72 

765.4-2 

811.864 

1412.33 

38 

4059.34 

7063.33 

20-29.  75 

3531.67 

1353.25 

2354.41 

1015.03 

765.83 

812.116 

1412.67 

39 

4060.57 

7065.00 

2030.36 

3532.50 

1353.66 

2355.00 

1015.34 

766.25 

812.363 

1413.00 

40 

4061.81 

7066.67 

2030.98 

3533.33 

1354.07 

2355.56 

1015  65 

766.67 

812  609 

1413.33 

41 

4063.07 

7068.33 

2031.61 

3534.17 

1354.50 

2356.11 

1015.9(5 

1767.08 

812.862 

1413.67 

42 

4064.33 

7070.00 

2032.24 

3535.00 

1354.92 

2356.61 

1016.28 

767.50 

S13.114 

1414.00 

43 

4065.59 

7071.67 

2032.87 

3535.83 

1355.34 

2357.22 

1016.59 

767.92 

813  3(56 

1414.33 

44 

4066.8517073.33 

2033.50 

3536.67 

1355.76 

2357.78 

1016.91 

768.33 

813.  61H 

1414.67 

45 

4068.11 

7075.00 

2034.13 

3537.50 

1356.18 

2358.33 

1017.22 

7  68  .  75 

813.87'0 

1415.00 

46 

4069.37 

7076.67 

2034.76 

3538.33 

1356.60 

23xS.89 

1017  54 

769.17 

814.122 

1415.33 

47 

4070.60 

7078.33 

2035.38 

3539.17 

1357.01 

2359.44 

1017.85 

769.58 

814.3(59 

1415.67 

48 

4071.83 

7080.00 

2035.99 

3540.00 

1357.42 

2360.00 

1018.16 

77'0.00 

814.615 

1416.  (X) 

49 

4073.09 

7081.67 

2036.62 

3540.83 

1357.84 

2360.56 

1018.47 

770.42 

814.868 

1416.33 

50 

4074.35 

7083.33 

2037.25 

3511.67 

1358.26 

2361  .  1  1 

1018.79 

770.83 

815.120 

1416  67 

51 

4075.61 

7085.00 

2037.88 

3542.50 

1358.68 

23(51.67 

1019.10 

77"  25 

815.372 

1417.00 

52 

4076.88 

7086.67 

2038.51 

3543.33 

1359.10 

2362.22 

1019.42 

771  !  67 

815.624 

1417.33 

53 

4078.14 

7088.33 

2039.14 

3544.17  1359  52 

•2362.  78 

1019.73 

772.08 

815.876 

1417.67 

54 

4079.  40  [7090.  00 

2039.77 

3545.001359.942363.33 

1020.05 

772.50 

816.128 

1418.00 

55 

4  080.  6C>  7091.67 

2040.40 

3545.83  1360.36  2363.89 

1020.36 

772  .  92 

816.381 

1418.33 

56 

4081  .  92  7093  .  33  '  204  1  .  03  !  354(3  .  67  1  360  .  78  2364  .  44 

1020.68 

773.33 

816.  633[1418.  67 

57 

4083  .  15  7095  .  00  2041  .  65  3547  .  50  1  361  1  9  23(55  .  00 

1020.99 

773  .  75 

816.879 

1419.00 

58 

4084  .  3S  7096  .  67  2042  .  27  3548  .  33  1  301  .  60 

2365  .  56 

1021.29 

774.17 

817.126 

1419.33 

59 

4085  .  64  1  7098  .  33  !  2042  .  90  1  3549  .  1  7  1362  .  02 

2366.11 

1021.61 

1774.58 

817.378ll419.67 

186 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

70° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |   Arc. 

M. 

668.960  1166.67 

573.486 

1000.00 

501.896875.000 

446.223777.778 

401.703700.000 

o 

669.165lll66.94 

573.6621000.24 

502.051  875.208 

446.360777.963401.827 

700.167 

1 

669.370  1167.22 

573.838 

1000.48 

502.205 

875.417 

446.497 

778.148401.950 

700.333 

669.576  1167.50 

574.014 

1000.71 

502.359 

875.625 

446.634 

778.333 

402.073 

700.500 

3 

669.781  1167.78 

574.190 

1000.95 

502.513 

875.833 

446.771 

778.519 

402.197 

700.667 

4 

669.991  1168.06 

574.370 

1001.19 

502.671 

876.042 

446.911 

778.704 

402.323 

700.833 

5 

670.2021168.33 

574.551 

1001.43 

502.828 

876.250 

447.051 

778.889 

402.449 

701.000 

6 

670.407jll68.61 

574.727 

1001.67 

502.982 

876.458 

447.188 

779.074 

402.573 

701.167 

7 

670.612lll68.89 

574.903 

1001.91 

503.137 

876.667 

447.325 

779.259 

402.696 

701.333 

8 

670.823  1169.17 

575.083 

1002.14 

503.294 

876.875 

447.465 

779.444 

402.822 

701.500 

9 

671.0:331160.44 

575.263 

1002.38 

503.452 

877.083 

447.606 

779.630 

402.948 

701.667 

1O 

671.238)1169.72 

575.439 

1002.62 

503.606 

877.292 

447.  743  1779.815 

403.072 

701.833 

11 

671.444 

1170.00 

575.615 

1002.86 

503.760 

877.500 

447.880780.000 

403.195 

702.000 

12 

671.654 

1170.28 

575.796 

1003.10 

503.918 

877.708 

448.  020  1780.  185 

403.321 

702.167 

13 

671.864 

1170.56 

575.976 

1003.33 

504.075 

877.917 

448.160 

780.370 

403.447 

702.333 

14 

672.069 

1170.83 

576.152 

1003.57 

504.230 

878.125 

448.297 

780.556 

403.571 

702.500 

15 

672.275 

1171.11 

576.328 

1003.81 

504.384 

878.333 

448.434 

780.741 

403.694 

702.667 

16 

672.485 

1171.39 

576.508 

1004.05 

504.541 

878.542 

448.574 

780.926 

403.820 

702.833 

17 

672.695 

1171.67 

576.688 

1004.29 

504.699 

878.750 

448.715 

781.111 

403.947 

703.000 

18 

672.900 

1171.94 

576.864 

1004.52 

504.853 

878.958 

448.852 

781.296 

404.070 

703.167 

19 

673.106 

1172.22 

577.040 

1004.76 

505.007 

879.167 

448.989 

781.481 

404.193 

703.333 

2O 

673.316 

1172.50 

577.221 

1005.00 

505.165 

879.375 

449.129 

781  667 

404.319 

703.500 

21 

673.526 

1172.78 

577.401 

1005.24 

505.323 

879.583 

449.269 

781.852 

404.446 

703.667 

22 

673.732 

1173.06 

577.577 

1005.48 

505.477 

879.792 

449.406 

782.037 

404.569 

703.833 

23 

673.937 

1173.33 

577.753 

1005.71 

505.631 

880.000 

449.543 

782.222 

404.692 

704.000 

24 

674.147 

1173.61 

577.933 

1005.95 

505.789 

880.208 

449.683 

782.407 

404.819 

704.167 

25 

674.357 

1173.89 

578.113 

1006.19 

505.946 

880.417 

449.823 

782.593 

404.945 

704.333 

26 

674.563 

1174.17 

578.289 

1006.43 

506.100 

880.625 

449.960 

782.778 

405.068 

704.500 

27 

674.768 

1174.44 

578.466 

1006.67 

506.254 

880.833 

450.097 

782.963 

405.191 

704.667 

28 

674.978 

1174.72 

578.646 

1006.91 

506.412 

881.042 

450.238 

783.148 

405.318 

704.833 

29 

675.189 

1175.00 

578.826 

1007.14 

506.570 

881.250 

450.37'8 

783.333 

405.444 

705.000 

30 

675.399 

1175.28 

579.006 

1007.38 

506.728 

881.458 

450.518 

783.519 

405.570 

705.167 

31 

67'5.609 

1175.56 

579.186 

1007.62 

506.885 

881.667 

450.658 

783.704 

405.696 

705.333 

32 

675.814 

1175.83 

579.362 

1007.86 

507.039 

881.875 

450.795 

783.889 

405.820 

705.500 

33 

676.020 

1176.11 

579.539 

1008.10 

507.193 

882.083 

450.932 

784.07'4 

405.943 

705.667 

34 

676.230 

1176.39 

579.719 

1008.33 

507.351 

882.292 

451.072 

784.259 

406.069 

705.833 

35 

676.440 

1176.67 

579.899 

1008.57 

507.509 

882.500 

451.213 

784.444 

406.195 

706.000 

36 

676.650 

1176.94 

580.079 

1008.81 

507.667 

882.708 

451.353 

784.630 

406.322 

706.167 

37 

676.860 

1177.22 

580.259 

1009.05 

507.824 

882.917 

451.493 

784.815 

406.448 

706.333 

38 

677.066 

1177.50 

580.435 

1009.29 

507.978 

883.125 

451.630 

785.000 

406.571 

706.500 

39 

677.271 

1177.78 

580.611 

1009.52 

508.132 

883.333 

451.767 

785.185 

406.695 

706.667 

40 

677.481 

1178.06 

580.792 

1009.76 

508.290 

883.542 

451.907 

785.370 

406.821 

706.833 

41 

677.692 

1178.33 

580.972 

1010.00 

508.448 

883.750 

452.047 

785.556 

406.947 

707.000 

42 

677.902 

1178.61 

581.152 

1010.24 

508.606 

883  958 

452.188 

785.741 

407.073 

707.167 

43 

678.112 

1178.89 

581.332 

1010.48 

508.7'63 

884.167 

452.328 

785.92C 

407.199 

707.333 

44 

678.322 

1179.17 

581.512 

1010.71 

508.921 

884.375 

452.468 

786.111 

407.326 

707.500 

45 

678.532 

1179.44 

581.693 

1010.95 

509.079 

884.583 

452.608 

786.296 

407.452 

707.667 

46 

678.738 

1179.72 

581.8651 

1011.19 

509.233 

884.792 

452.745 

786.481 

407.575 

707.8:33 

47 

678.943 

1180.00 

582.045 

1011.43 

509.387 

885.000 

452.882 

786.667 

407.698 

708.000 

48 

679.153 

1180.28 

582.225 

1011.67 

509.545 

885.208 

453.022 

786.852 

407.825 

708.167 

49 

679.364 

1180.56 

582.405 

1011.91 

509.702 

885.417 

453.163 

787.037 

407.951 

708.333 

5O 

679.574 

1180.83 

582.585 

1012.14 

509.860 

885.625 

453.303 

787.222 

408.077 

708.500 

51 

679.784 

1181.11 

582.765 

1012.38 

510  018 

885.8:33 

453.443 

787.407 

408.203 

708.667 

52 

679.994 

1181.39 

582.946 

1012.62 

510.17'. 

886.042 

458.588 

787.593 

408.330 

708.833 

53 

680.204 

1181.67 

583  126 

1012.86 

510..')33 

886.250 

453.723 

787.778 

408.456 

709.000 

54 

680.414 

1181.94 

583.306 

1013.10 

510.491 

886.458 

453.864 

787.963 

408.582 

709.167 

55 

680.625 

1182.22 

583.486 

1013.33 

510.648 

886.667 

454.004 

788.148408.708 

709.333 

56 

680.830 

1182.50 

583.662 

1013.57 

510.802 

886.875 

454.141 

788.333408.832 

709.500 

57 

681.035 

1182.78 

583.838 

1013.81 

510.957 

887.083 

454.278 

788.5191408.955 

709.667 

58 

681.2461183.06 

584.019 

1014.05 

511.114 

887.292 

454.418 

788.  704  1409.081 

1)9.833 

59 

187 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


71° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

1ST 
~~<F 

Tan. 
4086.90 

Arc. 

Tan. 

Arc. 

3550700 

Tan.  I   Are. 
i:^62l44!2:B667o7 

Tan. 

Arc. 

Tan. 
8177030 

Arc. 

7100.00 

2043.53 

1021.92 

1775.00 

1420.00 

i 

4088.16 

7101.67 

2044.16 

3550.83 

1362.  86  J23G7.22 

1022.24 

1775.42 

817.882 

1420.33 

2 

4089.42 

7103.33 

2044.79 

3551.67 

1363  28  '.'367.78 

1022.55 

1775.83 

818.134 

1420.67 

3 

4090.68 

7105.00 

2045.42 

3552.50 

1363.702308  .33 

1022.87 

1776.25 

818.387 

1421.00 

4 

4091.94 

7106.67 

2046.05 

3553.33 

1  364.  I,!  2308.  89 

1023.18 

1776.67 

818.039 

1421.33 

5 

4093  20 

7108.33 

2046.68 

3554.17 

1364.542309.44 

1023.50 

1777.08 

818.891 

1421.67 

6 

4094.47 

7110.00 

2047.31 

3555.00 

1304.902370.00 

1023.81  1777.50 

819.143 

1422.00 

7 

4095.73 

7111.67 

2047.94 

3555.83 

1365.382370.56 

1024.13  1777.92 

819.395 

1422.33 

8 

4096.99 

7113.33 

2048.57 

3550.67 

1365.802371.11 

1024.44  1778.33 

819.648 

1422.67 

9 

4098.25 

7115.00 

2049.20 

3557.50 

1366.222371.67 

1024  70 

1778.75 

819.900 

1423.00 

10 

4099.51 

7116.67 

2049.83 

3558.33 

1366.64 

2372.22 

1025.08 

1779.17 

820.152 

1423.33 

11 

4100.77 

7118.33 

2050.46 

3559.17 

1367.00 

2372.78 

1025.39  1779.58 

820.  404  i  1423.  67 

12 

4102.03 

7120.00 

2051.09 

3560.00 

1367.48 

2373.33 

1025.71  1780  00 

820.050il424  00 

13 

4103.29 

7121.67 

2051  .  72 

3560.83 

1367.90 

^375.89 

1026.02  1780.42 

820.908  1424.33 

14 

4104.55 

7123.33 

2052.35 

3501  .  07 

1308.32 

2374.44 

1020.34  1780.83 

821.161 

1424.67 

15 

4105.81 

7125.00 

2052.98 

3->02.50 

1368.74 

2375.00 

1020.051781.25 

821.413 

1425.00 

16 

4107.07 

7126.67 

2053.61 

3503.33 

1369.16 

2375  .  50 

1026.971781.07 

821.605 

1425.33 

17 

4108.33 

7128.33 

2054.24 

3564.17 

1369.58 

2370.11 

1027.2811782.08 

821.917 

1425.67 

18 

4109.59 

7130.00 

2054.87 

3565.00 

1370.00 

2370.07 

1027.60:1782.50 

822.109 

1420.00 

19 

4110.85 

7131.67 

2055.50 

3565.83 

1370.43 

2377.22 

1027.91 

1782.92 

822.422 

1420.33 

20 

4112.11 

7133.33 

2056.13 

3566.67 

1370.85 

2377.78 

1028.23 

1783.33 

822.674 

1426.67 

21 

4113.37 

7135.00 

2056.76 

3507.50 

1371.27 

2378.33 

1028.54  !  1783.  15 

822.920 

1427.00 

22 

4114.63 

7136.67 

2057.39 

3508.33 

1371.09 

2378.89 

1028.861784.17 

823.178 

1427.33 

23 

1115.89 

7138.33 

2058.02 

3569.17 

1372.11 

4379.44 

1029.  17|  1784.  58 

823.430 

1427.67 

34 

1117.15 

7140.00 

20.)8.65 

3570.00 

1372.53 

23  SO.  00 

10^9.49;i785.00 

823.682 

1428.00 

25 

4118.42 

7141.67 

2059.28 

3570.83 

1372.95 

2380.50 

1029.80  1785.42 

823.935 

1428.33 

2G 

4119.6-! 

7143.33 

2059.91 

3571.67 

1373.37 

2381.11 

1030.12  1785.83 

824.187 

1428.07 

27 

4120.90 

7145.00 

2060.56 

3572.50 

1373.80 

2381.67 

1030.44  1780.25 

824.445 

1429.00 

28 

4122.2o 

7146.6? 

2061.20 

3573.33 

1374.23 

2382.22 

1030.70 

1786.67 

824.703s  1429.  33 

29 

1123.51 

7148.33 

2061.83 

3574.17 

1374.6.3 

2382.78 

1031.08 

1787.08 

824.955 

1429.07 

30 

4124.78 

7150.00 

2062.46 

3575.00 

1375.07 

2383.33 

1031.39 

1787.50 

825.207 

1430.00 

31 

4126.04 

7151.67 

2063.09 

3575.83 

1375.49 

2333.89 

1031.71 

1787.92 

825.459 

1130.33 

32 

4127.30 

7153.33 

2)63.72 

3576.67 

1315.91 

2384.44 

1032.02 

1788.33 

825.711 

1430.07 

33 

4128.56 

7155.00 

2064.35 

3577.50 

1376.33 

2385.00 

1032.34 

1788.75 

825.904 

1431.00 

34 

4129.82 

7156.67 

2004.98 

3578.33 

1376.75 

2335.56 

1032.05 

1789.17 

826.216 

1431.33 

35 

4131  08 

7158.33 

2065.61 

3579.17 

1377  17 

2386.11 

1032.97 

1789.58 

826.468 

1431.07 

36 

4132.34 

7160.00 

2066.24 

3580.00 

1377.59 

2386.67 

1033.28 

1790.00 

826.720  1432.00 

37 

4133.63 

7161.67 

2066.89 

3580.83 

1378.02 

2387.22 

1033.01 

1790.42 

826.  978  jl  432.  33 

38 

4134.92 

7103.33 

2067.53 

3581.67 

1378.45 

2387.78 

1033.93 

1790.83 

827.230  1432.07 

39 

4136.18 

7105.00 

2068.10 

3582.50 

1378.87 

2388.33 

1034.24 

1791.25 

827.488 

1433.00 

40 

4137.44 

7166.67 

2068.79 

3583.33 

1379.29 

2388.89 

1034.56 

1791.67 

827  740 

1433.33 

41 

4138.70 

7168.33 

2069.42 

3584.17 

1379.71 

2389.44 

1034.87 

1792.08 

827.9921433.07 

42 

4139.96 

7170.00 

2070.06 

3585.00 

1380.13 

2390.  OH 

1035.19 

1792.50 

828.245  1434.00 

43 

4141.22 

7171.07 

2070.69 

3585.83 

1380.55 

2390.56 

1035  51 

1792.92 

828.497  1434.33 

44 
45 

4142.48 
4143.77 

7173.33 
7175.00 

2071.323580.07 
2071.963-87.50 

1380.97 
1381.40 

2391.11 
2391.67 

1035.82 
1036.14 

1793.33 
1793.75 

828.749  1431.07 
829.007  1435  00 

46 

4145.06 

7176.6? 

2072.  60  3  188.  33 

1381.83 

2392.22 

1030.47 

1794.17 

829.205  1435.33 

47 

4146.32 

7178.33 

2073.243589.17 

1382.25 

2392.78 

1030.78 

1794.58 

829.517J1435.07 

48 

4147.58 

7180.03 

2073.87 

3590.00 

1382.67 

2393.33 

1037.10 

179x00 

829.769  1436.00 

49 

4148.84 

7181.67 

2074.50 

3.J90.83 

1383.09 

2393.89 

1037.41 

1795.42 

830.021 

1436.33 

50 

4150.10 

7183.33 

2075.13 

3591.67 

1383  .51 

2394.44 

1037.73 

1795.83 

830.274 

1436.67 

51 

4151.39 

7185.00 

2075.773592.50 

1383.94 

2395.00 

1038.05  1796.25 

830.  531  11437.  00 

52 

4152.68 

7186.67 

2076.423593.33 

1384.37 

2395.56 

1038.37 

1796.67 

830.789  1437.33 

53 

4153.94 

7188.33 

2077.053594.17 

13S4.79 

2396.11 

1038.09  1797.  OS 

831.042  1437.67 

54 

4155.20 

7190.  €0 

2077.683595.00 

1385.21 

2390.67 

1039.00  1797.50 

831.2941438.00 

55 

4156.46 

7191.67 

2078.31  3595.83  1385.03 

2397.22 

1039.32  1797.92 

831.546  1433.33 

5G 

4157.72 

7193.33 

2078.943596.67  1386.05 

2397.78 

1039.031798.33 

831.798  1438.07 

57 

4159.01 

7195.00 

2079.583597.50  1386.48 

2398.33 

1039  951798.75 

83  i.  056  1439.00 

58 

4160.30 

7190.07 

2080.233598.33  1380.91 

2398.89 

1040.28  1799.1? 

832.314  1439.33 

59 

4161.56 

7198.33 

2080.863599.17  1387.33 

2399.44 

1040.59  1799.58 

832.5001439.67 

188 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

71° 

Tan. 

681.456 

Arc. 
1183.33 

Tan. 

Arc. 

Tan. 
511.272 

Arc. 

887.500 

Tan. 

Arc. 

Tan. 

Arc. 

710.000 

M. 

~o" 

584.199  1014.29 

454.558 

78S.889 

409.207 

881.666 

1183.61 

584.3791014.52511.430 

887.708 

454.698 

789.074 

409.334 

710.167 

1 

681.876 

1183.89 

584.  559  !l014.76 

511.587 

887.917 

454.839 

789.259 

409.460 

710.333 

2 

68-3.086 

1184.17 

584.7391015.00511.745 

888.125 

454.979 

789.444 

409.586  710.500 

3 

682.297 

1184.44 

584.919  1015.24 

511.903 

888.333 

455.119 

789.630 

409.712 

710.667 

4 

682.507 

1184.72 

585.100  1015.48 

512.060 

888.542 

455.259 

789.815 

409.838 

710.833 

5 

68-2.717 

1185.00 

585.2801015.71 

512.218 

888.750 

455.399 

790.000 

409.965 

711.000 

6 

682.927 

1185.28 

585.460 

1015.95 

512.376 

888.958 

455.540 

790.185 

410.091 

711.167 

7 

68,3.137 

1185.56 

585.640 

1016.19 

512.533 

889.167 

455.680 

790.370 

410.217 

711.333 

8 

683.347 

1185.83 

585.820 

1016.43 

512.691 

889.375 

455.820 

790.556 

410.343 

711.500 

9 

683.558 

1186.11 

586.001 

1016.67 

512.849 

889.583 

455.960 

790.741 

410.469 

711  667 

10 

683.768 

1186.39 

586.181 

1016.90 

513.007 

889.792 

456.100 

790.926 

410.596 

711.833 

11 

«83.»?8 

1186.67 

586.  361  11017.  14 

513.164 

890  000 

456.241 

791.111 

410.722 

712.000 

158 

684.188 

1186.94 

586.541 

1017.38 

513.322 

890.208 

456.381 

791.296 

410.848 

712.167 

13 

684.398 

1187.22 

586.721 

1017.62 

513.480 

890.417 

456.521 

791.481 

410.974 

712.333 

14 

684.609 

1187.50 

586.901 

1017.86 

513.637 

890.625 

456.661 

791.667 

411.100 

712.500 

15 

684.819 

1187.78 

587.082 

1018.  10!513.  795 

890.833 

456.801 

791.852 

411.227 

712.667 

16 

685.029 

1188.06 

587.262 

1018.33 

513.953 

891.042 

456.942 

792.037 

411.353 

712.833 

17 

685.239 

1188.33 

587.442 

1018.571514.  110 

891.250 

457.082 

792.222 

411.479 

713.000 

18 

685.449 

1188.61 

587.622 

1018.81 

514.268 

891.458 

457.222 

792.407 

411.605 

713.167 

19 

685.659 

1188.89 

587.802 

1019.05 

514.426 

891.667 

457.362 

792.593 

411.732 

713.333 

20 

685.870 

1189.17 

587.983 

1019.29 

514.583 

891.875 

457.502 

792.778 

411.8:8 

713.500 

31 

686.080 

1189.44 

588.163 

1019.52514.741 

892.083 

457.643 

792.963 

411.984 

713.667 

22 

686.290 

1189.72 

58S.343 

1019.76514.899 

S92.292 

457.783 

793.148 

412.110 

713.833 

23 

686.500 

1190.00 

588.523 

1020.00 

515.057 

892.500 

457.923 

793.333 

412.236 

714.000 

24 

686.710 

1190.28 

5S8.703 

1020.24  515.214 

892.708 

458.063 

793.519 

412.363 

714.167 

25 

686.921 

1190.56 

588.884 

1020.48 

515.372 

892.917 

458.203 

793.704 

412.489 

714.333 

26 

687.135 

1190.83 

589.068 

1020.71 

515.533 

893.125 

458.347 

793  889 

412.618 

714.500 

27 

687.350 

1191.11 

589.252 

1020.95 

515.694 

893.333 

458.490 

794.074 

412.747 

714.667 

2S 

C87.561 

1191.39 

589.432 

1021.19515.852 

893.54-^ 

458.630 

794.259 

412.873 

714.833 

29 

687.771 

1191.67 

589.612 

1021.43516.010 

893.750 

458.771 

794.444 

412.999 

715.000 

30 

687.981 

1191.94 

589.793 

1021.67 

516.168 

893.958 

458.911 

794  630 

413.1-<!6 

715.167 

31 

688.191 

1192.22 

589.973 

1021.90 

516.325 

894.167 

459.051 

794.815 

413.252 

715.333 

32 

688.401 

1192.50 

590.153 

1022.14516.483 

894.375 

459.191 

795.000 

413.378 

715.500 

33 

688.612 

1192.78 

590.333 

1022.38516.641 

894.583 

459.331 

795.185 

413.504 

715.667 

34 

688.822 

1193.06 

590.513 

1022.62 

516.798 

894.792 

459.472 

795.370 

413.630 

715.8:33 

35 

689.032 

1193.33 

590.694 

10C2.86 

516  956 

895.000 

459.612 

795.556 

413.757 

716.000 

36 

689.247 

1193.61 

590.87'8 

1023.10517.117 

895.208 

459.755 

795.741 

413.886 

716.167 

37 

689.462 

1193.89 

591.062 

1023.33517.279 

895.417 

459.899 

795.926 

414.015 

716.333 

38 

689.672 

1194.17 

591.242 

1023.57 

517.436 

895.625 

460.039 

796.111 

414.141 

716.500 

39 

689.882 

1194.44 

591.422 

1023.81 

517.594 

895.833 

460.179 

796.296 

414.267 

716.667 

40 

690.092 

1194.72 

591.603 

1024.05517.752 

896.042 

460.319 

796.481 

414.393 

716.833 

41 

690.303 

1195.00 

591  .  783 

1024.29 

517.909 

896.250 

460.459 

796.667 

414.520 

7  7.000 

43 

690.513 

1195.28 

591.963 

1024  52518.067 

896.458 

460.600 

796.852 

414.646 

7  7.167 

43 

690.723 

1195.56 

592.143 

1024  .  76 

518.225 

896.667 

460.740 

797.037 

414.772 

7  7.333 

44 

690.938 

1195.83 

592.327 

1025.00 

518.386 

896.875 

460.883 

797.222 

414  901 

7  7.500 

45 

691.153 

1196.11 

592.512 

1025.24  518.547 

897.083 

461.027 

797.407 

415.030 

7  7.667 

46 

691.363 

1196.39 

592.692 

1025.48 

518.705 

897.  *92 

461.167 

797  59'- 

415.156 

7  7.833 

47 

691.573 

1196.67 

592.872 

1025.71  518.863 

897.500 

461.307 

797^778 

415.283 

718.000 

48 

691.783 

1196.94 

593.052 

1025.95 

519.020 

897.708 

461.447 

797.963 

415.409 

718.167 

49 

691.994 

1197.22 

593.233 

1026.19 

519.178 

897.917 

461.587 

798.148 

415  535 

718.333 

5O 

692.209 

1197.50 

593.417 

1026.43 

519.339 

898.125 

461.731 

798.333 

415.664 

718.500 

51 

692.423 

1197.78 

593.601 

1026.67 

519.501 

898.333 

461.874 

798.519 

415.793 

718.667 

52 

692.634 

1198.06 

593.781 

1026.90519.658 

898.542 

462.014 

798.704 

415.919 

718.833 

53 

692.844 

1198.33 

593.961 

1027.14 

519.816 

898.750 

462.155 

798.889 

416.046 

71  9.  (XX) 

54 

693.054 

1198.61 

594.142 

1027.38519.974 

898.958 

462.295 

799.074 

416.172 

719.167 

55 

tt»3  264 

1198.89 

594.322 

1027.62 

520.131 

899.167 

462.435 

799.259 

416.298 

719.333 

56 

693.479 

1199.17 

594.506 

1027.86 

520.293 

899.375 

462.578 

799.444 

416.427 

719.500 

57 

693.694 

1190.44 

594  .  690 

1028.10 

520.454 

899.583 

462.722 

799.630 

416.556719.067 

58 

693.904 

1  1  99  .  72  594  .  87  1  i  1  028  .  33  520  .612  899  .  792  462  .  862 

799.815 

416.  682|719.  833 

59 

189 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


72° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Iwt7 

Tan. 

Arc. 

7200.00 

Tan. 

Arc. 

Tan. 

Arc. 
2400.00 

Tan. 

Arc. 

Tan. 

Arc. 

0 

4162.  82 

2081.49 

3600.00 

1387.75 

1040.91 

1800.00 

832.818 

1440.00 

1 

4164.11 

7201.67 

2082.13 

3600.83 

1388.18 

2400.56  1041.23 

1800.42 

833.076 

1440.33 

2 

4165.40 

7203.33 

2082.78 

3601.67 

1388.61 

V401.ll 

1041  .  55 

1800.83 

833.334 

1440.67 

3 

4166.66 

7205.00 

2083.41 

3602.50 

1389.03 

2401.67 

1041.87 

1801.25 

833.586 

1441.00 

4 

4167.92 

7206.67 

2084.04 

3603.33 

1389.45 

2402.22 

1042.18 

1801.67 

833.838 

1441.33 

5 

411J9.21 

7208.33 

2)84.68 

3604.17 

1389  88 

2402.78 

1042.50 

1802.08 

834.096 

1441.67 

G 

4170.50 

7210.00 

2085.33 

3605.00 

1390.31 

2403.33 

1042  83 

1802.50 

834.354 

1442.00 

7 

4171.76 

7211.67 

2085.96 

3605.83 

1890.78 

2403.89 

1043.14 

1802.92 

834.606 

1442.33 

8 

4173.02 

7213.33 

2086.59 

3606.67 

1391.15 

2404  .  44 

1043.46 

1803.33 

884.859 

1442.67 

9 

4174.31 

7215.00 

2087.23 

3607.50 

1391.58 

2405.00 

1043.78 

1803.75 

835.117 

1443.00 

1O 

4175.60 

7216.67 

2087.88 

3608.33 

1392.01 

2405.56 

1044.10 

1804.17 

835.374 

1443.33 

11 

4176.86 

7218.33 

2088.51 

3609.17 

1392.43 

2406.11 

1044.42 

1804.58 

835.627  1443.67 

12 

4178.12 

7220.00 

2089.14 

3610.00 

1392.85 

2406.67 

1044.73 

1805.00 

835.879  1444.00 

13 

4179.41 

7221.67 

2089.78 

3610.83 

1393.28 

2407.22 

1045.05 

1805.42 

836.137 

1444.33 

14 

4180.70 

7223.33 

2090.42 

3611.67 

1393.71 

2107.78 

1045.38 

1805.83 

836.395 

1444.67 

15 

4181.96 

7225.00 

•'091.06 

3612.50 

1394.13 

2408.33 

1045.69 

1806.25 

836.647 

1445.00 

16 

4183.22 

7226.67 

2091.69 

3613.33 

1394.55 

2408.89 

1046.01 

1806.67 

836.899 

1445.33 

17 

4184.51 

7228.33 

2092.33 

3614.17 

1394.98 

2409.44 

1046.33 

1807.08 

837.  1  57  !  1445.  67 

18 

4185.80 

7230.00 

2092.97 

3615.00 

1395.41 

2410.00 

1046.65 

1807.50 

887.4151446.00 

19 

4187.08 

7231.67 

2093.62 

3615.83 

1395.84 

2410.56 

1046.97 

1807.92 

837.673 

1446.33 

20 

4188.37 

7233.33 

2094.26 

3616.67 

1396.27 

2411.11 

1047.30 

1808.33 

837.931 

1446.67 

21 

4189.63 

7235.00 

2094.89 

3617.50 

1396.69 

2411.67 

1047.61 

1808.75 

838.183 

1447.00 

22 

4190.90 

7236.67 

2095.52 

3618.33 

1397.11 

2412.22 

1047.93 

1809.17 

838.435 

1447.33 

23 

4192.18 

7238.33 

2096.17 

3619.17 

1397.54 

2412.78 

1048.25 

1809.58 

838  693 

1447.67 

24 

4193.47 

7240.00 

,5096.81 

3620.00 

1397.97 

2413.33 

1048.57 

1810.00 

838.951  1448.00 

25 

4194.76 

7241.67 

2097.46 

3620.83 

1398.40 

2413.89 

1048.89 

1810.42 

839.209 

1448.33 

26 

4196.05 

7243.33 

#88.10 

3621.67 

1398.83 

2414.44 

1049.22 

1810.83 

839.467 

1448.67 

27 

4197.31 

7245.00 

2098.73 

3622.50 

1399.25 

2415.00 

1049.53 

1811.25 

839  719 

1449.00 

28 

4198.57 

7246.67 

2099.36 

36*3.33 

1399.67 

2415.56 

1049.85 

1811.67 

839.971 

1449.33 

39 

4199.86 

7248.33 

2100.01 

3624.17 

1400.10 

2416.11 

1050.17 

181.2.08 

840.229 

1449.67 

30 

4201  .  15 

7'250.00 

2100.65 

3625.00 

1400.53 

2416.67 

1050.49 

1812.50 

840.487 

1450.00 

31 

4202.44 

7251.67 

2101.30 

•1625.83 

1400.96 

2417.22 

1050.81 

1812.92 

840.745 

1450.33 

32 

4203.73 

7253.  33 

2101.94 

3626.67 

1401.39 

2417.78 

1051.14 

1813.33 

841.003 

1450.67 

33 

4205.0^ 

7255.00 

2103.59 

3627.50 

1401.82 

2418.33 

1051  46 

1813.75 

841.261 

1451.00 

34 

4206.31 

7256.67 

2103.23 

3628.33 

1402.25 

2418.89 

1051.78 

1814.17 

841.519 

1451.33 

35 

4207.57 

7258.33 

2103.86 

3629.17 

1402.67 

2419.44 

1052.10 

1814.58 

841.771 

1451.67 

36 

4208.83 

7260.00 

2104.49 

3630.00 

1403.09 

2420.00 

1052.41 

1815.00 

842.023 

1452.00 

37 

4210.12 

7261.67 

2105.14 

3630.83 

1403.52 

2420.56 

1052.73 

1815.  4-J 

842.281 

1452.33 

38 

4211.41 

7263.33 

2105.78 

3631.67 

1403.95 

2421.11 

1053.06 

1815.83 

842.539 

1452.67 

39 

4212.70 

7265.00 

2106.43 

3032.50 

1404.38 

2421.67 

1053.38 

1816.25 

842.797 

1453.00 

4O 

4213.99 

7266.67 

2107.07 

3633.33 

1404.81 

2422.22 

1053.70 

1816.67 

843  055 

1453.33 

41 

4215.27 

7268.  3  i 

2107.71 

3634.17 

1405.24 

2422.78 

1054.02 

1817.08 

843  312 

1453.67 

42 

4216.56 

7270.00 

2108.36 

3635.00 

1405.67 

2423.33  1054.35 

1817.50 

843.570 

1454.00 

43 

4217.85 

7271.67 

2109.00 

3635.83 

1406.10 

2423.89 

1054.67 

1817.92 

843.828 

1454.33 

44 

4219.14 

7273.33 

2109.65 

3636.67 

1406.53 

2424.44 

1054.99 

1818.33 

844  086 

1454.67 

45 

4220.40 

7275.00 

;110.28 

3637.50 

1406.95 

2425.00 

1055.31 

1818.75 

844  338 

1455.00 

46 

4221.66 

7276.67 

.'110.91 

3638.33 

1407.37 

2  425.  56  1055.62 

1819.17 

844.591 

1455.33 

47 

4222.95 

7278.33 

2111  55 

3639.17 

1407.80 

2426.11 

1055  9411819.58 

844.  84S 

1455.67 

48 

4224  24 

7280.00 

2112.20 

3640.00 

1408.23 

2426.67 

1056.27 

1820.00 

845.106 

1456.00 

49 

4225.53 

7281.67 

2112.84 

3640.83 

1408.66 

2427.22 

1056.59 

1820.42 

845.364 

1456.33 

50 

4226.82 

7283.33 

•2113.49 

3641.67 

1409.09 

2427.78 

1056.91 

1820.83 

845.622 

1456.67 

51 

4228.11 

7385.  ft) 

2114.13 

3642.50 

1409.51 

2428.33  1057.23 

1821.25 

845.880 

1457.00 

53 

422!).  40 

7286.  (57 

2114.78 

3643.33 

1409.94 

2428.89  1057.55 

1S21.67 

846.138 

1457.33 

53 

4230.61) 

7288.83 

2115  42 

3644.17 

1410.37 

2429.441057.88 

1822.08 

846.31)6 

1457.67 

54 

4231.98 

7290.00 

2116.07 

3645.00 

1410.80 

2430.00  1058.20 

1822.50 

S46.654 

1458.00 

55 

4233.27 

7291.67 

2116.71 

3645.83 

1411.23 

2430.56  1058.52 

1822.92 

846.912 

1458.33 

56 

4234.56 

7293,33 

2117.36 

3646.67 

1411.66 

2431.11  1058  84 

1823.33 

847.170 

1458.67 

57 

4235.84 

7295.00 

2118.003647.50 

1412.09 

2431.67  1059.17 

1823.75 

847.428 

1459.00 

58 

4237.13 

7296  67 

2118.64  3648.33 

1412.52 

2432.22  1059  49 

1824.17 

847.686 

1459.33 

59 

4238.42 

7298.  33  12119.  29  36  49.  17 

1412.95 

2432.78  1059.81 

1824  58 

847.  943!  1459.  67 

190 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

73° 

Tari. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

694.114 

1200.00 

595.051 

1028.57 

520.769 

900.  001 

463.00-J 

soo.ooo 

416.805 

720.  00( 

Q~ 

694.329 

1200.28 

595.235 

1028.81 

520.931 

900.208 

463.145 

800.185 

416.938 

720.167 

1 

694.544 

1200.56 

595.419 

1029.05 

521.092 

900.417 

463.289 

800.370 

417.067 

720.333 

2 

694.755 

1200.83 

595.599 

1029.29 

521.250 

900.625 

463.429 

800.556 

417.193 

720.501 

3 

694.965 

1201.11 

595.780 

1029.52 

521.407 

900.833 

463.569 

800.741 

417.319 

720.667 

4 

695.180 

1201.39 

595.964 

1029.76 

521.569 

901.042 

463.713 

800.926 

417.448 

720.833 

5 

695.395 

1201.67 

596.148!  1030.  00 

521.730 

901.250 

463.856 

801.111 

417.577 

721.000 

6 

695.605 

1201.94 

596.328 

1030.24 

521.887 

901.458 

463.996 

801.  29b 

417.704 

721.167 

7 

695.815 

1202.22 

596.509 

1030.48 

522.045 

901.607 

464.13(5 

801.481 

417.830 

721.333 

8 

696.030 

1202.50 

596.693 

1030.71 

522.206 

901.875 

464.280 

801.667 

417.959 

721.500 

9 

696.245 

1202.78 

596.877 

1030.95 

522.368 

902.083 

464.423 

801.852 

418.088 

721.667 

1O 

696.455 

1203.06 

597.057 

1031.19 

522.525 

902.292 

464.563802.037 

418.214 

721.833 

11 

696.  665!  1203.  33 

597.238 

1031.43 

522.683902.500 

464.704 

802.222 

418.340 

722.000 

696.880 

1203.61 

597.4221031.67 

522.844902.708 

464.847 

802.407 

418.470 

722.167 

13 

697.095 
697.305 

1203.89 
1204.17 

597.606  1031.9U 
597.  786*1032.14 

523.006902.917 
523.163903.125 

464.990 
465.131 

802.593 

802.778 

418.599 
418.725 

722.333 

722.500 

14 
15 

697.516 

1204.44 

597  966 

1032.38 

523.321 

903.333 

465.271 

802.963 

418.851 

722.667 

16 

697.731 

1204.72 

598.151 

1032.62 

523.482 

903.542 

465.414 

803.148 

418.980 

722.833 

17 

697.946 

1205.00 

598.335 

1032.86 

523.644903.750 

465.558 

803.333 

419.109 

723.000 

18 

698.160 

1205.28 

598.519 

1033.10 

523.805 

903.958 

465.701 

803.519 

419.238 

723.167 

19 

698.375 

1205.56 

598.704 

1033.33 

523.966 

904.167 

465.844 

803.704 

419.367 

723.333 

20 

698.586 

1205.83 

598.884 

1033.57 

524.124 

904.375 

465.985 

803.889 

419.494 

723.500 

21 

69S.796 

1206.11 

599.064 

1033.81 

524.282904.583 

466.125 

804.074 

419.620 

723.667 

22 

699  01  1 

1206.39 

599.248 

1034.05 

524.443 

904.792 

466.268 

804.259 

419.749 

723.833 

23 

699.226 

1206.6; 

599.432 

1034.29 

524.604905.000 

466.411 

804.444 

419.878 

724.000 

24 

699.441 

1206.94 

599.617 

1034.52 

524.765905.208 

466.555 

804.630 

420.007 

724.167 

25 

699.656 

1207.22 

599.801 

1034.76 

524.927 

905.417 

466.698 

804.815 

420.136 

724.333 

26 

699.866 

1207.50 

599.981 

1035.00 

525.084 

905.625 

466.838 

805.000 

420.262 

724.500 

27 

700.076 

1207.78 

600.161 

1035.24 

525.242 

905.833 

466.979 

805.185 

420.389 

724.667 

28 

700.291 

1208.06 

600.346 

1035.48 

525.403 

906.042 

467.122 

805.370 

420.518 

724.833 

29 

700.506 

1208.33 

600.530 

1035.71 

525.565 

906.250 

467.265 

805.556 

420.647 

725.000 

30 

700.721 

1208.61 

600.714 

1035.95 

525.726 

906.458 

467.409 

805.741 

420.776 

725.167 

31 

700.93(5 

1208.89 

(500.899 

1036.19 

525.887 

906.667 

467  552 

805.926 

420.905 

725.333 

32 

701.151 

1209.17 

601.083 

1036.43 

526.048906.875 

467.696 

806.111 

421.034 

725.500 

33 

701.366 

1209.44 

601.267 

1036.67 

526.210 

907.083 

467.839 

806.296 

421.163 

725.667 

34 

701.576 

1209.72 

601.447 

1036.90 

526.367 

907.292 

467.979 

806.481 

421.289 

725.833 

35 

701.786 

1210.00 

601.627 

1037.14 

526.525 

907.500 

468  119 

806.667 

421.415 

726.000 

36 

702.001 

1210.28 

601.812 

1037.38 

526.686907.708 

468.263 

806.852 

421.544 

726.167 

37 

702  216 

1210..r>6 

601  .  996 

1037.62 

526.848 

907.917 

468.406 

807.037 

421.674 

726.333 

38 

702.431 

1210.83 

602.180 

1037.86 

527.009 

908.125 

468.550 

807.222 

421.803 

7'26.500 

39 

702.646 

1211.11 

602.365 

1038.10 

527.170 

908.333 

468.693 

807.407 

421.932 

726.667 

4O 

702.861 

1211.39 

602.549 

1038.33 

527.  331  1908.542 

468  836 

807.593 

422.061 

726.833 

41 

703.076 

1211.67 

602.733 

1038.57 

527.493908.750 

468.980 

807.778 

422.190 

727.000 

42 

703.291 

1211.94 

602.917 

1038.81 

527.654 

908.958 

469.123 

807.963 

422.319 

7'27.167 

43 

703.506 

1212.2-J 

603.102 

1039.05 

527.815909.167 

469.266 

808.148 

422.448 

727.333 

44 

7r3  716 

1212.50 

603.282 

1039.29 

527.973 

909.375 

469.407 

808.333 

422.574 

727.500 

45 

703.926 

1212.78 

603.462 

1039.52 

528.131 

909.583 

469.547 

808.519 

422.700 

727.667 

46 

704.141 

1213.06 

603.646 

1039.76 

528.292909.792 

469.690 

808.704 

422.830 

727.833 

47 

704.356 

1213.33 

603.831 

1040.00 

528.453 

910.000 

469.834 

808.889 

422.959 

728.000 

48 

7'04.571 

1213.61 

604.015 

1040.24 

528  614  910.20S 

469.977 

809.074 

423.088 

728.167 

49 

704.786 

1213.89 

604.199 

1040.48 

")28.  776  910.  41  7 

470.120 

809.259 

423.217 

728.333 

5O 

705.001 

1214.17 

604.383 

1040.71 

528.937 

910.625 

470.264 

809.444 

423.346 

728.500 

51 

705.216 

1214.44 

604.568 

1040.95 

529.098910.833 

470.407 

809.630 

423.475 

728.667 

52 

705.431 

1214.72 

504.752  1041.19 

529.260 

911.042 

470  551 

809.815 

423.604 

728.833 

53 

705.646 

1215.00 

604.936  1041.43 

529.421 

911.250 

470.694 

810.000 

423.733 

729.000 

54 

705.861 

1215.28 

605.121  1041.67 

529.582911.458 

470.837 

810.185 

423.862 

729.167 

55 

706.076 

1215.56 

605.30511041.90 

529  743 

911.667 

47X3.981 

810.370 

423.991 

729.333 

56 

706  291 

1215.83 

605.4891042.14 

529.905911.875 

471.124 

810.556 

424.120 

729.500 

57 

706.506 

1216.11 

605.  6731  042.  38  530.  066 

912.083 

471.267 

810.741 

424.249 

729.667 

58 

706  721  1216.39 

605.858  1042.62  530.227 

912.  2921471.  411 

810.926 

424.379 

729.833 

59 

191 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


73° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M7 

Tail. 

Arc. 

Tan. 

Are. 

Tan. 

Arc. 

Tau.      Arc.      Tun. 

Arc. 

~~o 

4239.71  7300.00 

2119.93 

3650.66 

1413.38 

2433.33 

1060.13  1825.00848.201 

1460.00 

1 

4-241.007301.67 

2120.58 

3650.83 

1413.81 

2433.89 

1060.46  1825.42848.459 

1460.33 

3 

4242.29 

7303.33 

2121.22 

3651.67 

1414.24 

2434.44 

1060.78  1825.83848.717 

1460.67 

3 

4  -343.58 

7305.00 

2121.87 

3652.50 

1414.67 

2435.00 

1061.10 

1826.25 

848  975 

1461.00 

4 

4214.87 

7306.67 

2122.51 

3653.33 

1415.10 

2435.56 

1061.42 

1826.67 

849.233 

1461.33 

5 

4-240.16 

7308.33 

2123.16 

3654.17 

1415.53 

2436.11 

1061.75 

1827.08849.491 

1461.67 

6 

4247.45 

7310.00 

2123.80 

3655.00 

1415.96 

2436.67 

1062.07 

1827.50849.749 

1462.00 

7 

4248.74 

7311.67 

2124.45 

3655.83 

1416.39 

2437.22 

1062.39 

1827.  92!  850.  007 

1402.33 

8 

4250  03 

7313.33 

2125.09 

3656.67 

1416.82 

2437.78 

1062.71 

1828.33 

850.265 

1462.67 

9 

4251.31 

7315.00 

2125.74 

3657.50 

1417.25 

2438.33 

1063.03 

1828.75 

850.523 

1463.00 

1O 

4252.60 

7316.67 

2126.38 

3658.33 

1417.68 

2438.89 

1063.36 

1829.17 

850.780 

1463.33 

11 

4253.92 

7318.33 

2127.04 

3659.17 

1418.12 

2439.44 

1063.69  1829.58 

851.044 

1463.67 

13 

4255.24 

7320.00 

2127.70 

3660.00 

1418.56 

2440  00 

1064.02  1830.00 

851.308 

1464.00 

13 

4256.53 

7321.67 

2128.34 

3660.83 

1418.99 

2440.56 

1064.34  1830.42 

851.566 

1464.33 

14 

4257.82 

7323.33 

2128.99 

3661.67 

1419.42 

2441.11 

1064.66  1830.83 

851.824 

1464.67 

15 

4259.11 

7325.00 

2129.63 

3862.50 

1419.85 

2441.67 

1064.981831.25 

852.082 

1465.00 

1(5 

4260.40 

7326.67 

2130.28 

3663.33 

1420.28 

2442.22 

1065.  31!  1831.  67 

852.339 

1465.33 

17 

1261.69 

7328.33 

2130.92 

3664.17 

1420.71 

2442.78 

1065.63  1832.08 

852.597 

1465.67 

18 

4262  .  97 

7330.00 

2131.57 

3665.00 

1421.14 

2443.33 

1065.95  1832.50 

852.855 

1466.00 

19 

4264.26 

7331.67 

2132.21 

3665.83 

1421.57 

2443.89 

1066.27 

1832.92 

853.113 

1466.33 

30 

4265.55 

7333.33 

2132.85 

3666.67 

1422.00 

2444.44 

1066.59 

1833.33 

853.371 

1466.67 

21 

4266.84 

7335.00 

2133.50 

3667.50 

1422.43 

2445.00 

1066.92  1833.75 

853.629 

1467.00 

a  3 

4268.13 

7336.67 

2134.14 

3668.33 

1422.86 

2445.56 

1067.24  1834.17 

853.887 

1467.33 

33 

4269.45 

7333.33 

2134.80 

3669.17 

1423.30 

2446.11 

1067.57  1834.58 

854.151 

1467.67 

34 

427'0.77 

7310.00 

2135.46 

3670.00 

1423.74 

2446.67 

1067.90  1835.00 

854.414 

1468.00 

25 

4272.06 

7341.67 

2136.11 

3670.83 

1424.17 

2447.22 

1068.22  1835.42 

854.672 

1468.33 

36 

4273.34 

7343.33 

2136.75 

3671.67 

1424.59 

2447.78 

1068.54  1835.83 

854.930 

1468.67 

37 

4274.63 

7345.00 

2137.40 

3672.50 

1425.02 

2448.33 

1068.87  1836.25 

855.188 

1469.00 

38 

4275.92 

7346.67 

2138.04 

3673.33 

1425.45 

2448.89 

1069.19  1836  (37 

855.446 

1469.33 

39 

4277.24 

7348.33 

2138.70 

3674.17 

1425.89 

2449.44 

1069.52 

1837.08 

855.709 

1469.67 

30 

4278.56 

7350.00 

2139.36 

3675.00 

1426.33 

2450.00 

1069  85 

1837.50 

855.973 

1470.00 

31 

4279.85 

7351.67 

2140.00 

3675.83 

1426.76 

2450.56 

1070.17 

1837.92 

856.231 

1470.33 

32 

4281.14 

7353.33 

2140.65 

3676.67 

1427.19 

2451.11 

1070.49 

1838.33 

856.489 

1470.67 

33 

4282.  4H 

7355.00 

2141.29 

3677.50 

1427.62 

2451.67 

1070.81 

1838.75 

856.747 

1471.00 

34 

4283.72 

7356.67 

2141.94 

3678.33 

1428.05 

2452.22 

1071.14 

1839.17 

857.005 

1471.33 

35 

4285.03 

7358.33 

2142.60 

3679.17 

1428.49 

2452.78 

1071.47 

1839.58 

857.268 

1471.67 

36 

4286.35 

7360.00 

2148.25 

3680.00 

1428.93 

2453.33 

1071.801840.00 

857.532 

1472.00 

37 

4287.61 

7361.67 

2143.90 

3680.83 

1429.36 

2453  .  89 

1072.12 

1840.42 

857.790 

1472.33 

38 

4288.93 

7363.33 

2144.54 

3681.67 

1429.79 

2454.44 

1072.44 

1840.83 

858.048 

1472.67 

39 

4290.22 

7365.00 

2145.19 

3682.50 

1430.22 

2455.00 

1072.76 

1841.25 

858.306 

1473.00 

4O 

4291.51 

7366.67 

2145.83 

3683.33 

1430.65 

2455.56 

1073.08 

1841.67 

858  564 

1473.33 

41 

4292.83 

7368.33 

2146.49 

3684.17 

1431.09 

2456.11 

1073.41 

1842.08 

858.827 

1473.67 

43 

4294.14 

7370.00 

2147.15 

3685.00 

1431.53 

2456.07 

1073.74 

1842.50 

859.091 

1474.00 

43 

4295.43 

7371.67 

2147.80 

3685.83 

1431.96 

2457.22 

1074.07 

1842.92 

859.349 

1474.33 

44 

4296.72 

7373.33 

2148.41 

3686.67 

1432.39 

2457.78 

1074.39 

1843  33 

859.607 

1474.67 

45 

4298.01 

7375.00 

2149.10 

3687.50 

1432.83 

2458.33 

1074.72 

1843  75 

859.870 

1475.00 

46 

4299.  3t> 

7376.67 

2149.76 

3688.33 

1433.27 

2458.89 

1075.05 

1844.17 

860.134 

1475.33 

47 

4300.65 

7378.33 

2150.40 

3689.17 

1433.70 

2459.44 

1075.37 

1844.58 

860.392 

1475.67 

48 

4301.94 

7380.00 

2151.05 

3690  00 

1434.13 

2460.00 

1075  69 

1845.00 

860.650 

1476.00 

49 

4303.25 

7381.67 

2151.71 

3690.  83  '1434.  57 

2460.56 

1076.02 

1845.42 

860.914 

1476.33 

5O 

4304.57 

7383.33 

2152.36 

3691  67 

1435.00'24G1.11 

1076.35 

1845.83 

861.177 

1476.67 

51 

4305.86 

7385.00 

2153.01  3692.50 

1435.  43  [246  1.67 

1076.67 

1846.25 

861.435 

1477.00 

53 

1307.  15 

7386.67 

2153.65 

369  >.  :-!3 

1435.862462.22 

1077.00 

1846.67861.693 

1477.33 

53 

4308.47 

7388.33 

2154.31 

3694.17 

1436.302462.78 

1077.33 

1847.  08801.  1)57 

1477.67 

54 
55 

4309.797390.00J2154.97 
43H.Or  7391.672155.62 

3695.00 
3695.83 

1436.74:2463.33 
1437.172463.89 

1077.66  1847.50:862.220 
1077.9811847.928(12  478 

1478.00 
1478.33 

56 

4312.367393.332156.26 

3696.67 

1437.602464.44 

1078.  30  11848.33  862.  7  36 

1478.67 

57 

4313.68  7395.002156.92 

3697.50 

1438.042465.00 

1078.63  1848.75  863.  000 

1479.00 

58 

4315.007396.672157.58 

3698.33 

1438.482465.56 

1078.96  1849.17.S63.2G3 

1479.33 

59 

4316  29  7398.33  21  58.  22i  3699.  17 

1438.91  2466.11 

1079.28  1849.  58  1863.  521 

1479.67 

193 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

73° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

roe.  930 

1210.07 

t506.04ii 

1042.86 

530.388 

912.500 

471.554 

811.111 

424.508 

730.000 

0 

707.150 

1210.94 

000.220 

1043.10 

530.550 

912.708 

471.698 

811.296 

424.637 

730.167 

1 

707.305 

1217.22 

000.411 

1043.33 

530.711 

912.917 

471.841 

811.481 

424.766 

730.333 

2 

707.680 

1217.50 

000  .  595 

1043.57 

530.872 

913.125 

471.984 

811.667 

424.895 

730.500 

3 

707.795 

1217.78 

006.771) 

1043.81 

531.034 

913.333 

472.128 

811.852 

425.024 

730.667 

4 

70S.  010 

1218.06 

606.963 

1044.05 

531  .  195 

913.542 

472.271 

812.037 

425.153 

730.833 

5 

708.225 

1218.33 

607.1-18 

1044.29 

531.356 

913.750 

472.415 

812.222 

425.282 

731.000 

6 

708.440 

1218.61 

607.332 

1044.52 

531.517 

913.958 

472.558 

812.407 

425.411 

731.167 

7 

708.656 

1218.89 

007.510 

1044.70 

531.679 

914.167 

472.701 

812.593 

425.540 

731.333 

8 

708.870 

1219.17 

607.701 

1045.00 

531.840 

914.375 

472.845 

812.778 

425.669 

731.500 

9 

709.085 

1219.44 

607.885 

1045.24 

532.001 

914.583 

472.988 

812.963 

425.798 

731.667 

10 

709  305 

1219.72 

008.073 

1045.48 

532.166 

914.792 

473.135 

813.148 

425.930 

731.833 

11 

709.525 

1220.HO 

008  .  202 

1045.71 

532.331 

915.000 

473.281 

813.333 

426.062 

732.000 

12 

709.740 

1220.28 

008.440 

1045.95 

532.492 

915.208 

473.425 

813  519 

426.191 

732.167 

13 

709.955 

1220.50 

008.030 

1046.19 

532.654 

915.417 

47'3.568 

813.704 

426.320 

732.333 

14 

710.161) 

1220.83 

008.814  1016.43 

532.815 

915.625 

473.711 

813.889 

426.450 

732.500 

15 

710.384 

1221.11 

008  999  1046.67 

532.976 

915.833 

473.855 

814.074 

426.579 

732.667 

16 

710  599 

1221.39 

009.183  1046.90 

533.137 

916.042 

473.998 

814.259 

426.708 

732.833 

17 

710.814 

1221.07  009.30711047.14 

533.299 

916.250 

474.142 

814.444 

426.837 

733.000 

18 

711.029 

1221.94 

009.551  1047.38 

533.460 

916.458 

474.285 

814.630 

426.966 

733.167 

19 

711.244 

1222  22 

609.73611047.62 

533.621 

916.667 

474.428 

814.815 

42".  095 

733.333 

20 

711.459 

1222.50  009.920 

1047.86 

533.782 

916.875 

474.572 

815.000 

427  227 

733.500 

21 

711.074 

1222.78610.104 

1048.10 

533.944 

917.083 

474.715 

815.185 

42".  359 

733.667 

22 

711.894 

1223.00010.293 

1048.33 

534.109 

917.292 

474.862 

815.370 

42".  488 

733.833 

23 

712.114 

1223.33  010.481 

1048.57 

534.273 

917.500 

475.008 

815.556 

42".  017 

734.000 

24 

712.331 

1223.01  010.005 

1048.81 

534  435 

917.708 

475.152 

815.741 

42".  746 

734.167 

25 

71:2.544 

1223.89  010.850 

1049.  (5 

534.596 

917.917 

475.295 

815.926 

42".  875 

734.333 

26 

712.759 

1224.17  Oil.  034 

1049.29 

534.  7  o7 

918.125 

475.438 

816.111 

428  004 

734.500 

27 

712.973 

1224.  441011.218 

1049.52 

534.  91  U 

918.333 

475.582 

816.290 

428.133 

734.667 

28 

713.193 

1224.72 

011.407 

1049.76 

535.083 

918.542 

475.728 

810.481 

428.265 

734.833 

29 

713.413 

1225.00 

611.595 

1050.00 

5a5.248 

918.750 

475.875 

816.667 

428.397 

735.000 

30 

713.028 

1225.28 

611.779 

1050.24 

535.410 

918.958 

476.018 

816.852 

428.526 

735.167 

31 

713.843 

1225.50 

611.904 

1050.48 

535.571 

919.167 

476.162 

817.037 

428.655 

735.333 

32 

714.058 

1225.83 

612.148 

1050.71 

535.732 

919.375 

470.305 

817.222 

428  784 

735.500 

33 

714.273 

1226  11 

612.332 

1050.95 

535.893 

919.583 

470.448 

817.407 

428.914 

735.667 

34 

714.493 

1226.39 

612.520 

1051.19 

536.058 

919.792 

470.595 

817.593 

429.045 

735  833 

35 

714  712 

1226.07 

612.709 

1051.43 

536.223 

920.000 

476.742 

817.778 

429.177 

736.000 

36 

714.927 

1226.94 

612.893 

1051.67 

536.384 

920.208 

476.885 

817.963 

429.307 

736.167 

37 

715.142 

1227.22 

613.077 

1051.90 

536  546 

920.417 

477.028 

818.148 

429.436 

736.333 

38 

715.357 

1227.50 

613.262 

1052.14 

536.707 

920.625 

477.172 

818.333 

429.565 

736.500 

39 

715.572 

1227.78 

613  446 

1052.38 

536.868 

920.833 

477.315 

818.519 

429.694 

736.667 

40 

715.792 

1228.06 

613.634 

1052.62 

537.033 

921.042 

477.462 

818.704 

429.826 

736.833 

41 

716.012 

1228.33)613.823 

1052.86 

537.198 

921.250 

477.608 

818.889 

429.958 

737.000 

42 

710.227 

1228.61  614.007 

1053.10 

537.359 

921.458 

477.7-52 

819.074 

430.087 

737.167 

43 

716.441 

1228.89614.191 

1053.33 

537.520 

921.667 

477.895 

819.259 

430.216 

737.333 

44 

716.661 

1229.17614.380 

1053.57 

53  T.  685 

921.875 

478.042 

819.444 

430.348 

737.500 

45 

716.881 

1229.44  614.568 

1053.81 

537.850 

922.083 

478.188 

819.630 

430.480 

737.667 

46 

717.090 

1229.72614.752 

1054.05 

538.011 

922.292 

478.332 

819.815 

430.609 

737.833 

47 

717.311 

1230.00614.937 

1054.  29  1538.173 

922.500 

47'8.475 

820.000 

430.738 

738.000 

48 

717.531 

1230.28 

615.125 

1054.52 

538.338 

922.708 

478.622 

820.185 

430.870 

738.167 

49 

717.750 

1230.56 

615.313 

1054.76 

538.502 

922.917 

478.768 

820.370 

431.002 

738.333 

5O 

717.905  1230.83  015.498 

1055.00  53S.664 

923.125 

478.912 

820.556 

431.131 

7'38.500 

51 

718.180I1231.11  015.082 

1055.24538.825 

923.333 

479.055 

820.741 

431.260 

738.667 

52 

718.400  12.11.39015.870 

1055.48538.900 

923.542 

479.201 

820.926 

431.392 

738.833 

53 

718.020,1231.07016.059 

1055.71  539.155 

923.750 

479.348 

821.111 

431.524 

739.000 

54 

718  83511231.94:616.213 

1055.95  539.310 

923.958 

479.491 

821.296 

431.653 

739.167 

55 

719.050  1232.22610.427 

10:>6.19539.477 

924.167 

479.635 

821.481 

431.782 

739.333 

56 

719.209  1232.50010.610 

1056.43539.642 

924.375 

479.781 

821.067 

431.914 

739.500 

57 

719.489  1232.78616.804 

1056.67539.807 

924.583 

479.928 

821.852 

432.046 

739.667 

58 

719.704  1233.06  616.988  1056.90  539.  968  1924.  792 

480.071 

822.037 

432.175 

739.833 

59 

193 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


740 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

4317.58 

Arc. 

7400.00 

Tan. 

Arc. 
3700.00 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

2158.87 

1439.34 

2466.07 

1  07  9  .  GO  1  <S5u  .  00  i  t>63  .  77'9 

1480.00 

1 

4318.90 

7401.67 

2159.53 

3700.83 

1439.78 

2467.22 

1  07  9.  93  i  1850.  42  864.  043 

1480.33 

2 

4320.21 

7403  33 

2160.19 

3701.67 

1440.22 

2467.78 

1080.26 

1850.83864.307 

1480.07 

3 

4821.58 

7405.00 

2160.84 

3702.50 

1440.66 

2468.33 

1080.59 

1851.  25  864.  570 

1481.00 

4 

4322.85 

7'406.67 

2161.50 

3703.33 

1441.10 

2468.89 

1080.92 

1851.67864.834 

1481.33 

5 

4324.14 

7408.33 

2162.15 

3704.17 

1441.53 

2469.44 

1081.24 

1852.08865.092 

1481.67 

0 

7 

4325.43 
4326  75 

7410.00 
7411.67 

2162.79 
2163.45 

3705.00 
3705.83 

1441.96 
1442.40 

2470.00 
2470.56 

1081.57 
1081.90 

1852.50865.350 
1852.92865.613 

1482.00 
1482.33 

8 

4328.06 

7413  33 

2164.11 

3706.67 

1442.84 

2471.11 

1082.23 

1853.  33  1865.877 

1482.67 

9 

4329.38 

7415.00 

2164.77 

3707  50 

1443.28 

2471.67 

1082.55 

1853.75 

866.141 

1483.00 

10 

4330.70 

7416  67 

2165.43 

3708.33 

1443.71 

2472.22 

1082.88 

1854.17 

866.404 

1483.33 

11 

4331.99 

7418.33 

3166.07 

3709.17 

1444.14 

2472.78 

1083.21 

1854.58 

866.6(52 

1483.67 

12 

4333.28 

7420.00 

2166.72 

3710.00 

1444.57 

2473.33 

1083.53 

1855.00 

866.920 

1484.00 

13 

4334  59 

7421.67 

2167.38 

3710.83 

1445.01 

2473.89 

1083.86 

1855.42 

867.184 

1484.33 

14 

4335.91 

7423.33 

2168.04 

3711.67 

1445.45 

2474.44 

1084.19 

1855.83867.447 

1484.67 

15 

4337.23 

7425.00 

2168.69 

3712.50 

1445.89 

2475.00 

1084.52 

1856.25867.711 

1485.00 

16 

4338.55 

7426.67 

2169.35 

3713.33 

1446.33 

2475  56 

1084.85 

1856.67 

867.975 

1485.33 

17 

4339.87 

7428.33 

2170.01 

3714.17 

1446.77 

2476.11 

1085.18 

1857.08 

868.238 

1485.67 

18 

4341.18 

7430.00 

2170.67 

3715  .  00 

1447.21 

2476.67 

1085.51 

1857.50 

868.502 

1486.00 

19 

4342.47 

7431.67 

2171.32 

3715.83 

1447.64 

2477.22 

1085.83 

1857.92 

868.760 

1486.33 

20 

4343.76 

7433.33 

2171.96 

3716.67 

1448.07 

2477.78 

1086.15 

1858.33 

869.018 

1486.67 

21 

4345.08 

7435.00 

2172.62 

3717.50 

1448.51 

2478.33 

1086.48 

1858.75 

869.281 

1487.00 

22 

4346.40 

7436.67 

2173.28 

3718.33 

1448.95 

2478.89 

1086.81 

1859.17 

869.545 

1487.33 

23 

4347.72 

7438.33 

2173.94 

3719.17 

1449.39 

2479.44 

1087.14 

1859.58 

869.809 

1487.67 

24 

4349.03 

7440.00 

2174.60 

3720.00 

1449.83 

2480.00 

1087.47 

1860.00 

870.072 

1488.00 

25 

4350.35 

7441.67 

2175.26 

3720.81 

1450.27 

2480.56 

1087.80 

1860.42870.336 

1488.33 

26 

4351.67 

7443.33 

2175.91 

3721.67 

1450.71 

2481.11 

1088.13 

1860.83 

870.600 

1488.67 

27 

4352.99 

7445.00 

2176.57 

3722.50 

1451.15 

2481.67 

1088.46 

1861  25 

870.863 

1489.00 

28 

4354.30 

7446.67 

2177.23 

3723.33 

1451.58 

2482.22 

1088.79 

1801.67871.127 

1489.33 

29 

4355.62 

7448.33 

2177  89 

3724.17 

1452.02 

2482.78 

1089.12 

1862.08 

871.391 

1489.67 

3O 

4356.94 

7450.00 

2178.55 

3725.00 

1452.46 

2483.33 

1089.45 

1862.50 

871.654 

1490.00 

31 

4358.26 

7451.67 

2179.21 

3725.83 

1452.90 

2483.89 

1089.78 

1862.  92  ;  871.  918 

1490.33 

32 

4359.58 

7453.33 

2179.87 

3726.67 

1453.34 

2484.44 

1090.11 

1S63.33872.182 

1490.67 

33 

4360.89 

7455.00 

2180.53 

3727.50 

1453.78 

2485.00 

1090.43 

18(53.75872.445 

1491.00 

34 

4362.21 

7456.67 

2181.19 

3728.33 

1454.22 

2485.56 

1090.76 

1  864.  17  !  872.  709 

1491.33 

35 

4363.53 

7458.33 

2181.84 

3729.17 

1454.66 

2486.11 

1091.09 

1864.58872.972 

1491.67 

36 

4364.85 

7460.00 

2182.50 

3730.00 

1455.10 

2486.67 

1091.42 

1865.00873.236 

1492.00 

37 

4366.17 

7461.67 

2183.16 

3730.83 

1455.54 

2487.22 

1091.75 

1865.42873.500 

1492.33 

38 

4367.48 

7463.33 

2183.82 

3731.67 

1455.98 

2487.78 

1092.08 

1865.83  873.763 

1492.67 

39 

4368.80 

7465.00 

2184.48 

3732.50 

1456.42 

2488.33 

1092.41 

1866.25 

874.027 

1493.00 

40 

4370.12 

7466.67 

2185.14 

3733.33 

1456.86 

2488.89 

1092.74 

1866.67 

874.291 

1403.33 

41 

4371.44 

7468.33 

2185.80 

3734.17 

1457.30 

2489.44 

1093.07 

1867.08874.554 

1493.67 

42 

4372.75 

7470.00 

2186.45 

3735.00 

1457.73 

2490.00 

1093.40 

1867.  50  874.  818 

1494.00 

43 

4374.07 

7471.67 

2187.12 

3735.83 

1458.17 

2490.56 

1093.73 

1867.92875.082 

1494.33 

44 

4375.39 

7473.33 

2187.78 

3736.67 

1458.61 

2491.11 

1094.06 

1868.33875.345 

1494.67 

45 

4376.71 

7475.00 

2188.43 

3737.50 

1459.05 

2491.67 

1094.39 

1868.75875.609 

1495.00 

46 

4378.03 

7476.67 

2189.09 

3738.33 

1459.49 

2492.22 

1094.72 

1869.17875.873 

1495.33 

47 

4379.  34 

7478.33 

2189.75 

3739.17 

1459.93 

2492.78 

1095.05 

1869.58876.136 

1495.07 

48 

4380.66 

7480.00 

2190.41 

3740.00 

1460.37 

2493.33 

1095.38 

1870.00876.400 

1496.00 

49 

4381.98 

7481.67 

2191.07 

3740.83 

1460.81 

2493.89 

1095.71 

1870.42876.663 

1496.33 

5O 

4383.30 

7483.33 

2191.73 

3741.67 

1461.25 

2494.44 

1096  04 

1870.83876.927 

1496.67 

51 

4384.61 

7485.00 

2192.39 

3742.50 

1461.69 

2495.00 

i  one.  37 

1871.25877.191 

1407.00 

52 

4385  93 

7486.67 

2193.05 

3743.33 

1462.13 

2495.5(5 

1096.70 

1871.67877.454 

1497.33 

53 

4387.25 

7488.33 

2193  71 

3744.17 

1462.57 

2496.11 

1097  03 

1872.08877.718 

1497.67 

54 

4388.57 

7490.00 

2194.36 

3745.00 

1463.0! 

2496.67 

1097.35 

1872.50877.982 

1498.00 

55 

4389.89 

7491.67 

2195.02 

3745.83 

1463.45 

2497.22 

1097.68 

1872.92878.245 

1498.83 

56 

4391.20 

7493.33 

2195.68 

3746.67 

1468.80 

2497.78 

1098.01 

1873.33878.509 

14  98.  (57 

57 

4392.52 

7495.00 

2196.34 

3747.50 

1464.3-2 

2498.33 

1098.34 

1873.75878.773 

1400  00 

58 
59 

4393.84 
4395.19 

7496.67 
7498.  33 

2197.00 
2197.67 

3748.33 
3749.17 

1464.76 
1465.21 

2498.89 
2499.44 

1098.67 
1099.01 

1  874.  1  7  879.  036  j  1499.  33 
1874.58879.30611499.07 

194 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

74° 
M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

71  9.  U  19  '1233.  33 

617.172 

1057.14 

540.130 

925.000480.215 

822.222 

432.304 

740.000 

O 

720.139  1.233.61 

617.361 

1057.38 

540.294 

925.208480.361 

822.40? 

432.436 

740.1(57 

1 

720.358  .1233.  89 

617.549 

1057.62 

540.459 

925.417480.508 

822.593 

432.568 

740.333 

2 

720.578  1234.17 

617.  788 

1057.86 

540.624 

925.625480.654 

822.778 

488.700 

740.500 

3 

720.798:1234.44 

617.926 

1058.10 

540.789 

925.833480.801 

822.963 

43  J.  832 

740.667 

4 

721.013  1234.72 

618.110 

1058.33 

540.950 

926.042 

480.944 

823.148 

432.961 

740  833 

5 

721.228  1235.00 

61  S.  295 

1058.5? 

541.112 

926.250 

481.088 

823.333 

433.090 

741.000 

6 

7  2  1.  448  1235.  28 

618.483 

1058.81 

541.276 

926.458 

481.234 

823.519 

433.222 

741.167 

7 

721.667  1*35.56 

618.671 

1059.05 

541.441 

926.66? 

481.381 

823.704 

433.  354 

741.333 

8 

721.887 

1235.83 

618.860 

1059.29 

541.606 

926.875 

481.528 

823.889 

433.486 

741.500 

9 

722.107 

1236.11 

619.048 

1059.52 

541.771 

927.083 

481.674 

824.074 

433.618 

741.667 

1O 

722  3221236.39 

619  232  1059.76 

541  932 

927.292 

481.817 

824.259 

433.74? 

741.833 

11 

722.5371236.67 

619.417 

1060.00 

542.093927.500 

481.961 

824.444 

433.876 

742.000 

12 

722.756 

1236.94 

619  605 

1060.24 

542.258927.708 

482.10? 

824.630 

434.008 

742.167 

13 

722.976 

1237.2V 

619.793 

1060.48 

542.  423  927..  91  7 

482.254 

824.815 

434.140 

742.333 

14 

723.196 

1237.50 

619.U82 

1060.71 

542.588928.125 

482.401 

825.000 

434.272 

742.500 

15 

723.416 

1237.78 

620.170 

1060.95 

542.753928.333 

482.547 

825.185 

434.404 

742,66? 

16 

723.635 

1238.06 

620.358 

1061.19 

542.918928.542 

482.694 

825.370 

434.536 

742.833 

17 

723.855 

1238.33 

620.547 

1061.43 

543.083928.750 

482.840 

825.556 

434.668 

743.000 

18 

724.070 

1238.61 

620.731 

1061.67 

543.244 

928.958 

482.984 

825.741 

434.79? 

743.167 

19 

724.285 

1238.89 

620.915 

1061.90 

543.405 

929.167 

483.127 

825.926 

434.926 

743.333 

20 

724.505 

1239.1? 

621.104 

1062.14 

543.570929.375 

483.274 

826.111 

435.058 

743.500 

21 

724.725 

1239.44 

621.292 

1062.38 

543.735929.583 

483.420 

826.296 

435.190 

743.66? 

22 

724.944 

1239.72 

621.481 

1062.62 

543.900929.792 

483.56? 

826.481 

435.322 

743  833 

23 

725.164 

1240.00 

621.669 

1062.86 

544.065  930.000 

483.713 

826.667 

435.454 

744.000 

24 

725.384 

1240.28 

621.857 

1063.10 

544.230930.208 

483.860 

826.852 

435.586 

?44.16? 

25 

725.603 

1240.56 

622.046 

1063.33 

544.394 

930.41? 

484.007 

827.03? 

435.718 

744  333 

26 

725.823 

1240.83 

622  234 

1063.57 

544.559 

930.625 

484.153 

827.222 

435.  84  (J 

744.500 

21 

726.043 

1241.11 

622.422 

1063.81 

544.724 

930.833 

484.300 

827.407 

435.981 

744.60? 

28 

726.263 

1241.39 

622.611 

1064.05 

544.889 

931.042 

484.  44G 

827.593 

436.113 

744.833 

29 

726.482 

1241.67 

622.799 

1064.29 

545.054 

931.250 

484.593 

827  778 

436.245 

745  000 

3O 

726.702 

1241.94 

622.988 

1064.52 

545.219 

931.458 

484.739 

827.963 

436.37? 

745.16? 

31 

726.922 

1242  22 

623.176 

1064.76 

545.384 

931.66? 

484.886 

828.148 

436.501) 

745.333 

32 

727.142 

1242.50 

623.364 

1065.00 

545.548 

931.875 

485.033 

828.333 

436.641 

745.500 

33 

727.361 

1212.78 

623  553 

1065.24 

545.713 

932.083 

485.179 

828.519 

436.773 

745.667 

34 

727.581 

1243.0(5 

623.741 

1065.48 

545.878 

932.292 

485.326 

828  704 

436.905 

745.833 

35 

727.801 

1243  33 

623.929 

1065.71 

546.043 

932.500 

485.472 

828.889 

437.037 

746  000 

36 

728.021 

1243.61 

624.118 

1065.95 

546.208 

932.708 

4S5.619 

829.074 

437.16'J 

746.16? 

37 

728.240 

1243.89 

G24.306 

10(56.19 

546.37'3 

932  917 

485.765 

829.259 

437.301 

746.333 

38 

728.460 

1244.17 

624.495 

1066.43 

546.538 

933.125 

485.912 

829.444 

437.433 

746.500 

39 

728.680 

1244.44 

624.683 

1066.6? 

546.70-2 

933  333 

486  059 

829.630 

437.565 

746.667 

40 

728.899 

1244.72 

624.871 

1066.90 

546.86? 

933.542 

486.205 

829.815 

437.697 

746.833 

41 

729.119 

1245.00 

625.060 

1067.14 

547.032 

933.750 

486  352 

830.000 

437.829 

747.000 

42 

729  339 

1245.28 

625.248 

1067.3h 

547.197 

933.958 

486.498 

830.185 

437.961 

7'47.167 

43 

729.559 

1245.56 

625  .  436 

10(57.62 

547.362 

934.167 

486.645 

830.370 

438.093 

747.333 

44 

729  .  77H 

1245.83 

625.635 

1067.86 

547.527 

934  375 

486.791 

830.556 

438.225 

747.500 

45 

729.998 

1246.11 

625.813 

1068.10 

547.692 

934.583 

486.938 

830  741 

438.356 

747.667 

4C 

730.218 

1246.3! 

626.002 

1068.33 

547.856 

934.792 

487.085 

830.926 

438.488 

747.833 

47 

730.438 

124(5.6? 

626.190 

1068.57 

548.021 

935.000 

487.231 

831.111 

438.620 

748.000 

48 

730.657 

1246.91 

626.378 

1068.81 

548.186 

935.208 

487.378 

831.296 

438.752 

748.167 

49 

730.877 

1247.22 

626.567 

1069.05 

548  351 

935.41? 

487.524 

831.481 

438.884 

748.333 

5O 

731.097 

1247.50 

626.755 

1069.29 

548.516 

935.625 

487.671 

831.66? 

439.016 

7'48  500 

51 

731.317 

1247.78 

626.943 

1069.52 

548  681 

935.833 

487.817 

831.852 

439.148 

748.667 

52 

731.536  1248.  01 

627.132 

10(59.7( 

548.846 

936.042 

487.964 

832.03? 

439.280 

748.833 

53 

731.751511248.33 

627.320 

1070.00 

549.010 

93(5.250 

488.111 

832.222 

439.412 

749.000 

54 

73  1.97  6  j  1248.  61 

627.509 

1070.24 

549.175 

936.458 

488.25? 

832.407 

439.544 

749  167 

55 

732.1%  1248.89 

(  '.27.  (597 

107'0.4S 

549.340 

93<>.667 

488.404 

832.593 

489.676 

749.333 

56 

732.  41  5i  1249.1? 

6-J7.8S5 

1070.71 

549.505 

936.  875 

488.550 

832.778 

439.808 

749  500 

57 

732.  (535  1249.44 

628.074 

1070.95 

549.670 

937.083 

488.69? 

832.963 

439.940 

7'49.667 

58 

732.860  1249.7:. 

628.266 

1071.19 

549.838937.292 

488.84? 

833.148 

440.075 

749.833 

59 

195 


TA35LE   XIY. — ACTUAL   TANGENTS,    ETC. 


75° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tau. 

Arc. 

Tan. 

Arc. 

Tan. 

A  rc. 

0 

43'.)6.53 

7500.00 

2198.35 

3750700 

1465~66 

2500.00 

1099.35 

1875.00 

879.575 

1500.00 

1 

4897.85 

7501.67 

2199.01 

3750.83 

1466.10 

2500.56 

1099.68 

1875.42 

879.839 

1500.3:] 

2 

4399.17 

7503.33 

2199.663751.6; 

1406.54 

2501.11 

1100.01 

1875.83 

880.102 

1500.6; 

3 

4400.49 

7505.00 

2200  32  3752.50 

1466.98 

2501.67 

1100.33 

1876.25 

880.  360 

1501.  Oil 

4 

4401.80 

7506.67 

2200.98 

3753  .  33 

14f,7.42 

2502.22 

1100.66 

1876.67 

880.030 

1501.33 

5 

4408.12 

7508.33 

2201.64 

3754.17 

1467.86 

2502.7!- 

1100.99 

1877.08 

880.893 

1501.67 

6 

4404.44 

7510.00 

2202.30 

3755.00 

1468.30 

2503.3°. 

1101.32 

1877.50 

881.157 

1502.00 

7 

4405.79 

7511.67 

2202.97 

3755.83 

1468.75 

2503.89 

1101.66 

1877.92 

881.426 

1502.33 

8 

4407.13 

7513  33 

2203  65 

3756.67 

1469.20 

2504.44 

1102.00 

1878.33 

881.696 

1502.67 

9 

4408.45 

7515.00 

2204.31 

3757.50 

1469.63 

2505.00 

1102.33 

1878.75 

881.959 

1503.00 

1O 

4409.77 

7516.67 

2204.96 

3758.33 

1470.07 

2505.56 

1102.66 

1879.17 

882.223 

1503.33 

It 

4411  09 

7518  33 

2205.62 

3759.17 

1470.51 

2506.11 

1102.99 

1879.58 

882.487 

1503.67 

12 

4412.40 

7520.00 

2206.28 

3760.00 

1470.95 

2506.67 

1103.31 

1880.00 

882.750 

1504.00 

13 

4413.75 

7521.67 

2206.96 

3760.83 

1471.40 

2507.  2'.' 

1103.65 

1880.42 

883.020 

1504.33 

14 

4415.10 

7523.33 

2207.63 

3761.67 

1471.85 

2507.78 

1103  99 

1880.83 

883.289 

1504.67 

15 

4416.41 

7525.00 

2208.29 

3762.50 

1472.29 

2508.33 

1104.32 

1S81.25 

883.553 

1505.00 

16 

4417.73 

7526.67 

2208.95 

3763  33 

1472.73 

2508.89 

1104.65 

1881.67 

883.816 

1505.33 

17 

4419.05 

7528.33 

2209.61 

3764.17 

1473.17 

2509.44 

1104.98 

1882  08 

884.080 

1505.67 

18 

4420.37 

7530.00 

2210.26 

3765.00 

1473.61 

2510.00 

1105.31 

1882.50 

884.344 

1506.00 

19 

4421.71 

7531.67 

2210.94 

3765.83 

1474.06 

2510.56 

1105.64 

1882.92 

884.613 

1506.3:] 

20 

4423.06 

7533  33 

2211.61 

3766.67 

1474.51 

2511.11 

1105.98 

1883.33 

884.882 

1506.67 

21 

4424.38 

7535.00 

2212.27 

3767.50 

1474.94 

2511.67 

1106  3: 

1883.75 

885.146 

1507.00 

22 

4425.70 

7536.6: 

2212.93 

3768.33 

1475.38 

2512.22 

1106.64 

1884.17 

885.410 

1507.33 

23 

4427.04 

7538.33 

2213.60 

3769.17 

1475.83 

2512.78 

1106.98 

1884.58 

885  679 

1507.67 

24= 

4428.39 

7540.00 

2214.28 

3770.00 

1476.28 

2513.33 

1107.31 

1885.00 

885.948 

1508.00 

25 

4429.71 

7541.67 

2214.93 

3770.83 

1476.72 

2513.  S9 

1107.64 

1885.42 

886.212 

1508.33 

36 

1431.02 

7543.33 

2215.59 

3771.67 

1477.16 

2514.44 

1107.97 

1885.83 

886.476 

1508.67 

37 

4432.37 

7545.00 

2216.27 

3772.50 

1477.61 

2515.00 

1108.31 

1886.25 

886.745 

1509.00 

28 

4433.72 

7546.67 

2216.94 

3773.33 

1478.06 

2515.56 

1108.64 

1886.67 

887.014 

1509.33 

39 

4435.04 

7548.33 

2217.60 

3774.17 

1478.50 

2516.11 

1108.97 

1887.08 

887.278 

1509.67 

30 

4436.35 

7550.00 

°218.26 

3775.  CO 

1478.94 

2516  67 

1109.30 

1887.50 

887.542 

1510.00 

31 

4437.70 

7551.67 

2218.93 

3775.83 

1479.39 

2517.22 

1109  64 

1887.92 

887.811 

1510.33 

33 

4439.05 

7553.33 

2219.00 

3776.67 

1479.83 

2517.78 

1109  98 

1888.33 

888.080 

1510.67 

33 

4440.30 

7555.00 

2220.26 

3777.50 

1480.27 

2518.33 

1110.31 

1888.75 

888.344 

1511.00 

34 

4441.68 

7556.67 

2220.92 

3778.33 

1480.71 

2518.89 

1110.64 

1889.17 

888.608 

1511.33 

35 

4443  03 

7558.33 

2221.60 

3779.17 

1481.16 

2519.44 

1110.97 

1889.58 

888.877 

1511.67 

36 

4444.37 

7560.00 

2222.27 

3180  00 

1481.61 

2520  00 

1111.31 

1890.00 

889.146 

1512.00 

37 

4445  72 

7561.67 

2222.94 

3780.83 

1482.06 

2520.56 

1111.65 

1890.42 

889.416 

1512.33 

38 

4447.07 

7563.33 

2223.  6v! 

3781.67 

1482.51 

2521.11 

1111.98 

1890.83 

889  .  685 

1512.67 

39 

4448  .  39 

7565.00 

2221.27 

3782.50 

1482.95 

2521.67 

1112.31 

1891.25 

889.949 

1513.00 

4O 

4449.70 

7566.67 

2224.93 

3783.33 

1483.39 

2522.  2  J 

1112.64 

1891.67 

890.213 

1513.33 

41 

4451.05 

7568  33 

2225.61 

3784.17 

1483.84 

2522  78 

1112.98 

1892.08 

890.482 

1513.67 

43 

4452  40 

7570.00 

2026.28 

3785.00 

1484  28 

2523.33 

1113.31 

1892.50 

890.751 

1514.00 

43 

4453.71 

7571.67 

2226.94 

3785.83 

1484.72 

2523  89 

1113.64 

1892.92 

891.015 

1514.33 

44 

4455.03 

7573.33 

2227.60 

37'86.67 

1485.16 

2524.44 

1113.97 

1893.33 

891.279 

1514.67 

45 

4456.38 

7575.00 

2228.27 

3787.50 

1485.61 

2525.00 

1114.31 

1893.75 

891  548 

1515.00 

46 

4457.72 

7576.67 

2228.91 

3788  33 

1486.06 

2525.56 

1114.65 

1894.17 

891.817 

1515.33 

47 

44r9.07 

7578.33 

2229.62 

37'89.17 

1486.51 

2526.11 

1114.98 

1894.58 

892.087 

1515.67 

48 

4460.42 

7580.00 

2230.29 

3790.00 

1486.96 

2526.67 

1115.32 

1895.00 

892.356 

1516.00 

49 

4461.76 

7581.67 

2230.96 

3790.83 

1487.41 

2527.22 

1115.60 

1895.42 

892.625 

1516.33 

50 

4463.11 

7583.33 

2231.64 

3791.67 

1487.86 

2527.78 

1115.99 

1895.83 

892.895 

1516.67 

51 

4464.43 

7585.00 

2232.3013792.50 

1488.302528.33 

1116.32 

1896.25 

893.158 

1517.00 

53 

4465  75 

7586.67 

2232  96  13793.  33 

1488.74  2528.89 

1116.65 

1896.67 

893.422 

1517.33 

53 

4467.09 

7588.33 

2233.633794  17 

1489.18  2529.44 

1116.99 

1897.08 

893.691 

1517.67 

54 

446S.44 

7590.00 

2234.  3:)  13795  00 

1489.632530.00 

1117.33 

1897.50 

893.961 

1518.00 

55 

4469  79 

7591.67 

2234.  97  J3795.  as 

1490.082530.56 

1117.66 

1897.92 

894  230 

1518.33 

56 

4471  .  13 

7593.33 

2235.6-)]  3796  67 

1490.532531.11 

1118.00 

1898.33 

894.500 

1518.67 

57 

4472.48 

7595.00 

2286.32  3797  50 

1490.982531.67 

1118.34 

1898.75 

894.769 

1519.00 

58 

4473.83 

7596.67 

2236  99  3798.33 

1491.432532.22 

1118.67 

1899.17 

81)5.038 

1519.33 

59 

4475.17 

7598.33 

2237.67.3799.17 

1491.882532  78 

1119.01 

1899.58 

895.308 

1519.67 

196 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

75° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

733.084 

250.00628.459 

1071.43 

a50.007 

937.500 

488.996 

833.333 

40.209 

"50.000 

O 

733.304 

1250.28  628.647 

1071.67 

a50.172 

937.708 

489.143 

833.519 

40.341 

"50.167 

1 

733.533 

250.56628.835 

1071.90 

050.336  937.917 

489.289 

833.704 

40.473 

50.333 

2 

733.743 

1250.83629.024 

1072.14 

350.501 

938.125 

489.436 

833.889 

40.605 

T>0.500 

3 

733.963 

1251.11  629.212 

1072.38 

>50.000 

138.333 

489.583 

834.074 

440.737 

"50.667 

4 

734.183 

1251.  3'.)  629.  400 

1072.62 

350.831 

W8.542 

489.729 

834.259 

10.869 

'50.833 

5 

734.40:3 

1251.67629.589 

1072.86 

a50.996 

J38.750 

489.876 

834.444 

441.001 

"51.000 

6 

734.627 

1251.94629.781 

1073.10 

351.164 

J38.958 

490.026 

83  1  .  630 

441.136 

'51.167 

7 

734.851 

252.22 

629.974 

1073.  33 

>5  1.333 

)39.107 

490.175834.815 

441.271 

"51.333 

8 

735.071 

252.50 

630.162 

1073.57 

351.498 

J39.375 

490.322 

835.000 

441.403 

"51.500 

9 

735.291 

1252.78 

630.350 

073.81 

551  .663 

939.583 

490.468 

835.185 

441.535 

"51.667 

10 

735.511 

1253.06 

630.539 

074.05 

351.827 

>39.792 

490.615 

835.370 

441.667 

751.833 

11 

7:35.730 

1253.33 

630.727 

074.29 

o51.992 

9IO.UH) 

490.762 

835.556 

441.799 

"52.000 

12 

735.955 

1253.61 

630.920 

074.52 

)52.161 

J  40.  208 

490.911 

835.  7-M 

m.933 

"52.167 

13 

736  179 

1253.89 

631.112 

074.70 

o52.329 

J  40.  417 

491.061 

833.926 

442.068 

"32.333 

14 

736.399 

1254.17 

631.301 

1075.0,i 

>52.49l 

)  40.  025 

491  .208 

836.111 

442.200 

752.500 

15 

736.619 

1254.44 

631.489 

075.24 

552.659 

JIO  833 

191.354 

836.  2-1)6 

442.332 

~52.667 

16 

736.839 

1254.72 

631.677 

1075.48 

>52.824 

J4  1.042 

491.501 

836.481 

442.464 

752.833 

17 

737.058 

1255.00 

631.866 

075.71 

552.989 

J4  1.250 

491.647 

836.067 

442  596 

"53.000 

18 

737.283 

1255.28 

632.058 

1075.95 

553.157 

941.458 

491.  79  T 

836.852 

442.731 

753.167 

19 

737.507 

1255.56 

632.251 

076.19 

553.325 

941.667 

491.947 

837.037 

442.866 

753.333 

20 

737.727 

1255.83 

032.43d 

1076.43 

>53.4i)0 

941.875 

492.093 

837.222 

442.998 

753.500 

21 

737.947 

1256.11 

632.627 

1076.67 

353  .  055 

J  42.  083 

492.240 

837.407 

443.130 

753.667 

22 

738.171 

1256.39 

632.820 

1076.90 

053.824 

J  42.  292 

492.390 

837.51)3 

443.264 

753.833 

23 

738.396 

1256.67 

633.012 

1077.14 

053.992 

942.500 

492.540 

837.778 

443.399 

754.000 

34 

738.616 

1256.94 

633.201 

1077.38 

351.157 

J  42.  708 

492.  6S6 

837.963 

443.531 

754.167 

25 

738.835 

1257.22 

633.3.30 

1077.62 

354.322 

J42.917 

492.833 

838.148 

443.663 

754.333 

26 

739.060 

1257.50 

635.582 

1077.80 

354.490 

J43.125 

492  982 

838.333 

443.798 

754.500 

27 

73  J.  284 

1257.78 

633.774 

1078.10 

35  1.059 

J43.333 

493.132 

838.519 

443.933 

754.667 

28 

739.504 

1258.06 

633.962 

1078.  3  i 

354.824 

943.542 

193.279 

833.704 

444.065 

754.833 

29 

739.724 

1258.33 

634.151 

1078.57 

554.988 

)  13.  750 

493.425 

838.889 

444.197 

755.000 

30 

739.918 

1258.61 

634.313 

1078.81 

555.157 

J43.958 

493.575 

839.074 

444.331 

755.167 

31 

740.173 

1258.89 

634  .  536 

1079.05 

555.325 

914.167 

493.725 

839.259 

444.466 

755.333 

32 

740.393 

1259.17 

634.724 

1079.2U 

555.490 

944.375 

493.871 

839.444 

444.598 

755.500 

33 

740.612 

1259.44 

634.912 

1079.52 

555  .  655 

944.583 

494.018 

839.630 

444.730 

753.667 

34 

740.837 

1  259  .  72 

635.105 

1079.70 

355.823 

144.792 

194.108 

839.815 

444.865 

755.833 

35 

741.061 

1260.00 

035.297 

1080.00 

555.992 

945.000 

494.318 

840.000 

445.000 

756.000 

36 

741.286 

1260.28 

63.3.  49  J 

1080.24 

o56.160 

J45.208 

494.467 

840.185 

445.135 

756.167 

37 

741.510 

1260.56 

035.08: 

1080.48 

)56.329 

945.417 

11)4.617 

840.370 

445.269 

756.333 

38 

741.730 

1260.83 

635.871 

1080.71 

356.494 

945.625 

494.764 

840.556 

445.401 

756.500 

39 

741.951 

1261.11 

636.059 

1080.95 

556.658 

945.833 

494.910 

840.741 

445.  533 

756.667 

4O 

742.174 

1261.3;) 

63<>  252 

1081.19 

J56.827 

946.042 

495.060 

840.  92C 

445.668 

756.833 

41 

742.399 

1261.67 

636.444 

1081.43 

556.995 

946.250 

495.210 

841.111 

445.803 

757.000 

42 

742.619 

1261.91 

636.632 

1081.67 

557.160 

946.458 

495.356 

841.  29( 

445.935 

757.167 

43 

742.838 

1262.22636.821 

1081.90 

557.  325 

946.667 

495.503 

841.481 

446.067 

757.3:33 

44 

743.063 

1262.50  637.013 

1082.14 

557.494 

946.875 

495.653 

841.667 

446.202 

757.501 

45 

743.287 

1262.78 

637.206 

1082.38 

557.002 

947.083 

495.802 

841.852 

446.337 

757.667 

46 

743.512 

1263.06 

037.393 

1082.62 

557.830 

947.29v 

495.95'. 

842.037 

446.471 

757.83: 

47 

743.736 

1263.33 

037.5'.)! 

1082.86 

557.991 

947.500 

196.102 

842.222 

446.606 

758.000 

48 

743.961 

1263.61 

637.783 

1083.10 

558.16; 

947.708 

496.252 

842.407 

446.741 

758.  I0r 

49 

744.18: 

1263.89 

037.970 

1083.33 

558.336 

947.917 

496.401 

842.593 

446.876 

758.3* 

5O 

744  40." 

1264.17 

038.  164 

1083.57 

558.501 

948.125 

496.548 

842.778 

447.008 

758.500 

51 

741.625 

1264.44 

638.352 

1083.81 

558.665 

94S.333 

41)6.695 

842.963 

447.140 

758.60" 

52 

744.849 

1254.72 

638.545 

1084.0: 

558.831 

948.54", 

496.844 

843.148 

447.274 

758.8* 

53 

74:>.  074 

12ii5.00638.73; 

1084.21 

559  00, 

948  75 

496.99- 

843.333 

447.409 

759.000 

54 

745  .  208  1  2(35  .  28  638  .  9-Jl 

1084.5;. 

559.171 

918.958 

497.144 

843.519 

447.544 

759.16' 

55 

745.523  12(55.56  039.12', 

1084  7b 

559.339 

949.167 

497.294 

843.704 

447.679 

759.33- 

56 

745.747  1265.  83  639.31' 

1085.00 

559.508 

949.375 

497.443 

843.889 

447.814 

759.  5(K 

57 

715.972!  1266.  11  639.507 

1085.24 

559.676 

949  583 

497.593 

844.074 

447.949 

759.66 

58 

746.196  1266.39,639.700 

1085.48 

559.845919.792 

497.743 

844.259 

448.  0831759.  83: 

59 

197 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


76° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.       Arc. 

0 

4476.52.7600.00 

2238.34 

3800.00 

149*5.33 

2533.33 

1119.35 

1900.00895.577  1520.00 

1 

4477.84 

7601.67 

2239.00 

3800.83 

1492.  77 

2533.  8U 

1  1  1  9  .  6S 

1  900.  42  895.  84  M  520.  33 

2 

4479.15 

7603.33 

2239  66 

3801.67 

1493.21 

2534.44 

1120.01 

1900.83896.104  1520.67 

3 

4480.50 

7605.00 

2240.33 

3802.50 

1493.65 

2535.00 

1120.34 

1901.25896.374 

1521.00 

4 

4481.85 

7606.67 

2241.01 

3803.33 

1494.10 

2535  .  5U 

11  20  .-68 

1901  671896.643 

1521.33 

5 

4483.19 

7608.33 

2241.683804.17 

1494.55 

2536.11 

1121.02 

1902.08896.913 

1521.67 

6 

4484.54 

7610.00 

2242.  35  '3805.  00 

1495.00 

2536.67 

1121.35 

1902.50 

897.182 

1522.00 

7 

4485.89 

7'611.67 

2243.033805.83 

1495.45 

2537.22 

1121.69 

1902.92 

897.451 

1522.33 

8 

4487.23!  76  13.  33 

2243.703806.67 

1495.90 

2537.78 

1122.03 

1903.33 

897.721 

1522.67 

9 

4488.58J7615.00 

2244.37 

3807.50 

1496.35 

2538.33 

1122.36 

1903.75 

897.990 

15:23.00 

1O 

4489.93 

7616.67 

2245.05 

3808.33 

1496.80 

2538.89 

1122.70 

1904.17 

898.259 

1523.33 

11 

4491.27 

7618.33 

2245.72 

3809.17 

1497.24 

2539.44 

1123.04 

1904.58 

898.529  1523.67 

12 

4492.62 

7620.00 

2246.39 

3810.00 

1497.69 

2540.00 

1123.37 

1905.00 

898.7981524.00 

13 

4493.97 

7621.67 

2247.06 

3810.83 

1498.14 

2540.56 

1123.71 

1905.42:899.068  1524.33 

14 

4495.31 

7623.33 

2247.74J3811.67 

1498.59 

2541  .  1  1 

1  1  24  .  05  !  1  905  83  899  .  337  1  524  .  67 

15 

4496.60 

7625.00 

2248.  41  13812.  50 

1499.04 

2541.67 

1124.38 

1906.25 

899.606  1525  00 

16 

4498.00 

7626.67 

2219.08 

3813.33 

1499.49 

2542.22 

1124.72 

1906.67 

899.876 

1525.33 

17 

4499.35 

7628.33 

2249.76 

3814.17 

1499.94 

2542.78 

1125.06 

1907.08 

900.145 

1525.67 

18 
19 

4500.70 
4502.04 

7630.00 
7631.67 

2250.43 
2251.10 

3815.00 

3815.83 

1500.39 
1500.84 

2543.33 
2543.89 

1125.39 
1125.73 

1907.50 
1907.92 

900.414 
900.684 

1526.00 
1520.33 

20 

4503.39 

7633  33 

2251.78 

3816.67 

1501.28 

2544  44 

1126  07 

1908.33 

900.953 

1526.67 

21 

4504.74 

7635.00 

2252.45 

3817.50 

1501.73 

2545.00 

1126.40 

1  90S.  75 

901.223  1527  00 

22 

4506.08 

7636  67 

2253.12 

3818.33 

1502.18 

2545.56 

1126.74 

1909.17 

901.492 

1527.33 

23 

4507.43 

7638.33 

2253.80 

3819.17 

1502.63 

2546.11 

1127.08 

1909.58 

901.761 

1527  67 

24 

4508.78 

7640.  00 

2254.47 

3820.00 

1503.08 

2546.67 

1127.41 

1910.00 

902.031 

1528.00 

25 

4510.12 

7641.67 

2255.14 

3820.83 

1503.53 

2547.22 

1127.75 

1910.4V 

902.300 

1528.33 

26 

4511.47 

7643.33 

2255.82 

3821.67 

1503.98 

2547.  7M 

1128.09 

1910.83 

902.56'J 

1528.67 

27 

4512.82 

7645.00 

2256.49 

3822.50 

1504.43 

2548.3:3 

1128.42 

1911.2.') 

902  839 

1529.00 

28 

4514.16 

7646.67 

2257.16 

3823.33 

1504.88 

2548.89 

1128.76 

1911.67 

903.108 

1529.33 

29 

4515.54 

7648.33 

2257.85 

3824.17 

1505  33 

2549.44 

11*9.10 

1912.08 

903.383 

1529.67 

3O 

4516.91 

7650.00 

2258.54 

3825.00 

1505.79 

2550.00 

1129.45 

1912.50 

903.658 

1530.00 

31 

4518.26 

7651  .  67 

2259.21 

3825.83 

1506.24 

2550.56 

1129.78 

1912.92 

903.928 

15:30.33 

32 

4519.61 

7653.33 

.'259.89 

3826.67 

1506.69 

2551  .  1  1 

1180.1* 

1913.33 

904.197 

1530.67 

33 

4520.95 

7655.00 

£360.56 

3827.50 

1507.14 

2551.  (37 

1130.46 

1913.75 

904.467 

1531.00 

34 

4522.30 

7656.67 

£>61.23 

3828.33 

1507.59 

2552.22 

1130.79 

1914.17 

904.736 

1531.33 

35 

4523.64 

7658.33 

2:261.91 

3829.17 

1508.04 

2552.78 

1131.13 

1914.58 

905.005 

1531.67 

36 

4524.99 

7660.00 

£262.58 

3830.00 

1508.49 

2553.33 

1131.47 

1915.00 

905.275 

1532  00 

37 

4526.34 

7661.67 

2263.25 

3830.83 

1508.93 

2553.89 

1131.80 

1915.42 

905.544 

1532.33 

38 

4527.68 

7663.33 

£263.92 

3831.67 

1509.38 

2554.44 

1132.14 

1915.83 

905.813 

1532.67 

39 

4529.06 

7665.00 

£264.61 

3832.50 

1509.84 

2555.00 

1132.48 

1916.25 

906.088 

1533.00 

40 

4530.43 

7666.67 

2265.30 

3833.33 

1510.30 

2555.56 

1132.83 

1916.67 

906.364 

1533.33 

41 

4531.78 

7668.33 

2265.97 

3834  17 

1510.75 

2556.11 

1133.16 

1917.08 

906.633 

533.67 

42 

4533.13 

7670.00 

2266.65 

3835.00 

1511.20 

2556.67 

1133.50 

1917.50 

906.902 

1534.00 

43 

4534.47 

7671.67 

2267.32 

3835.83 

1511  65 

2557.22 

1133.84 

1917.92 

907.172 

1534.33 

44 

4535.82 

7673.33 

2267.99 

3836  67 

1512.10 

2557.78 

1134.17 

1918.33 

907.441 

1534.67 

45 

4537.20 

7675.00 

2268.68 

3837.50 

1512.55 

2558.33 

1134.52 

1918.75 

907.716 

1535.00 

46 

4538.57 

7676.67 

2269.37 

3838.33 

1513.01 

£558.89 

1134.86 

1919.17 

907.991 

1535.33 

47 

4539.92 

7678.33 

2270.04 

3839.17 

1513.46 

2559.44 

1135.20 

1919.58 

908.261 

1535.67 

48 

4541.26 

7680  00 

2270.71 

3840.00 

1513.91 

2560.00 

1135.54 

1920.00 

908.530 

1536.00 

49 

4542.61 

7681.67 

2271.39 

3840.83 

1514.36 

2560.56 

1135.87 

1920.42 

908.799 

1536.33 

50 

4543.96 

7683.33 

2272.06 

3841.67 

151  4.  SI 

2561.11 

1136.21 

1920.83 

909.069 

1536.67 

51 

4545.33 

7685.00 

2272.75 

3842.50 

1515.27 

2561.6! 

1136.55 

1921.25 

909.344 

1537.00 

52 

4546.71 

7'686.67 

2273.44 

3843.33 

1515.72 

2562.22 

1136.90 

1921.67 

909.619 

1537.33 

53 

4548.05 

7688.33 

2274.11 

3844.17 

1516.17 

2562.  7H 

1137.23 

1922.  OS 

909.888 

1537.67 

54 

4549.40 

7690.00 

2274.78 

3845.00 

1516.62 

2563.  33 

1137.57 

1922.50 

910  15S 

1538.00 

55 

4550.77 

7691.67 

2275.47 

3845.83 

1517.08 

25(53.89 

1137.91 

1922.92 

910.433 

153S.*3 

56 

4552.15 

7693  33 

2276.16 

3846.67 

1517.54 

2564  44 

11?8.26 

1923.33 

910  70K 

15.-S8.67 

57 

4553  50 

7695.00 

2276.83 

3847.50 

1517.99 

2565.00 

1138.59  1923.75 

910.977 

1539.00 

58 

4554.84 

7696.67 

2277.50 

3818.33 

1518.44 

2565.5(5 

1138.93 

1924.17 

911.247 

1539.33 

59 

4556.22 

7698.33 

2278.19 

3849.17ll5l8.90 

2566.11 

1139.28 

1924.58 

911.522 

1539.67 

198 


TABLE  XIT.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  C 

Lirve. 

Arc. 

9°  Curve. 

1O°  Curve. 

76° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

746.421 

1266.67639.892 

1085.71 

560  013 

950.000 

497  893 

844.444 

448.218 

760.000 

0 

746.641 

1266.94  640.080 

1085.95560.178 

950.208 

498.039 

844.630 

448.350 

760.167 

1 

746.860 

1267.22640.269 

1086.19 

560.343 

950.417 

498.186 

844.815 

448.482 

760.333 

2 

747.085 

1267.50!640  461 

1086.43 

560.511 

950.625 

498.336 

845.000 

448.617 

760.500 

3 

747.309 

1267.78640.654 

1086.67 

560.680 

950.833 

498.485 

845.185 

448.752 

760.667 

4 

747.534 

1268.06640.846 

1086.90 

560.848 

951.042 

498.635 

845.370 

448.887 

760.833 

5 

747.758 

1268.33641.039 

1087.14 

561.016 

951.250 

498.785 

845.556 

449.021 

761.000 

6 

747.988 

1268.  61  1641.231 

1087.38 

561.185 

951.458 

498  935 

845.741 

449.156 

761.167 

7 

748.208 

1268.89641.424 

1087.62 

561.353 

951.667 

499.084 

845.926 

449.291 

761.333 

8 

748.432 

1269.17 

641.616 

1087.86 

561.522 

951.875 

499.234 

846.111 

449.426 

76  1.50C 

9 

748.657 

1269.44 

641.809 

1088.10 

561  .  690 

952.083 

499.384 

846.296 

449.561 

761.667 

10 

748.881 

1269.72 

642.001 

1088.33 

561.859 

952.292 

499.534 

846.481 

449.695 

761.833 

11 

749.106 

1270.00 

642.194 

1088.57 

562.027 

952.500 

499.683 

846.667 

449.830 

762.000 

12 

749.330 

1270.28 

642.386 

1088.81 

562.196 

952.708 

499.833 

846.852 

449.965 

762.167 

13 

749.555 

1270.56 

642.578 

1089.05 

562.364 

952.917 

499.983 

847.037i450.100 

762.333 

14 

749.779 

1270  83642.771 

1089.29 

562.532 

953.125 

500  133 

847.222 

450.235 

762.500 

15 

750.004 

1271.11  642.963 

1089.52 

562.701 

953  333 

500.282 

847.407 

450.370 

762.667 

16 

750.228 

1271.39643.156 

1089.76 

562.869 

953.542 

500.432 

847.593 

450.504 

762.833 

17 

750.453 

1271.67 

643.348 

1090.00 

563.038 

953.750 

500.582 

847.778 

450.639 

763.000 

18 

750.677 

1271.94 

643.541 

1090.24 

563.206 

953.958 

500.73-,' 

847.963 

450.774 

763.167 

19 

750.902 

1272.22 

643.733 

1090.48 

563.375 

954.187 

500.881 

848.148 

450.909 

763.333 

20 

751.126 

1272.  50  1643.  926 

1090.71 

563.543 

954.375 

501  031 

848.333 

451.044 

763.500 

21 

751.351 

1272.78 

644.118 

1090.95 

563  712 

954.583 

501.181 

848.519 

451.178 

763.667 

22 

751.575 

1273.06 

644.311 

1091.19 

563.880 

954.792 

501.331 

848.704 

451.313 

763.833 

23 

751.800 

1273.33 

644.503 

1091.43 

564  .  048 

955.000 

501.48,. 

848.889 

451.448 

764.  000 

24 

752.024 

1273.61 

644.696 

1091.67 

564.217 

955.208 

501.630 

849.074 

451.583 

764.167 

25 

752.249 

1273.89 

644.888 

1091.90 

564.385 

955.417 

501.780 

849.259 

451.718 

764.333 

2G 

752.473 

1274.17 

645.081 

1092.14 

564.554 

955.625 

501.930 

849.444 

451.853 

764.500 

21 

752.69* 

1274.44 

645.273 

1092.38 

564.722 

9.-)5.833 

502.079 

849.630 

451.987 

764.667 

28 

752.927 

1274.72 

645.470 

1092.62 

564.894 

956.042 

502.232 

849  815 

452.125 

764.833 

29 

753.156 

1275.00 

645.666 

1092.86 

565.066 

956.250 

502.385 

8'>0.000 

452.263 

765.000 

30 

753.381 

127'5.28 

645.859 

1093  10 

565.235 

956.458 

502.535 

850.185 

452.398 

765.167 

31 

753.605 

1275.56 

646.051 

1093.33 

565.403 

956.667 

502.685 

850  370 

452132 

765.333 

32 

753.830 

1275.83 

646.244 

1093.57 

565.572 

956  875 

502.835 

850  556 

452.667 

765.5(Hi 

33 

754.054 

1276.11 

646.436 

1093.81 

565.740 

957.083 

502.984 

850.741 

452  >02 

765.667 

34 

754.279 

1276  39 

646.621) 

1094.05 

565.909 

957  292 

503  134 

850.926 

452.937 

765.833 

35 

734.508 

1276  67 

646.821 

1094.29 

566.077 

957.500 

503.284 

851.111 

453.072 

7(5.6.000 

30 

754.728 

1276.94 

647.013 

1094.52 

566  245 

957.708 

503.434 

851.296 

453.206 

766.167 

37 

754.952 

1277.22 

647.206 

1094.76 

566.414 

957.917 

503.583 

851.481 

453.341 

766.333 

38 

755.182 

1277.50 

647.402 

1095.00 

566.586 

958.125 

503.736 

851.667 

453.479 

766.500 

39 

755.411 

1277.78 

647.599 

1095.24 

566.758 

958.333 

503.889 

851.852 

453.617 

766  .  C67 

40 

755.636 

1278.06 

647.792 

1095.48 

566.926 

958.542 

504.039 

852.037 

453.751 

766.833 

41 

755.860 

1278.33 

647.984 

1095.71 

567.095 

958.750 

504.189 

852.222 

453.886 

767.000 

42 

756  0&5 

1278.61 

648.176 

1095.95 

567.263 

958.958 

504.339 

852.407 

454.021 

767.167 

43 

756.309  1278.89 

648.369 

1096.19 

567.432 

959.167 

504.488 

852..  '.93 

454.156 

767.33 

44 

756.538  1279.17 

648.566 

1096.43 

567.604 

959.375 

504.641 

852.77)-' 

454.294 

767.  50( 

45 

756.768 

1279.44 

648.762 

1096.67 

567.776 

959.583 

504.794 

852.963 

454.431 

767.667 

40 

756.992 

1279.72 

648.955 

1096.90 

567.944 

959.792 

504.944 

853.14** 

454.566 

767.833 

47 

757.217 

1280.00 

649.147 

1097  14 

568.113 

960.000 

505.094 

853.883 

454.701 

768.  OCX? 

48 

757.441 

1280.28 

649.339 

1097.38 

568.281 

960.208 

505.244 

853.519 

454.836 

768.167 

49 

757.  606 

1280.56 

649.532 

1097.62 

568.449 

960.417 

505.393 

853.704 

454.971 

768.333 

50 

757.895 

1280.83 

649.729 

1097.8(5 

568  622 

960.625 

505  546 

853.889 

455.108 

768.500 

51 

758.124 

1281.11 

649.925 

1098.10 

568.794 

960.833 

505.699 

854.074 

455.246 

768.667 

52 

758.349 

1281.39 

650.118 

1098.33 

568.9(52 

961.042 

505.849 

854.259 

455.381 

768.833 

53 

758.573 

1281.67 

650  310 

1098  57 

569.130 

961.250 

505.999 

854.444 

455.516 

769.000 

54 

758.803 

1281.94 

650.507 

1098  81 

569.302 

961.458 

506.152 

854.630 

455.  (553 

769.167 

55 

759.032 

1282.22 

650.703 

1099.05 

569.474 

961.  C67 

506.305 

854.815 

455.791 

769.333 

50 

759.256 

1282.50 

(550.896 

1099.29 

569.643 

961.875 

506.454 

855.000 

455.926 

769.500 

57 

759.481 

1282.78 

651.088 

1099.52 

569.811 

962.083 

506.604 

855.185 

456.061 

769  (567 

58 

759.710 

1283.06 

651.285 

1099.76 

569.983 

962.292 

506.757 

855.370 

456.198 

769.833 

59 

199 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


77° 
M. 

1°  Curve. 

2°  Curve. 

3°  C 

Tan. 

urve. 

Arc. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.  |    Arc. 

~~O~ 

45  7.59 

7700.00 

2278.88 

385'i.0( 

151!)  35 

2566.67 

1139.62 

1925.00 

911.797 

1540.00 

1 

4558.  W 

7701.07 

2279.55 

3850.83 

1M0.81 

2567.22  11:39.90 

1925.42 

912  000 

1540.33 

g 

4360.29 

7703.33 

2280.23 

3851  67 

1520  25 

2507.78  1140.29 

1925.83 

912.330 

1540.07 

3 

4501  60 

7705.00 

2280.91 

3852.50 

1520.71 

2508.  33 

1140.04 

1920.25 

912.611 

1541.00 

4 

4503.04 

7700  07 

2281.60 

3853.33 

1521.17 

2508.89 

1140.98 

1920.67 

912.880 

1541.33 

5 

4504.38 

7708.33 

2282.27 

3854.17 

1521.02 

2509.44 

1141.32 

1927.08 

913.155 

1541.07 

6 

4505  .  7'3 

7710.00 

2282.95 

3855.00 

1522.07 

2570.00 

1141.65 

1927.50 

913.425 

1542.00 

7 

4507.10 

7711.67 

2283.64 

3855.83 

1522  52 

2570.56 

1142.00 

1927.92 

913.700 

1542.133 

8 

4508.48 

7713.33 

2284.32 

3856.67 

1522.98 

•2571.11 

1142.34 

1928.33 

913.975 

1542.67 

9 

4509.83 

7715.00 

2285.00 

3857.50 

1523.43 

2571.67 

1142.68 

1928.75 

914.244 

1543.00 

1O 

4571.17 

7716.67 

2285.67 

3858.33 

1523.88 

2572  22 

1143.01 

1929.17 

914.514 

1543.33 

11 

457:2.55 

7718.  as 

2286.30 

3859.17 

1524.34 

257  2.  '78 

1143.30 

1929.58 

914.789 

1543.07 

12 

4573.9-2 

7720.00 

2287.04 

3860.00 

1524.80 

2573.33 

1143.7< 

1930.00 

915.064 

1544.00 

13 

4575  .  30 

7721.67 

2287.73 

3860.83 

1525.26 

2573.89 

1144.05 

1930.42 

015.339 

1544.33 

14 

4570.07 

7723.33 

2288.42 

3801.67 

1525.71 

2574.44 

1144.39 

19:30.83 

915.614 

1544.07 

15 

4578.04 

7725.00 

2289.0:) 

3802.50 

1526.10 

2575.00 

1144.73  1931.25 

915.883 

1545.00 

16 

4579.37 

7726.67 

2289.77 

3863.33 

1526.61 

2575  .  50 

1145.00  1931.07 

916.153 

1545.33 

17 

4580.74 

7728.33 

2290.45 

3804.17 

1527.07 

2570.11 

1145.41  1932.08 

916.428 

1545.67 

18 

4582.1-2 

7730.00 

2291.14 

3805.00 

1527.53 

2576.07 

1145.75  19:32.50 

916.70:3 

1546.00 

19 

4583.49 

7731.67 

2291.83 

3865.83 

1527.99 

2577.22 

1140.09 

1932.92 

1)16.978 

1546.33 

20 

4584.87 

7733.33 

2292.52 

3866.67 

15-28  45 

2577.78 

1146.44 

1933.33 

917.253 

1546.67 

21 

4580.21 

773o.OO 

2293.19 

3867.50 

152S.89 

2578.33 

1146.78 

1933.75 

1)17.52:3 

1547.00 

22 

4587.50 

7736.67 

2293.80 

3808.33 

1529.34 

2578.89 

1147.11 

1934.17 

917.792 

1547.33 

23 

4588  93 

7738.33 

2294.55 

3809.17 

1529.80 

2579.44 

1147.46 

1934.58 

918.007 

1547.67 

24 

4590.31 

7740.00 

J295.24 

38  7'Q.OO 

1530.20 

2580.00 

1147.80 

19-35.00 

918.342 

1548.00 

25 

4591.08 

7741.67 

2295.93 

3870.83 

1530.72 

2580.50 

1148.14 

1935.42 

918.617 

1548.33 

26 

4593.00 

7743.33 

2290.01 

3871.67 

1531.18 

2581.11 

1)48.49 

1935.83 

918.892 

1548.07 

27 

4594.43 

7745.00 

2297.30 

3872.50 

1531.04 

.'581.07 

1148.83 

1936.25 

919.108 

1549.00 

28 

4595.81 

7746.67 

2297.99 

3873.33 

1532.09 

2582.22 

1149.17 

1936.07 

1)19.443 

1549.33 

29 

4597.10 

7748.33 

2298.60 

3874.17 

1532.54 

2582.78 

1149.51 

1937.08 

919.712 

1549.67 

30 

4598  50 

7750.00 

2299.34 

3875.00 

1532.99 

2583.33 

1149.85 

1937.50 

919.981 

1550.00 

31 

4599.88 

7751.67 

2300.02 

3875.83 

1533.45 

2583.89 

1150.19 

1037.92 

920.257 

1550.33 

32 

4601.25 

7753.33 

2300.71 

3876.67 

153:3.91 

2584.44 

1150.54 

1938.33 

1)20.532 

1550.67 

33 

4002.63 

7755.00 

2301.40 

3877.50 

1534.37 

2585.0) 

1150.88 

1938.75 

920.807 

1551.00 

34 

4004.00 

7756.67 

2302.09 

3878.33 

1534.83 

2585.  50 

1151.22 

19:39.17 

921.082 

1551.33 

35 

4605.38 

7758.33 

2302  77 

3879.17 

1535.28 

2580.11 

1151.57 

1939.58 

1)21.357 

1551.67 

30 

4606.75 

7760.00 

J303.40 

3880.00 

535.74 

2580.67 

1151.91 

1940.  OJ 

921.032 

1552.00 

37 

4008.13 

7761.67 

2304.15 

3880.83 

536.20 

2587.2,' 

1152.20 

1940.42 

921.907 

1552.33 

38 

4609.50 

7763.33 

2304.84 

3881.07 

1536.00 

2587.  7S 

1152.60 

1940.83 

922.182 

1552.67 

39 

4010.88 

7765.00 

2305.52 

3882.50 

1537.12 

2588.33 

1152.94 

1941.25 

922.457 

1553.00 

40 

4612.25 

77'66.67 

2306.21 

3883.33 

1537.58 

2588.89 

1153.29 

1941.67 

922.732 

1553.33 

41 

4613.63 

7768.33 

2300.90 

3884.17 

1538.03 

2589.44 

1153.63 

1942.08 

923.008 

1553.67 

42 

4015.00 

7770.00 

2307.59 

3885.00 

1538.49 

2590.00 

1153.97 

1942.50 

.)23.28:3 

1554.00 

43 

4010.38 

7771.67 

2308,27 

3885.83 

1538.95 

2590.50 

1154.32 

1942.92 

923.5f,8 

1554.33 

44 

4617.75 

7773.33 

2308.90 

3880.67 

1539.41 

2591.11 

1154.66 

1943.33 

923.833  1554.  07 

45 

4019.13 

7775.  UO 

2309.05 

3887.50 

539.87 

2591.67 

1155.01 

1943.75 

924.108  1555.00 

46 

4020.50 

7776.67 

2310.34 

3888.33 

1540.33 

2592.22 

1155.35 

1944.17 

924.383 

1555.33 

47 

4621.88 

7778.33 

2311.02 

3889.17 

1540  79 

2592.78 

1155.69 

1944.58 

924.658 

1555  07 

48 

4023.25 

7780.00 

2311.71 

J890.00 

1541.21 

3593.33 

1156.04 

1945.00 

924.933 

1550.00 

49 

4024.63 

7781.07 

2312.40 

3890.83 

1541.70 

2593.89 

1156.38 

1945.42 

925.208 

1550.33 

50 

4626.00 

7783.33 

2313.09 

3891  .  67 

542.16 

2594.44 

1156.73 

1945.83 

025.48-1 

1556.67 

51 

4627.38 

7785.00 

2313.77 

3892.50 

542.62 

25D5.00 

1157.07 

11)40.2:, 

)25.759 

1557.00 

52 

4028.70 

77'86.67 

2314.40 

3893.33 

1543.  OS 

2595.50 

1  57.41 

1940.07 

120.034 

1557.33 

53 

4630.13 

7788.33 

2315.15 

3894.17 

543.54 

2596.11 

1  57.70 

1917.0^ 

J20.309 

557.07 

54 

4631.51 

7790.00 

2315.84 

3895.00 

1543.99 

2596.67 

1    58.10 

11)47.50 

>2ii.584 

ir-58.00 

55 

4032.88 

7791.67 

2316.53 

3895.83 

544.45 

2597.22 

:>8.44 

1  947  .  9  -'  1)20  .  85!)  j  1  .",58  .  33 

56 

4034.20 

7793.33 

2317.21 

3896.67 

544.91 

2ot)7'.7H 

1  58.79 

1948.33  927.  13  ]|  1558.  07 

57 

1035.03 

7795.00 

2317.90 

3897.50 

545.37 

25D8.33 

1  59.13 

11)48.75 

927.  40U  1559.00 

58 

4037.01 

7796.67 

2318.59 

3898.33 

545.83 

2598.89 

159.48 

1919.17 

327.084  155!).:]:] 

59 

4638.38 

7798.33 

2319.28 

3899.17 

546.29 

2599.44 

1159.82 

1919.58 

1)27.  900  11559.  07 

200 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

77° 

Tan.       Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

759.939  1283.33 

651.481 

1100.00 

570.155 

962  500 

506.910 

855.556 

456.336770.000 

0 

700.1641283.61 

651.674 

1100.24 

570.324 

9()2.708 

507.000 

855.741 

456.471  770.167 

1 

760.388  1283.89 

651.  8615 

1100.48 

570.492 

962.917 

507.210 

855.920 

456.606770.333 

2 

700.  01  8  1284.17 

652.063 

1100.71 

570.664 

903.125 

507.362 

856.111 

456.743770.500 

3 

760.847  1284.44 

652.259 

1100.95 

570  836 

963.333 

507.515 

856.296 

456.  88  1  770.  667 

4 

701.072  1284.72 

652.452 

1101.19 

571.005963.542 

507.665 

856.481 

457.016  770.833 

5 

701.290  1285.00 

652.644 

1101.43 

571.173963.750 

507.815 

856.667 

457.151 

771.000 

6 

70  1.  525  '  1285.  28 

652.841 

1101.67 

571.345 

963.958 

507  968 

856.852 

457.288 

771.167 

7 

70  1.  755  !  1285.  50 

653.037 

1101.90 

571.517 

904.167 

508.121 

857.037 

457.426 

771.333 

8 

701.979 

1285.83 

653.230 

1102.14 

571.686 

964.375 

51)8.271 

857.222 

457.561 

771.500 

9 

762.204 

1286.11 

653.422 

1102.38 

571.854 

964.583 

508.420 

857.407 

457.696 

771.667 

10 

702.433 

1286.39 

653.619 

1102.62 

572.026 

964.792 

508  573 

857.593 

157.839 

771.833 

11 

762.002 

1280.07 

653.815 

1102  86 

572.198 

965  000 

508.726 

857.778 

457.971 

772.000 

12 

702.892 

1286.94 

654.012 

1103.10 

572.370 

965.208 

508.879 

857.963 

458.109 

772.167 

13 

703.121 

1287.22 

654.  2t9 

1103.33 

572.542 

965.417 

509.032 

858.148 

458.246 

772.333 

14 

703.345 

1287.50 

654.401 

1103.57 

572.711 

965.625 

509.182 

858.333 

458.381 

772.500 

15 

703.570 

1287.78 

654.593 

1103.81 

572.879 

965.833 

509.332 

858.519 

458.516 

772  .  667 

10 

703.799 

1288.00 

(554.790 

1104.05 

573.051 

966.042 

509.485 

858.704 

458.654 

772.833 

17 

764.028 

1288.33 

654.987 

1104.29 

573.223 

966.250 

509.638 

858.889 

458.791 

773.000 

18 

704.258 

1288.61 

655.183 

1104.52 

573.395 

966.458 

509.790 

859.074 

458.929 

773.167 

19 

764.487 

1288.89 

655.380 

1104.76 

573.567 

966.667 

509.943 

859.259 

459.067 

773.333 

2O 

704.712 

1289.17 

055.572 

1105.00 

573.736 

966.875 

510.093 

859.444 

459.202 

773.500 

21 

764.93(5 

1289.44 

655.765 

1105.24 

573.904 

967.083 

510.243 

859.630 

459.336 

773.667 

22 

705.165 

1289.  7-; 

055.961 

1105.48 

574.076 

967.292 

510.390 

859.815 

459.474 

773.833 

23 

765.395 

1290.00 

656.158 

1105.71 

574.248 

967.500 

510.549 

860.000 

459  612 

774.000 

24 

705.024 

1290.28 

65C.35-J 

1105.95 

574.420 

967.708 

510.702 

860.185 

459.749 

774.167 

25 

705.853 

1290.56 

656.551 

1106.19 

574.592 

967  917 

510.855 

860.370 

459.887 

774.333 

20 

706.082 

1290.83 

056  .  7  48 

1106.43 

574.764 

968.125 

511.0U8 

860.556 

460.025 

774.500 

27 

760.812 

1291.11 

656.944 

1106.67 

574.936 

968.333 

511.101 

860.741 

460.162 

774.667 

28 

700.536 

1291.39 

657.137 

1106.90 

575.105 

968.542 

511.310 

860.926 

460.297 

774.833 

29 

766.761 

1291.67 

657.329 

1107.14 

575.273 

968.750 

511.460 

861  111 

460.432 

775.000 

30 

760.990 

1291.94 

657  .  526 

1107.38 

575.445 

968.958 

511.613 

861.290 

460.570 

775.167 

31 

707.219 

1292.2, 

657.722 

1107.62 

575.617 

969.167 

511.766 

861.481 

460.707 

775.333 

32 

707.449 

1292.50 

657.919 

1107  86 

575.789 

969.375 

511.919 

861.667 

460.845 

775.500 

33 

707.078 

1292.78 

658.115 

1108.10 

575.961 

969.583 

512.072 

861.852 

460.983 

775.667 

34 

707.907 

1293  0(3 

658.312 

1108.33 

576.133 

969.792 

512.225 

862.037 

461.120 

775.833 

35 

768.137 

1293  33 

658.508 

1108.57 

576.305 

970.000 

512.378 

862.222 

461.258 

776.000 

30 

708.306 

1293.61 

658.705 

1108.81 

576.477 

970.208 

512.531 

862.407 

461.396776.167 

37 

768.595 

1293.89 

658.902 

1109.05 

576.649 

970.417 

512.684 

862.593 

461.534776.333 

38 

768.824 

1294.17 

659.098 

1109.29 

576.821 

970.62,-) 

512.837 

862.778 

461.671 

776.500 

39 

769.054 

1294.44 

659.295 

1109.52 

576.994 

970.833 

512.990 

862.963 

461.809 

776  .  667 

4O 

709.283 

1294.72 

659.491 

1109.76 

577.166 

971.042 

513.142 

863.148 

461.947)776.833 

41 

709.512 

1295.00 

659.688 

1110.00 

577.338 

971.250 

513.295 

863.333 

462.084 

777.000 

42 

709.742 

1295.28 

659  .  884 

1110.24 

577.510 

971.458 

513.448 

863  519 

462.222 

77".  167 

43 

769.971 

1295.50 

660.081 

1110.48 

577.682 

9,1.667 

513.601 

863.704 

462.  360  77'".  333 

44 

770.200 

1295.83 

660.277 

1110.71 

577.854 

971.875 

513.754 

863.889 

462.497  77".  500 

45 

770.429 

1296.11 

660.474 

1110.95 

578.026 

972.083 

513.907 

864.074 

462.635  77".  667 

40 

770.659 

1296.3!) 

660.671 

1111.19 

578.198 

972.292 

514.000 

864.259 

4  62.  773  '77".  833 

47 

770.888 

1296.67 

660.867 

1111.43 

578.370 

972.500 

514.213 

864.444 

462  910  778.000 

48 

771.117 

1296.94 

661.064 

1111.67 

578.542 

972.708 

514.366 

864.630 

463.048778.167 

49 

771.347 

1297.22 

661.260 

1111.90 

578.714 

972.917 

514.519 

864.815 

463.186'778.333 

50 

771.576 

1297.50 

661.457;ill2.14 

578.886 

973.125 

514.672 

865.000 

463.323778.500 

51 

771.  805  '1297.  78 

661.653  1112.38 

579^058 

973.333 

514.825 

865.185 

463.461  778.667 

52 

772.034  '1298.06 

0(51.850  1112.62 

579.230 

973.542 

514.978 

865.370 

463.599778.833 

53 

772.264  1298.88 

662.047 

1112.86 

579.402 

973.750 

515.131 

865.556 

463.737779.000 

54 

772.493  1298.61 

662.243 

1113.10 

579.574 

973.958 

515.284 

865.741 

463.874779.167 

55 

772.72^:1298.89 

662.440 

1113.33 

579.746 

974.167 

515.437 

865.926 

464.012779.333 

50 

772.9521299.17 

062.  63C> 

1113  57 

579.918 

974.375 

515.590 

866.111 

464.150779.500 

57 

773.181  1299.44 

662.833  1113.81 

580.090 

974.583 

515.743 

866.296 

464.287779.667 

58 

773.4101299.72 

663.029  1114.05 

580.262974.792 

515.890 

866.481 

464  425779.833 

59 

201 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


78° 

1°  Cnrve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M7 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

2000.00 

Tan. 

Arc. 

Tan.      Arc. 

o 

4639.767800.002319.96 

3900.00 

1546.74 

1160.16 

1950.00 

928.235 

1500.00 

1 

4641.16  7801.672320  60 

3900.83 

1547.21 

2600.50 

1160.51 

1950.42 

928.515 

1560.33 

3 

4012.  56  7803.  33 

2321.37 

3901.07 

1547.68 

2001.11 

1100.87 

1950.83 

928.790 

1500.07 

3 

4043.94  7805.00 

2322.05 

3902.50 

1548.14 

2601.67 

1101.21 

1951.25 

929.071 

1501.00 

4 

4645.31  7806.67 

2322.74 

3903.33 

1548.60 

2602.22 

1161.55 

1951.67 

929.347 

1501.33 

5 

4646.697808.33 

2323.43 

3904.17 

1549.06 

2002.78 

1161.90 

1952.08 

929.622 

1501.07 

6 

4648.067810.00 

0324   12 

3905.00 

1549.51 

2003.33 

1162.24 

1952.50 

929.897 

1502.00 

7 

4649.447811.67 

2324.80 

3905.83 

1549.97 

2603.89 

1162.58 

1952.92 

930.172 

1502.33 

8 

4650.81  7813.33 

2325.49 

3906.67 

1550.43 

2604.44 

1162.93 

1953.33 

930.447 

1562.67 

9 

4652.22 

7815.00 

2326.19 

3907.50 

1550.90 

2605.00 

1163.28 

1953.75 

930.728 

1563.00 

1O 

4653.62 

7816.67 

2326.90 

3908.33 

1551.37 

2G05.56 

1163.63 

1954.17 

931.009 

1563.33 

11 

4655.00 

7818.33 

2327.58 

39U9.17 

1551.83 

2606.11 

1163.97 

1954.58 

931.284 

1563  67 

13 

4656.37 

7820.00 

2328.27 

3910.00 

1552.28 

2006.07 

1164.32 

1955.00 

931.559 

1564.00 

13 

4657.75 

7821.67 

2328.96 

3910.83 

1552.74 

2007.22 

1164.66 

1955.42 

931  .  834 

1564.33 

14 

4659.12 

7823  33 

2329.65 

3911.67 

1553.20 

2607.78 

1165.01 

1955.83 

932.109 

1564.67 

15 

4660.50 

7825.00 

2330.33 

3912.50 

1553.66 

2608.33 

1165.35 

1956.25 

932.384 

1565.00 

16 

4661.87 

7826.67 

2331.02 

3913.33 

1554.12 

2608.89 

1165.69 

1956.07 

932.0591505.33 

17 

4663.28 

7828.33 

2331.72 

3914.17 

1554.59 

•2609.44 

1166.04 

1957.C8 

932.9401565.07 

18 

4004.68 

7830.00 

2332.43 

3915  00 

1555.05 

2610.00 

1166.40 

1957.50 

933.221  1500.00 

19 

4666.06 

7831.67 

2333.11 

3915.83 

1555.51 

•2610.56 

1166.74 

1957.92 

933.496 

1566.33 

30 

4667.43 

7833.33 

2333.80 

3916.67 

1555.97 

2611.11 

1167.08 

1958.33 

933.771 

1566.67 

31 

4008.83 

7835.00 

2334.50 

3917.50 

1550.41 

2611.67 

1107.43 

1  958.  75 

934  05-2 

1567.00 

33 

4070.24 

7836.67 

2335.20 

3918.33 

1550.91 

•2612.22 

1167.79 

1959.17 

934.333 

1507.33 

33 

4071.01 

7838.33 

2335.89 

3919.17 

1557.30 

2612.78 

1168.13 

1959.58 

934.008 

1507.07 

34 

4672.99 

7840.00 

2330.58 

3920.00 

1557.82 

2613.33 

1168.47 

11)00.00 

934.883 

1568.00 

35 

4674.30 

7841  67 

2337.27 

3920  83 

1558.28 

2613.89 

1168.8-2 

1900.4-2 

1)35.158 

1508.33 

36 

4075.74 

7843  33 

2337.95 

3921.67 

1558.?'4 

2014.41 

1169.10 

1900.83 

935.433 

1568.67 

37 

4077.14 

7845.00 

2338.00 

3922.50 

1559.21 

2015.00 

1109.51 

11)01  25 

935.714 

1509.00 

38 

4078.55 

7846.67 

2339.30 

3923.83 

1559.68 

2615.56 

1169.86 

11101.67 

935  995 

1569.33 

39 

4079.92 

7848.33 

2340.05 

3924.17 

1560.13 

2016.11 

1170.21 

1962.08 

936.270 

1509.07 

30 

4681  30 

7850.00 

2340.73 

3925.00 

1560.59 

2616.67 

1170.55 

1902.50 

936.545 

1570.00 

31 

4082.70 

7851.67 

•2341.44 

3925.83 

1501.00 

2617.22 

1170.90 

1902.92 

936.826 

1570.33 

33 

4684.10 

7853.33 

2342.14 

5926.671501.53 

•2617.78 

1171.25 

1903.33 

937.107 

1570.07 

33 

4685.48 

7855.00 

2342  83 

3927.50 

1561.99 

2618.33 

1171.60 

1903.75 

937.382 

1571.00 

34 

4086.85 

7856.67 

2343.51 

3;)28.33 

1562.45 

2618.8'J 

1171  94 

1904.17 

937.057 

1571.33 

35 

4688.26 

7858.33 

2344.21 

:;9.'9.17 

1562.91 

2619.44 

1172.29 

1904.58 

937.938 

1571.67 

36 

4689.60 

7860.00 

2344.92 

;93i).00 

1563.38 

2620.00 

1172.64 

1965.00 

938.219 

1572.00 

37 

4691.06 

7861.67 

2345.62 

3950.83 

1563.85 

2020.56 

1172.99 

1965.42 

938.500 

1572.33 

38 

4692.47 

7863.33 

2346.32 

3911.67 

1564.32 

2621.11 

11T3  34 

1965.83 

938.780 

1572.07 

39 

4093.84 

7865.00 

2347.01 

3932.50 

1504.78 

2621.67 

1173.69 

1966.25 

939.056 

1573.00 

40 

4695.22 

7866.67 

•2347.70 

3933.33 

1565.23 

2622.22 

M74  03 

1966.67 

939.331 

1573.33 

41 

4696.02 

7868.33 

2348.40 

3934.17 

1565  70 

20-22.78 

1174.38 

1967.08 

939.611 

1573.o7 

43 

4098.03 

7870.00 

2349.10 

3935.00 

1500.17 

•2623.33 

1174.73 

1967.50 

939.892 

1574.00 

43 

4699.43 

7871.67 

2349.80 

3935.83 

1566.64 

2623.89 

1175.09 

1967.92 

940.173 

1574.33 

44 

4700.83 

7873.33 

2350.50 

3930.67 

1567.11 

2624.44 

1175.44 

1908.33 

940.454 

1574.07 

45 

4702.21 

7875.00 

2351.19 

3937.50 

1567.56 

2025.00 

1175.78 

1908.75 

940.729 

1575.00 

46 

4703.58 

7876.67 

2351.88 

3938.33 

1568.02 

2625.56 

1176.12 

1969.17 

941.004 

1575.33 

47 

47'04.99 

7878.33 

2352.58 

3939.17 

1568.49 

2620.11 

1176.47 

1969.58 

941.285 

1575.07 

48 

4700.39 

7880.00 

2353.28 

3940.00 

1568.96 

2620.07 

1176.83 

1970.00 

1)41.566 

1576.00 

49 

4707.80 

7881.67 

2353.98 

3940.83 

1569.43 

2027.22 

1177.18 

1970.42 

941.847 

1576.33 

5O 

47'09.20 

7883.33 

2354.69 

3941.67 

1569.89 

2627  78 

1177.53 

1970.83 

942.128 

1576.07 

51 
53 

4710.57 
4711.95 

7885.002355.37 
7886.67.2350.06 

3942.50 
3943.33 

1570.35 
1570.81 

2028.33 

2628.89 

1177.87 
1178.22 

1971.25 
1971.67 

942.4031577.00 
942.6781577.33 

53 

4713.35 

7888.332356.763944.17 

1571.28 

2629.44 

1178.57  1972.08 

942.959  1577.07 

54 

4714.70 

7890.002357.463945  00 

1571.75 

2030.00 

1178.92 

1972.50 

943.239  1578.00 

55 

4716.16 

789  1.67  12358.  17  3945.  83 

157-2.22 

•2030.50 

1179.27 

1972.9-2 

943.520  1578.33 

56 

4717.56 

7893.332358.873946.67 

1572.68 

•2031  .  1  1 

li;9.  62 

1973.33 

943.801  1578.67 

57 

4718.97 

7895.002359.573947.50 

1573.15 

2031.67 

1179.97 

1973.75 

944.082  1571).  00 

58 

4720.37 

7'890.07,'2300.273948.33 

1573.62 

•203-2.22 

1180.32 

1974.17 

944.363  1579.33 

59 

4721.78 

7898.33,2360  973949.17 

1574.09 

2632.78 

1180.67 

1974  58 

944.644  1579.07 

202 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

78° 

Tan. 

Arc. 

Tan. 

603.220 

Arc. 

nir.29 

Tan.   1   Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

778.  wii 

1300.00 

580.434975.000 

516.048 

860  667 

464.563 

780.000 

O 

773.874  18UO.  28  6C3.  42? 

1114.52 

580.610 

975.208 

516.205 

860.  852 

464.703 

780.167 

1 

74.1U8 

1300.50 

663.627 

1114.70 

580.785 

975.417 

516.361 

867.037 

464.844 

780.333 

2 

74.337 

1300.83 

003.824 

1115.00 

580.957 

975.625 

516.514 

867.222 

464.981 

780.500 

3 

74.50(5 

1301.11 

004.020 

1115.2-1 

581.129 

975.833 

516.667 

867.407 

465.119 

780.067 

4 

74.795 

1301.39 

004.217 

1115.48 

581.301 

976.042 

516.820 

867.593 

465.257 

780.833 

5 

75.025 

1301.07 

004.414 

1115.71 

581.473 

976.250 

516.972 

867.778 

465.394 

781.000 

6 

75.254 

1301.94 

004.610 

1115.95 

581.645 

976.458 

517.125 

807.963 

405.532 

781.167 

7 

75.483 

1302.22 

604.807 

1116.19 

581.817 

976.067 

517.278 

868.148 

405.670 

781.333 

8 

775.717 

1302.50 

605.007 

1116.43 

581.993 

976.875 

517.435 

808.333 

465.810 

781.500 

9 

775.951 

1302.78 

665.208 

1116.67 

582  169 

977  083 

517.591 

868.519 

465.951 

781.667 

10 

770.181 

1303.00 

005.405 

1116.90 

582.  341 

977.292 

517.744 

868.704 

466.089 

781.833 

11 

776.410 

1303.33 

005.0'Jl 

1117.14 

582.513 

977.500 

517.897 

868.889 

466.220 

782.000 

12 

70.639 

1303.01 

065.798 

1117.38 

582.685 

977.708 

518.049 

869.074 

466.364 

782.167 

13 

76.809 

1303.89 

005.994 

1117.02 

582.857 

977.917 

518.202 

869.259 

466.502 

782.333 

14 

77.098 

1304.17 

000.191 

1117.80 

583.029 

978.125 

518.355 

809.444 

466.639 

782.500 

15 

77.887 

1304.44 

600.387 

1118.10 

583.201 

978.333 

518.508 

869.630 

406.777 

782  667 

16 

77.501 

1304.72 

600.588 

1118.33 

583.370 

978.542 

518.664 

869.815 

466.918 

782.833 

17 

777.795 

1305.00 

006  .  789 

1118.57 

583.552 

978.750 

518.821 

870.000 

467.058 

783.000 

18 

778.025 

1305.28 

600.985 

1118.81 

583.724 

978.958 

518.974 

870.185 

467.196 

783.167 

19 

778.254 

1305.56 

667.182 

1119.05 

583.890 

979.167 

519.126 

870.370 

467.334 

783.333 

20 

778.  48«  11305.  83 

067.382 

1119.29 

584.072 

979.375 

519.283 

870.556 

467.474 

783.500 

21 

778.1*2 

1300.11 

667.583 

1119.52 

584.247 

979.583 

519.439 

870.741 

467.615 

783.667 

22 

778.951 

1300.39 

067.780 

1119.70 

584.419 

979.792 

519.592 

870.926 

467.752 

783.833 

23 

779  181 

1300.07 

667.970 

1120.0U 

584.591 

980.000 

519.745 

871.111 

467.890 

784.000 

24 

779.410 

1306.94 

008.173 

1120.24 

584.763 

980.208 

519  898 

871.296 

468.028 

784  167 

25 

779.039 

1307.22 

668.369 

1120.48 

584.935 

980.417 

520.050 

871.481 

468.105 

784.333 

26 

779.873 

1307.50 

668  .  570 

1120.71 

585.111 

980.625 

520.207 

871.607 

468.300 

784.500 

27 

780.107 

1307.78 

008.771 

1120.95 

585.287 

980.83;} 

520.  30S 

871.852 

408.447 

784.667 

28 

780.337 

1308.00 

008.967 

1121.19 

.185.459 

981.042 

520.516 

872.037 

408.584 

784.833 

29 

780.560 

1308.33 

669.164 

1121.43 

585.631 

981.250 

520.669 

872.222 

468.722 

785.000 

30 

780.800 

1308.61 

(J69.365 

1121.67 

585.806 

981.458 

520.825 

872.407 

468.862 

785.167 

31 

781.084 

1308.89 

609.565 

1121.90 

585.982 

981.607 

520.981 

872.593 

469.003 

785.333 

32 

781.208 

1309.17 

009.702 

1122.14 

586.154 

981.875 

521.134 

872.778 

409.141 

785.500 

33 

781.493 

1309.44 

009.958 

1122.38 

586.320 

982.083 

521.287 

872.903 

409.278 

785.i>67 

34 

781.727 

1309.72 

070.159 

1122.62 

580.502 

982.29* 

521.443 

873.148 

409.419 

785.833 

35 

781.961 

1310.00 

070.300 

1122.80 

586.677 

982.500 

521.599 

873.333 

409.559 

786.000!  36 

782.195 

1310.28 

070.500 

1123.10 

586.853 

982.708 

521.755 

873.519 

469.700 

786.167 

37 

782.429 

1310.56 

070.701 

1123.33 

587.028 

982.917 

521.911 

873.704 

469.841 

786.333 

38 

782.  058  j  13  10.  83 

670.958 

1123.57 

587.200 

983.125 

522.064 

873.889 

409.978 

786.500 

39 

782.887 

1311.11 

671.154 

1123.81 

587.372 

983.333 

522.217 

874.074 

470.116 

786.667 

40 

783.  122'  131  1.39 

671.355 

1124.05 

587.548 

983.542 

522.373 

874.259 

470.257 

786.  833  !  41 

783.350 

1311.67 

671.555 

1124.29 

587.724 

983.750 

522.529 

874.444 

470.397 

787.000  42 

783.590 

1311.94 

671.756 

1124.52 

587.899 

983  958 

522.686 

874.030 

470.538 

787.107:43 

783.824  1312.22 

671.957 

1124.76 

588.075 

984.107 

522.842 

874.815 

470.678 

787.333'  44 

784.053 

1312.50 

672.153 

1125.00 

588.247 

984.375 

522.995 

875.000 

470.810 

787.500:  45 

784.282 

1312.78 

672.350 

1125.24 

588.419 

984.583 

523.148 

875.185 

470.954 

787.607  46 

784.510 

1313.00 

67'2.550 

1125.48 

58S.595 

984.792 

.323.304 

875.37X) 

471.094 

787.833  47 

784.750 

1313.33 

672.751 

1125.71 

588.770 

985.000 

523.460 

875.550 

471.235 

7'88.000  48 

784.984 

1313.61 

072.952 

1125.95 

588.946 

985.208 

523.016 

875.741 

471.375 

788.167 

49 

785.219 

1313.89 

673.152 

1126.19 

589.121 

985.417 

523.772 

875.926 

471.516 

788.333 

5O 

785.448 

1314.17 

073.349 

1126.43 

589.293 

985.625 

523.925 

876.111 

471.053 

788.500  51 

785.077 

1314.44 

073.540 

1126.67 

589.465 

985.833 

524.  078!  870.  296 

471.791 

788.007  52 

785.911 

1314.72673.740 

1126.90 

589.641 

986.042 

524.234 

876.481 

471.9^-- 

788.833  53 

780.145!  1315.  00  !  673.  947 

1127.14 

589.817 

986.250 

524.390 

876.007 

472.072 

789.000  54 

786.379  131  5.  28674.148 

1127.38 

589.992 

980.458 

524.546 

876.852 

472.213 

789.107  55 

786.613 

1315.  50:674.  348 

1127.62 

590.168 

986.067 

524.703 

877.037 

472.353 

789.333  50 

786.847 

1315.83:674.549 

1127.80 

590.344 

986.875 

524.859 

877.222 

472.494 

789.500  57 

787.08','  1316.  11  '674.  750 

1128.10 

590.519 

987.083 

525.015 

877.407 

472.034 

789.007  58 

787.  31611316.  39'674.  950 

1128.33590.095 

987.292 

525.171 

877.593 

472.775 

789.833  59 

203 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


79° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan.       Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

4723.18 

7900.00 

2361.683950.00 

1574.56 

2633.33 

1181.02 

1975.00 

944.924 

1580.00 

1 

4724.58 

7901.67 

2362.383950.83 

1575.02 

2633.  89 

1181.37 

1975.42 

945.205 

1580.33 

3 

4725.99 

7903.33 

2363.083951.67 

1575.49 

2634.44 

1181  73 

1975.83 

945.486 

1580.67 

3 

4727.3t 

7905.00 

2363.773952.51 

1575.95 

2635.00 

11S2.01 

1976.25 

945.761 

1581.00 

4 

4728.7'! 

7906.67 

2364.463953.33 

1576.41 

2635.50 

1182.41 

1976.67 

946.036 

1581.33 

5 

4730.14 

7908.33 

2365.163954.17 

1576.88 

2636.11 

1182.76 

1977.0;* 

946.311 

1581.67 

6 

4731.51 

7910.00 

2365.863955.00 

1577.34 

2636.67 

1183.12 

11)77.50 

946.598 

1582.00 

7 

4~.5W.tto 

7911.67 

2366.563955.83 

1577.81 

2637.22 

1183.47 

1977.92 

946.879 

1582.33 

8 

473  L  35 

7913.33 

2367.263956.67 

1578.28 

2637.78 

1183.82 

1978.33 

947.161 

1582.67 

9 

4735.76 

7915.00 

2367.963957.50 

1578.75 

2638.33 

1184.17 

1978.75 

947.441 

1583.00 

10 

4737.16 

7916.67 

2368.673958.33 

1579.22 

2638.89 

1184.52 

1979.17 

947.721 

1583.33 

11 

4738.56 

7918.33 

2369.373959.17 

1579.68 

2639.44 

1184.87 

1979.5S 

948.002 

1583.67 

13 

4739.97 

7920.00 

2370.073960.00 

1580.15 

2640.00 

1185  22 

1980.00 

948.28-3 

1584.00 

13 

4741.37 

7921.67 

2370.773960.83 

1580.62 

2640.56 

1185.57 

1980.42 

948.564 

1584.33 

14 

4742.  ',8 

7923.33 

2371.473961.67 

1581.09 

2641.11 

1185.92 

1980.83 

948.845 

1584.67 

15 

4744.18 

7925.00 

2312.183962.50 

1581.56 

2641.67 

1186.2: 

1981.25 

949.126 

1585.00 

16 

4745.58 

7926.67 

2372.8831)63.33 

1582.02 

2642.22 

1186.63 

1981.67 

949.400 

1585.33 

17 

4746.99 

7928.33 

2373.583964.17 

1582.49 

2642.78 

1186.9S 

1982.0s 

949.  6S7 

1585.67 

18 

4748.39 

7930.00 

2374.  28  3965.  OJ 

1582.96 

2643.33 

1187.33 

1982.50 

949.968 

1586.00 

19 

4749.79 

7931.67 

2374.983965.83 

1583.43 

2643.89 

1187.68 

1982.92 

950.249 

1586.33 

20 

4751.20 

7933.33 

2375.693966.67 

1583.90 

2644.44 

1188.03 

1983.3:^ 

950.530 

1586.67 

31 

4752.60 

7935.00 

2376.393967.50 

1584.36 

2645.00 

1188.38 

1983.75 

1)50.811 

1587.00 

33 

4754.01 

7936.67 

2377.  09  3968.  33 

1584.83 

2645.56 

1188.73 

1984.17 

951.091 

1587.33 

33 

4755.44 

7938.33 

2377.81  3969.17 

1585.31 

2646.11 

1189.09 

1984.58 

951.378 

1587.67 

34 

4756.87 

1910.00 

2378.523970.00 

1585.79 

2646.67 

1189.45 

1985.00 

951.665 

1588.00 

35 

4758.21 

7941.67 

2379.223970.83 

1586.25 

2647.22 

1189.80 

1985.42 

951.945 

1588.33 

36 

4759.68 

i  9  43.  33 

2379.933971.67 

1586.72 

2647.78 

1190.15 

19S5.83 

952.226 

1588.67 

37 

4761.08 

7945.00 

2380.633972.50 

1587.19 

2648.33 

1190.50 

1986.25 

952.507 

1589.00 

38 

4762  49 

7946.67 

2381.333973.33 

1587.66 

2648.89 

1190.85 

19S6.67 

952.788 

1589.33 

39 

4763.89 

7948.33 

2382.033974.17 

1588.13 

2649.44 

1191.20 

1987.08 

953.069 

1589.67 

30 

4765.29 

7950.00 

2382.733975.00 

1588.59 

2650.00 

1191.55 

1987.50 

953.350 

1590.00 

31 

4766.70 

7951.67 

2383.443975.83 

1589.06 

2650.56 

1191.90 

1987.92 

953.630 

1590.33 

33 

4768.10 

7953.33 

2384.143976.67 

1589.53 

2651.11 

1192.26 

1988.33 

953.911 

1590.67 

33 

4769.53 

7955.00 

2384.853977.50 

1590.01 

2651.67 

1192.61 

1988.75 

954.198 

1591.00 

34 

4770.96 

7956.67 

2385.573978.33 

1590.49 

2652.22 

1192.97 

1989.17 

954.484 

1591.33 

35 

4772.37 

7958.33 

2386.273979.17 

1590.95 

2652.78 

1193.32 

1989.58 

954.765 

1591.67 

36 

4773.77 

7960.00 

23S6.973980.00 

1591.42 

2653.33 

1193.67 

1990.00 

955  046 

1592.00 

37 

4775.18 

7961.67 

2387.683980.83 

1591.89 

2653.89 

1194.03 

191)0.42 

955.327 

1592.33 

38 

4776  58 

7963.33 

2383.383981.67 

1592.36 

2654.44 

1194.38 

1990.83 

955.608 

1592.67 

39 

4777.98 

7965.00 

2339.  OS  3982.50 

1592.83 

2655.00 

1194.73 

1991.25 

955.889 

1593.00 

40 

4779.39 

7966.67 

2389.783983.33 

1593.29 

2655.56 

1195.08 

1991.67 

956.169 

1593.33 

41 

4780.82 

7968.33 

2390  5u  3984.  17 

1593.77 

2656.11 

1195.44 

1992.08 

956.456 

1593.67 

43 

4782.25 

7970.00 

2391.21   5985.00 

1594.25 

2656.67 

1195.79 

1992.50 

956.743 

1594.00 

43 

4783.66 

;9M.67 

239  1.92  3  JS5.  83 

1594.72 

2657.22 

1196.15 

1992.92 

957.023 

1594.33 

44 

4785.06 

7973.33 

2392.623JS6.67 

1595.18 

2657.78 

1196.50 

1993.33 

957.304 

1594.67 

45 

4786.49 

7975.00 

2393.333987.50 

1595.66:2658.33 

1196.85 

1993.75 

957.591 

1595.00 

46 

4787  .  92 

J  976.  67 

2394.053988.33 

1596.  14  :  2658.  89 

1197.21 

1994.17 

i)57  .  877 

1595.33 

47 

4789.33 

7978.33 

2394.753989.17 

1596.61  2659.44 

1197.56 

1994.58 

958.158 

1595.67 

48 

4790.73 

7980.00 

2395.453990.00 

1597.082660.00 

1197.92 

1995.00 

958.439 

1596.00 

49 

4792.14 

7981.67 

2396.163990.83 

1597.542660.56 

1198.27 

1995.42 

958.720 

1596.33 

50 

4793  54 

7933.33 

2396.863991.67 

1598.01 

2661.11 

1198.62 

1995.83 

959.001 

1596.67 

51 

4794.97 

7985.00 

2397.573992.50 

1598.49 

2661.67 

1198.98 

1996.25 

959.287 

1597.00 

53 

4796.40 

7986.67 

2398.293993.33 

1598.97 

2662.22 

1199.33 

1996.67 

959.574 

1597.33 

53 

4797.81 

7988.33 

2398.91)3994.17 

1599.43 

2662.78 

1199.68 

1997.08 

959.855 

1597.67 

54 

47'.i9.21 

7990.00 

2399.693995.00 

1599.90 

2663.33 

1200.04 

1997.50 

)60.136 

1598.00 

55 

1800.64 

7991  .  67 

2400.41  8995.83 

1600.38 

2663.89 

1200.39 

1997.92 

%0.422 

1598.33 

56 

4802  OS 

7993.  3  i 

2401.133996.67 

1600.86 

2664.44 

1200.75 

1998.33 

960.709 

159S.67 

57 

4S03.48 

7995.00 

2401.83391)7.50 

1601.33 

2(565.00 

1201.10 

1998.75 

%0.990 

1599.00 

58 

4804.88 

7996.67 

2402.533998.33 

1601.79 

2605.56 

1201.45 

1999.17 

K5  1.270 

1599.33 

59 

4806.32 

7998.33 

2403.25:3999.17 

1602.  2712666.  Ill  1201.  81 

1999.58 

961.557 

1599.67 

204 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

79° 

Tan. 

Arc. 

Tan. 
675  .  1  51 

Arc. 

Tan. 

Arc. 
987.500 

Tan. 
525.327 

Arc. 

S77.778 

Tan. 

Arc. 

790.000 

^iT 

787.550 

1310.67 

1128.57 

590.870 

472.916 

o 

787.784 

1316.94 

675.352 

1128.81 

591.046 

987.708 

525.483 

877.963 

473.056 

790.167 

i 

788.018 

1317.22 

675.552 

1129.05 

591.222 

987.917 

525.639 

878.148 

473.197 

790.333 

2 

788.24? 

1317.50 

675.749 

1129.29 

591.394 

988.125 

525.792 

878.333 

473.334 

790.500 

3 

788.476 

1317.78 

675.945 

1129.52 

591.566 

988.333 

525.945 

878.519 

473.472 

790.667 

4 

788.710 

1318.06 

676.146 

1129.76 

591.741 

988.542 

526.101 

878.704 

473.613 

790.833 

5 

788.944 

1318.33 

676.347 

1130.0J 

591.917 

988.750 

526.258 

878.889 

473.753 

791.000 

6 

789.179 

1318.61 

676.547 

1130.24 

592.092 

988.958 

526.414 

879.074 

473.894 

791.167 

7 

789.413 

1318.89 

676.  74S 

1130.48 

592.268 

989.167 

526.570 

879.259 

474.034 

791.333 

8 

789.647 

1319.17 

076.949 

1130.71 

592.444 

989.375 

526.726 

879.444 

474.175 

791.500 

9 

789.881 

1319.44 

677.149 

1130.95 

592.619 

989.583 

526.882 

879.630 

474.315 

791.667 

1O 

790.115 

1319.72 

677.350 

1131.19 

592.795 

989.792 

527.038 

879.815 

474.456 

791.833 

11 

790.849 

1320.00 

677.551 

1131.43 

592.971 

990.000 

527.194 

880.000 

474.596 

792.000 

13 

790.583  1320.  28 

677.751 

1131.67 

593.146 

990.208 

527.350 

880.185 

474.7*7 

792.167 

13 

790.817 

1320.56 

677.952 

1131.90 

593.322 

990.417 

527.507 

880.370 

474.878 

792.333 

14 

791.051 

1320.83 

678.153 

1132.14 

593.497 

990.625 

527.663 

880.556 

475.018 

792.500 

15 

791.285 

1321.11 

678.353 

1132.38 

593.673 

990.833 

527.819 

880.741 

475.159 

792.667 

16 

791.519 

1321.39 

678.554 

1132.62 

593.849 

991.042 

527.975 

880.926 

475.29i> 

792.833 

17 

791.753 

1321  .67 

678.755 

1132.86 

594.024 

991.250 

528.131 

881.111 

475.440 

793.000 

18 

791.987 

1321.94 

678.955 

1133.10 

594.200 

991.458 

528.287 

881.296 

475.580 

793.167 

19 

79-3.221 

1322.22 

679.156 

1133.33 

594.375 

991.667 

528  443 

881.481 

475.721 

793  333 

30 

792.455 

1322.50 

679.357 

1133.57 

594.551 

991.875 

528.599 

881.  6071475.  861 

793.500 

31 

792.  G90 

1322.78 

679.557 

1133.81 

594.727 

992.083 

528.756 

881.852 

476.002 

793.66; 

33 

792.928 

1323.06 

679.762 

1134.05 

594.906 

992.292 

528.915 

882.037 

476.145 

793.833 

33 

793.167 

1323.33 

679.967 

1134.29 

595.085 

992.500 

529.074 

882.222 

476.289 

794.000 

34 

793.401 

1323.61 

680.167 

1134  52 

595.261 

992.708 

529.230 

882.407 

476.429 

794.167 

25 

793.635 

1323.89 

680.368 

1134.76 

595.436 

992.917 

529.387 

882.593 

476  570 

794.333 

36 

793.869 

1324.17 

680.569 

1135.00 

595.612 

993.125 

529.543 

882.778 

476.711 

794.500 

37 

791.103 

1324.44 

680.769 

1135.24 

595.787 

993.333 

529.699 

882.963 

476.851 

794.667 

38 

794.338 

1324.72 

680.970 

1135.48 

595.963 

993.542 

529.855 

883.148 

476.992 

794.833 

39 

794.572 

1325.00 

681.173 

1135.71 

596.139 

993.750 

530.011 

8S3.333 

477.132 

795.000 

30 

794.806 

1325.28 

681.371 

1135.95 

596.314 

993.958 

530.167 

883.519 

47".  273 

795.167 

31 

795.040 

1325.56 

681.572 

1136.19 

596.490 

994.167 

530.323 

883.704 

47".  4  13 

795.333 

33 

795.279 

1325.83 

681.777 

1136.43 

596.669 

994.375 

530.483 

883.889 

47".  557 

795.500 

33 

795.517 

1326.11 

681.982 

1136.67 

596.848 

994.583 

530.642 

884.074 

47".  700 

795.667 

34 

795.752 

1326.39 

682.182 

1136.90 

597.024 

994.792 

530.798 

884.259 

47".  841 

795,833 

35 

795.986 

1326.67 

682.383 

1137.14 

597.200 

995.000 

530.954 

884.444 

4  7".  981 

796.000 

36 

796.220 

1326.94 

682.584 

1137.38 

597.375 

995.208 

531.110 

884.630 

478.122 

796.167 

37 

796.454 

1327.22 

682.784 

1137.62 

597.551 

995.417 

531.266 

884.815 

478.262 

796.333 

38 

796.688 

1327.50 

682.985 

1137.86 

597.726 

995.625 

531.423 

885.000 

478.403 

796.500 

39 

796  .  922 

1327.78 

683.185 

1138.10 

597.902 

995.833 

531.579 

885.185 

478.543 

796.667 

4O 

797.161 

1328.06 

683.390 

1138.33 

598.081 

996.042 

531.738 

885.370 

478  687 

796.833 

41 

797.400 

1328.33 

683.595 

1138.57 

598.260 

996.250 

531.897 

885.556 

478.830 

797.000 

43 

797.634 

1328.61 

683.796 

1138.81 

598.436 

996.458 

532.053 

885.741 

478.971 

797.167 

43 

797.  868  '1328.  89 

683.996 

1139.05 

598.612 

996.667 

532.210 

885.926 

479.111 

797.333 

44 

798.1  0(H329.  17 

684.201 

1139.29 

598.791 

996.875 

532.369 

886.111 

479.255 

797.500 

45 

798.345  1329.44 

684.406 

1139.52 

598.970 

997.083 

532.528 

886.296 

47'9.398 

;  97.  667 

46 

798.57<);1329.7'2 

684.606 

1139.76 

599.146 

997.292 

532.684 

886.481 

479.539 

797.833 

47 

798.813 

1330.00 

684.8071140.00 

599.321 

997.500 

532.841 

886.667 

479.679 

798.000 

48 

799.048 

1330.28 

685.008 

1140.24 

599.497 

997.708 

532.997 

886.852 

479.820 

798/167 

49 

799.282 

1330.56 

685.208 

1140.48 

599.672 

997.917 

533.153 

887.037 

479.960 

798.333 

5O 

799.520 

1330.83 

685.413  1140  71 

599.852 

998.125 

533.312 

887.222 

480.104 

798.500 

51 

799.759 

1331.11 

<5S5.(>18!1140.95 

600.031 

998.333 

533.471 

887.407 

480.247 

79S.667 

53 

799.993 

1331.39 

(K).  819  1141.19 

600.206 

998.542 

533.628 

887.  593  480.  38S 

798.833 

53 

800  22; 

1331.6; 

OSti.019  1141.43 

600.382 

998.750 

533.784 

887.  77'8  1480.528 

799.  OCX) 

54 

800.466 

1331.94 

i.SS.224,1141.67 

600.561 

998.958 

533.943 

887.  963  480.67'2 

799.167 

55 

800.705 

1332.32 

686.  129 

1141.90 

600.740 

999.167 

534.102 

888.148480.815 

799.333 

56 

800.939 

1332.50 

086.629 

1142.14 

600.916 

999.375 

534.258 

888.333480.956 

799.500 

57 

801.173 

1332.78 

(586.830 

1142.38 

601.092 

999.583 

534.415 

888.519481.096 

799.667 

58 

801.412 

1333.06 

687.035 

1142.62 

601.271 

999.792 

534.574 

888.704481.240 

799.833 

59 

205 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


8O° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 
~~O~ 

Tun. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.    1   Arc. 

Tan. 

Arc. 

4807.75 

8000.00 

2403.96 

4000.00 

1602.75 

2666.67 

1202.17j2000.00 

961.844 

1600.00 

1 

4809.18 

8001.67 

2404.68 

4000.83 

1603.23  2667.22 

1202.53:2000.42 

962.130 

1600.33 

2 

4810.61 

8003.33 

2405.40 

4001.67 

1603.70 

2667.78 

1202.89 

2000.83 

962.417 

1600.67 

3 

4812.02 

8005.00 

2406.10 

4002.50 

1604.17 

2668.  33 

1203.24 

2001.25 

962.698 

1601.00 

4 

4813  42 

8006.67 

2406.80 

4003.33 

1604.64 

2668.89 

1203.59 

20U1.67 

962.978 

1601.33 

5 

4814.85 

8008.33 

2407.52 

4004.17 

1605.12 

2669.44 

1203.95 

2002.08 

963.265 

1601.67 

6 

4816.29 

8010.00 

2408.23 

4005.00 

1605.59 

2670.00 

1204.30 

2002.50 

963.552 

1602.00 

7 

4817.69 

8011.67 

2408.93 

4005.83 

1606.06 

2670.56 

1204.66 

2002.92 

963.832 

1602.33 

8 

4819.09 

8013.33 

2409.64 

4006.67 

1606.53 

2671.11 

1205  01 

2003.33 

964.113 

1602.6? 

9 

4820.53 

8015.00 

2410.35 

4007.50 

1607.01 

2671.6? 

1205.37 

2003.75 

964.400 

1603.00 

10 

4821  96 

8016.67 

2411.07 

4008.33 

1607.49 

2672.22 

1205.72 

2004.17 

964.686 

1603.33 

11 

4823.  3'J 

8018.33 

2411.78 

4009.17 

1607.96 

2672.78 

1206.08 

2004.58 

964.973 

1603.67 

13 

4824.82 

8^0.00 

2412.50 

4010.00 

1608.44 

2673.33 

1206.44 

2005.00 

965.259 

1604.00 

13 

4826.26 

8021.67 

2413.22 

4010.83 

1608.92 

2673.89 

1206.80 

2005.42 

965.546 

1604.33 

14 

4827.69 

8023.33 

2413.93 

4011.6? 

1609.40 

2674.44 

1207.16 

2005.83 

965.833 

1604.67 

15 

4829.09 

8025.00 

2414.63 

4012.50 

1609.86 

2675.00 

1207.51 

2006.25 

966.113 

1605.00 

16 

4830.50 

8026.67 

2115  34 

4013.  33 

1610.33 

2675.56 

1207.86 

2006.67 

966.394 

1605.33 

17 

4831  .  93 

8028.33 

2416.05 

4014.17 

1610.81 

2676.11 

1208.22 

2007.08 

966.681 

1605.67 

18 

4833.36 

8030.00 

2416.77 

4015.00 

1611.29 

2676.67 

1208.57 

2007.50 

966.967 

1606.00 

19 

4834.79 

8031.67 

2417.49 

4015.83 

1611.76 

2677.22 

1208.93 

2007.92 

967.254 

1606.33 

30 

4836.23 

8033.33 

2418.20 

4016.67 

1612.24 

2677.78 

1209.29 

2008.33 

967.541 

1606.67 

21 

4837.66 

8035.00 

2418.92 

4017.50 

1612  72 

2678.33 

1209.65 

2008.75 

967.827 

1607.00 

22 

4839.09 

8036.67 

2419.63 

4018.33 

1613.20 

2678.89 

1210.01 

2009.17 

968.114 

1607.33 

23 

1840.5  J 

8038.33 

2420.35 

4019.17 

1613.67 

2679.44 

1210.37 

2009.58 

968.400 

1607.67 

34 

4841.96 

8040.00 

2421.07 

4020.00 

1614.15 

2680.00 

1210.72 

2010.00 

968.687 

1608.00 

25 

4843.36 

8041.67 

2421.77 

4020.83 

1614.62 

2680.56 

1211.07 

2010.42 

968.968 

1608.33 

26 

4844.76 

8043.33 

2422.47 

4021.67 

1615.09 

2681.11 

1211.43 

2010.83 

969.249 

1608.6? 

21 

4846.20 

8045.00 

2423.19 

4022.50 

1615.56 

2681.6? 

1211.78 

2011.25 

969.535 

1609.00 

2$ 

4847  63 

8046.67 

2423  90 

4023.33 

1616.04 

2682.22 

1212.14 

2011.67 

969.822 

1609.33 

39 

4849.06 

8048.33 

2424.62 

4024.1? 

1616.52 

2682.78 

1212.50 

2012.08 

970.106 

1609.67 

30 

4850.49 

8050.00 

2425.34 

4025.00 

1617.00 

2683.33 

1212.86 

2012.50 

970.395 

1610.00 

31 

4851.92 

8051.67 

2426.05 

4025.83 

1617.47 

2683.89 

1213.22 

2012.92 

970.681 

1610.33 

33 

4853.36 

8053.33 

2426.77 

4026.67 

1617.95 

2684.44 

1213  57 

2013.38 

970.968 

1610.67 

33 

4854.79 

8055.00 

2427.48 

4027.50 

1618.43 

2685.00 

1213.93 

2013.75 

971.255 

1611.00 

34 

4856.22 

8056.6? 

2428.20 

4028.33 

1618.91 

2685.56 

1214.29 

2014.17 

971.541 

1611.33 

35 

4857.65 

8058.33 

2428.92 

4029.1? 

1619.38 

'2686.11 

1214.65 

2014.58 

971.828 

1611.67 

36 

4859.09 

8060.00 

2429  63 

4030.00 

1619.86 

2686.67 

1215.01 

2015.00 

972.114 

1612.00 

37 

4860.52 

8061.67 

2430.35 

4030.83 

1620.34 

2687.22 

1215.3? 

2015.42 

972.401 

1612.33 

38 

4861.95 

8063.33 

2431.07 

4031.6? 

1620.82 

2687.78 

1215.72 

2015.83 

972.687 

1612.67 

39 

4863.38 

8065.00 

2131.78 

4032.50 

1621.30 

2688.33 

1216.08 

2016.25 

972.974 

1613.00 

40 

4864.82 

8066.67 

2132.50 

4033.33 

1621.77 

2688.89 

1216.44 

2016.67 

973.260 

1613.33 

41 

4866.25 

8068.33 

2433.21 

4034.1? 

1622.25 

2689.44 

1216.80 

2017.08 

973.547 

1613.67 

43 

4867.68 

8070.00 

2133.9:5 

4035.00 

1622.73 

2C90.00 

1217.16 

2017.50 

973.834 

1614.00 

43 

4869.11 

8071.67 

2434.65 

1035.83 

1623.21 

2690.56 

1217.51 

2017.92 

974.120 

1614.33 

44 

4870.55 

8073.33 

2435.36 

4036.67 

1623.08 

2691.11 

1217.87 

2018.33 

974.407 

1614.67 

45 

4872.01 

8075.00 

2436.09 

4037.50 

1624.17 

2691.67 

1218.24 

2018.75 

974.699 

1615.00 

46 

4873.47 

8076.6; 

2436.82 

4038.33 

1624.66 

2692.22 

1218.60 

2019.17 

974.991  1615.33 

47 

4874.90 

8078.33 

2437.54 

4039.17 

1625.13 

2692.78 

1218.96 

2019.58 

975.278  1615.67 

48 

4876.33 

8080.00 

2438.26 

4040.00 

1625.61 

2693.33 

1219.32 

2020.00 

975.565  1616.00 

49 

4877.77 

8081.67 

2438.9? 

4040.83 

1626.09 

2693.89 

1219.68 

2020.42 

975.851 

1616.33 

50 

4879.20 

8083.33 

2439.69 

4011.6? 

1626.57 

2694.44 

1220.04 

2020.83 

976.138 

1616  67 

51 

4880.63 

8085.00 

2440.40 

4042.51 

1627.04 

2695.00 

1220.39 

2021.25 

976.424  1617.00 

53 

4882.06 

8086.67 

2441.12 

4043.3° 

1627.52 

2695.56 

1220.75 

2021.6? 

976.711!  161  7.  33 

53 

4883.50 

80S8.33 

2441.84 

4044.1? 

1628.00 

2696.11 

1221.11 

202  .'.08 

976.99? 

1617.67 

54 

4884.93 

8090.00 

2442.55 

4045.00 

1628.48 

2696.67 

1221.47 

-,'022.50 

977.284 

1018.00 

55 

4886.39 

8091.67 

2443.28 

4045.83 

1628.96 

2697  22 

1221.83 

2022  .92 

977.576 

1618.33 

56 

1887.85 

8093.33 

2444.01 

4046.67 

1629.45 

2697.78 

1222  20 

2023.33 

977.869 

1618.67 

57 

188',).  28 

8095.00 

2444.73 

1047.50 

1629.93 

2698.33 

1222.56 

2023.75 

978.155 

1619.00 

58 

4890.  71!  8096.  67 

2445.45 

4048.33 

1630.41 

2698.89 

1222.92 

2024.17 

978.442 

1619.33 

59 

4892.1518098.33 

2446.16 

4049.1? 

1630.88 

2699.44 

1223.272024.58 

978.728 

1619.67 

206 


TABLE  XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

80° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

31. 

801.651 

1333733 

687.240 

1142.86 

601.450 

1000.00 

534.733 

888.889 

481.383 

800.000 

~o" 

801.890 

1333.61 

687.444 

1143.10601.6:29 

1000.21 

534.893 

889.074 

481.527 

800.167 

1 

802.129 

1333.89 

687.649 

1143.33601.808 

1000.42 

535.052 

889.259 

481.670 

800.333 

9 

802  363 

1334.17 

687.850 

1143  57 

601.  98  1 

1000.63 

535.208 

889.444 

481.811 

800.500 

3 

802.597 

1334.44 

688.050 

1143.81 

602.160 

1000  83 

535.364 

889.630 

481.951 

800.667 

4 

802.886 

1334.72 

688.255 

1144.05 

602.339 

1001.04 

535.523 

889.815 

482.095 

800.833 

5 

803.074 

1335.00 

688.460 

1144.29 

602.518 

1001.25 

535.683 

890.000 

482  238 

801.000 

6 

803.308 

1335.28 

688.661 

1144.52 

602.694 

1001.48 

535.839 

890.185 

482.379 

801.167 

7 

803.543 

1335.50 

688.861 

1144.76 

602.869 

1001.67 

535.995 

890.370 

482.519 

801.333 

8 

803.781 

1335.83 

689.066 

1145.00 

603.048 

1001.88 

536.154 

890.556 

482  663 

801.500 

9 

804.020 

1336.11 

689.271 

1145.24 

603.228 

1002.08 

536.314 

890.741 

482.806 

801.667 

1O 

804.259 

1336.39 

689.476 

1145.48 

603.407 

1002.29 

536.473 

890.926 

482.949 

801.833 

11 

804.498 

1336.67 

689.680 

1145.71 

603.586 

1002.50 

536.632 

891.111 

483.093 

802.000 

13 

804.737 

1336.94 

689.885 

1145.95 

603.765 

1002.71 

536.792 

891.296 

483.236 

802.167 

13 

804.976 

1337.22 

690.090 

1146.19 

603.944 

1002.92 

536.951 

891.481 

483.380 

802.333 

14 

805.210 

1337.50 

690  290 

1146.43 

604  .  120 

1003.13 

537.107 

891  667 

483.520 

802.500 

15 

805  444 

1337.78 

OW.4-J1 

1146.67 

604.296 

1003.33 

537.263 

891.852 

483.661 

802  (567 

16 

805.683 

1  338.06 

690.696 

1146.90 

604  475 

1003.54 

537.422 

892.037 

483.804 

802.833 

17 

805.9-21 

1  :«M  .  33 

690.901 

1147.14 

604.654 

1003.75 

537.582 

892  222 

483.948 

803.000 

18 

806.160 

1338.61 

691.105 

1147.38 

604.833 

1003.96 

537.741 

892.407 

484.091 

803.167 

19 

806.399 

1338.89 

691.310 

1147.62 

605.012 

1004.17 

537.900 

892.593 

484.234 

803.333 

20 

806.638 

1339.17 

691.515 

1147.86 

60').  192 

1004.38 

538.060 

892.778 

484.378 

803.500 

31 

806.877 

1339.44 

691.720 

1148.10 

605.371 

1004.58 

538.219 

892.963 

484.521 

803.667 

33 

807.116 

1339.72 

691.924 

1148.33 

605.550 

1004.79 

538.378 

893.148 

484.665 

803.833 

33 

807.354 

1340.00 

692.129 

1148.57 

605.729 

1005.00 

538.538 

893.333 

484.808 

804.000 

34 

807.589 

1340.28 

692.330 

1148.81 

605.905 

1005.21 

538.694 

893.519 

484.949 

804.167 

35 

807.823 

1340.56 

692.531 

1149.05 

606.080 

1005.42 

538.850 

893.704 

485.089 

804.333 

36 

808.061 

1340.83 

692.735 

1149.29 

606.260 

1005.63 

539.009 

81)3.889 

485.233 

804.500 

37 

808.300 

1341.11 

692.940 

1149.52 

606.439 

1005.83 

539.169 

894.074 

485.376 

804.667 

38 

808.539 

1341.39 

693.145 

1149.76 

606.618 

1006.04 

539.328 

894.259 

485.520 

804.833 

39 

808.778 

1341.67 

693.350 

1150.00 

606.797 

1006.25 

539.487 

894.444 

485.663 

805.000 

30 

809.017 

1341.94 

693  554 

1150.24 

606.976 

1006.46 

539.647 

894.630 

485.806 

805.167 

31 

809.256 

1342.22 

693.759 

1150.48 

607.156 

1006.67 

539.806 

894.815 

485.950 

805.333 

33 

809.495 

1342.50 

693.964 

1150.71 

607.335 

1006.88 

539.965 

895.000 

486.093 

805.500 

33 

809.733 

1342.78 

694.169 

1150.95 

607.514 

1007.08 

540.125 

895.185 

486.237 

805.667 

34 

809.972 

1343.06 

694.373 

1151.19 

607.693 

1007.29 

540.284 

895.370 

486.380 

805.833 

35 

810.211 

1348.88 

694.578 

1151.43607.872 

1007.50 

540.443 

895.556 

486.523 

806.000 

36 

810.450 

1343.61 

694.783 

1151.67  608.052 

1007.71 

540.602 

895.741 

486.667 

806.167 

37 

810.689 

1343.89 

694.  98S 

1151.90 

608.231 

1007.92 

540.762 

895.926 

486  810 

806.333 

38 

810.928 

1344.17 

695.192 

1152.14 

608.410 

1008.13 

540.921 

896.111 

486.954 

806.500 

39 

811.166 

1344.44 

695.307 

1152.38 

608.589 

1008.33 

541.080 

896.296 

487.097 

806.667 

4O 

811.405 

1344.72 

695.602 

1152.62 

608.768 

1008.54 

541.240 

896.481 

487.241 

806.833 

41 

811.644 

1345.00 

695.807 

1152.86 

608.948 

10C8.75 

541.399 

896  .  667 

487.384 

807.000 

43 

811.883 

1345.28 

696.011 

1153.10 

609.127 

1008  96 

541.558 

896.852 

487.527 

807.167 

43 

812.122 

1345.56 

696.216 

1  153.33 

609.306 

1009.17 

541.718 

897.037 

487.671 

807.333 

44 

812.365 

1345.83 

696.425 

1153,57 

609.  4K9 

1009.38 

541.880 

897.222 

487.817 

807.500 

45 

812.609 

1346.11 

696.634 

1153.81 

609.672 

1009.58 

542.043 

897.407 

487.963 

807.667 

46 

812.848 

1346.39 

696.839 

1154.05 

609.851 

1009.79 

542.202 

897.593 

488.107!  807.  833 

47 

813.087 

1346.67 

697.043 

1154.29 

610.030 

1010.00 

542.361 

897.778 

4H8.850  808.000 

48 

813.326 

1346.94 

697.248 

1154.52 

610.209 

1010.21 

542.521 

897.963 

488.  394  1  808.  167 

49 

813.564 

1347.22 

697.453 

1154.76 

610.388 

1010.42 

542.680 

898.148 

488.537 

808.333 

5O 

813.808 

1347.50 

697.658 

11  55.  00!  610.  567 

1010.63 

542.839 

898.333 

488.681 

808.500 

51 

814.04-2 

1347.78 

697.86-2 

1155.24  610.747 

1010.83 

542.999 

898.519 

488.824 

808.067 

53 

814.281 

1318.06 

698.067 

1155.48610.926 

1011.04 

543.158 

898.704 

488.967 

808.833 

53 

814.540 

1348.33 

698.272 

1155.71  611.105 

1011.25 

543  317 

898.889 

489.111 

809.000 

54 

814.763 

1348.61 

698.481 

1155.95611.288 

1011.46 

543.480 

899.074 

489.257 

809.167 

55 

815.007 

1348.89 

698  690 

1156.19611.471 

1011.67  543.642 

899.259 

489  403 

809.333 

56 

815.246 

1349.17 

698.894 

1156.43611  650 

1011.88 

543.802 

899.444 

489.547 

809.500 

57 

815.485 

1349.44 

699.099 

1156.67611.8-29 

1012.08 

543.961 

S99.630 

489.690 

809.667 

58 

815.724 

1349.72699.304 

1156.90012.008 

1012.29544.120 

899.815 

489.834 

809.833 

59 

207 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


81° 

1°  Curve, 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

4893.  58;  8100.  00 

2446788 

4050700 

[637.16 

2700.00 

1223.63 

2025.00979.015 

1620.00 

1 

481)5.01  8  101.  (57 

2447.60 

-1050.83 

1631.84 

2700.56 

1223.99 

2025.42979  301 

1620.33 

2 

4896.4-1 

8103.33 

2448.31 

4051.67 

1632.3-2 

2701.11 

1224.35 

2025.83979.588 

1620.67 

3 

4897.91 

8105.00 

2449.04 

4052.50 

1632.80 

27'01.67 

1224.71 

2026.25979.880 

1621.00 

4 

4899.37 

8106.67 

2449.77 

4053.33 

1633.29 

2702.22 

1225.08 

2026.67980.173 

1.621.33 

5 

4900.80 

8108.33 

2450.49 

4054.17 

1633.77 

2702.78 

1225.44 

2027.08980.459 

1021.67 

6 

4902.23 

8110.00 

2451.21 

4055.00 

1634.25 

2703.33 

1225.80 

2027.  50  1980.746 

1622.00 

7 

4903.6(3 

8111  67 

2451.92 

4055.83 

1634.72 

27'03.89 

1220.15 

2027.92981.032 

1622.33 

8 

4905.10 

8113.33 

2452.64 

4056.67 

1635.20 

2704.44 

1226.51 

2028.33981.319 

1622.67 

9 

4906.56 

8115.00 

2453.37 

4057.50 

1635  69 

2705.00 

1226.88 

2028.75 

981.611 

1623.00 

1O 

1908.02 

8116.67 

2454.10 

4058.33 

1636.17 

2705.56 

1227.24 

2029.17 

981.903 

1623.33 

11 

1909  45 

8118.33 

2  454.  82  14059.  17 

1636.65 

2700.11 

1227.00 

2029.58982.190 

1623.67 

12 

4910.88 

8120.00 

2455.534060.00 

1637.13 

2706.67 

1227.96 

2030  00  982.  477 

1624.00 

13 

4912.34 

8121.67 

2456.26 

4060.83 

1637.62 

^707.22 

1228.32 

2030.42982.769 

1624.33 

14 

4913.81 

8123.33 

2456.99 

4061.67 

1638.10 

2707.78 

1228.69 

2030.83983.061 

1624.67 

15 

1915.24 

8125.00 

2457.71 

4062.50 

1638.58 

2708.33 

1229.05 

2031.25983.348 

1625.00 

16 

4916.67 

8126.67 

2458.43 

4063.33 

1639.06 

2708.89 

1229.41 

2031.67983.634 

1625.33 

17 

4918.13 

8128.33 

2459.16 

4064.17 

1639.55 

27'09.44 

1229.77 

2032.  08  19813.927 

1625.67 

18 

4919.59 

8130.00 

2459.89 

4065.00 

1640.03 

2710.00 

1230.14 

2032  501984.219 

1626.00 

19 

4921.02 

8131.67 

2460.60 

4065.83 

1640.51 

2710.56 

1230.49 

2032.92 

984.506 

1626.33 

20 

4922  46 

8133.33 

2461.32 

4066.67 

1640.99 

2711.11 

1230.85 

2033.33 

984.792 

1626.67 

21 

4923.92 

8135.00 

2462.05 

4067.50 

1641.48 

2711.67 

1231.22 

2033.75 

985.084 

1627.00 

22 

192.").  38 

8136  67 

2462  .  78 

4068.33 

1641.96 

2712.22 

1231.58 

•2034.17 

985.377 

1627.33 

23 

4926.84 

8138.33 

2463.51 

4069.17 

1642.45 

2712.78 

1231  95 

2034.58 

985.669 

1627.67 

34 

4928.30 

8110.00 

2464.24 

4070.00 

1642.94 

2713.33 

1-232.31 

2035.00 

985  901 

1628.00 

25 

4929.73 

8141.67 

2464.96 

4070.83 

1643.41 

2713.89 

1232.07 

2035.42 

986.248 

10-28.33 

36 

4931.17 

8143.33 

2465.67 

4071  .  67 

1643.89 

2714.44 

1233.03 

2035.83 

986.534 

1628.67 

37 

4932.63 

8145.00 

2466.40 

4072.50 

1644.38 

2715.00 

1233.40 

2030.25 

986.827 

1029.00 

38 

49:54.09 

8146.67 

2467.13 

4073.33 

1644.87 

2715.56 

1233.70 

2»'36.67 

987.119 

1629.33 

39 

4935.55 

8148.33 

2467.87 

4074.17 

1645.35 

2716.11 

1234.13 

2037.08 

987.411 

1629.67 

3O 

1937.01 

8150.00 

2468  60 

4075.00 

1645.84 

2716.67 

1231.49 

2037.50 

987.704 

1630.00 

31 

4938.44 

8151.67 

2469.31 

4075.83 

1646.32 

2717.22 

1-231.85 

2037.92 

987.990 

1630.33 

33 

1939.88 

8153.33 

2470.03 

4076.67 

1646.79 

2717.78 

123-1  .  21 

2  33.33 

988.277 

1630.67 

33 

4941.34 

8155.00 

2470.76 

4077.50 

1647.28 

2718.33 

1235.57 

2088.75 

988.509 

1631.00 

34 

4942.80 

8156.67 

2471.49 

4078.33 

1047.77 

2718.89 

1  235  94 

2039.17 

988.861 

1631.33 

35 

4914.26 

8158.33 

2472.22 

4079.17 

1648.26 

2719.44 

123t5.30 

2039.58 

989.154 

1631.07 

36 

4945.72 

8160.00 

2472.95 

4080.00 

1648.74 

2720.0' 

1236.67 

2040.00 

989.446 

1032.00 

37 

4947.15 

8161.67 

2473.67 

4080.83 

1649.22 

2720.50 

1237.03 

2040.42 

989.733 

1632.33 

38 

4948.58 

8103.33 

2474.38 

4081.67 

1649.70 

2721.11 

1237.39 

2040.83 

990.019 

1632.07 

39 

4950.05 

81(35.00 

2475.11 

4082.50 

1650.18 

27-21.6I 

1237.75 

2041.25 

990.311 

1033.00 

4O 

4951.51 

8166.67 

2475.84 

4083.33 

1650.67 

2722  22 

1238.12 

2041.67 

990.604 

1633.33 

41 

4952.97 

8168.33 

2476.57 

4084.17 

1651.16 

2722^78 

1-238.48 

2042.08 

990.890 

1633.07 

43 

4954  .  43 

8170.00 

2477.30 

4085.00 

1651.65 

2723.33 

1238.85 

2042.50 

991.188 

1034.00 

43 

4955.89 

8171.67 

2478.04 

4085.83 

1652.13 

27553.89 

1239.21 

2042.92 

991.481 

1034.33 

44 

4957.35 

8173.33 

2478.77 

4086  .  07 

1652  62 

2724.44 

1239.58 

2013.33 

991.773 

1634.67 

45 

4958.81 

8175.00 

2479  50 

4087.50 

1653.11 

2725.00 

1239.94 

•2013.75 

992.065 

1035.00 

46 

4960.27 

8176.67 

2480.23 

4088.33 

1653.59 

2725.56 

1240.31 

2044.17 

992.358 

1035.33 

47 

49(51.73 

8178.33 

2480.96 

4089.17 

1654.08 

2726.11 

1240.67 

2044.58 

992.650 

1035.67 

48 

49(53.19 

8180.00 

2481.69 

4090.00 

1654.57 

2720.67 

1241  04 

204x00 

992.942 

1636.00 

49 

4964.66 

8181.67 

2482.42 

4090.83 

1655.06 

2727.22 

1241.40 

2045.42 

993.234 

1030.33 

5O 

4966.12 

8183.33 

2483.15 

4091.67 

1655.54 

2727.78 

1241.77 

2045.83 

993.527 

1036.67 

51 

4967.58 

8185.00 

2483.88 

4092.50 

1656.03 

2728.33 

1242  14 

2046.25 

993.819 

1637.00 

53 

4969.04 

8186.67 

2484.61 

4093.33 

1656.52 

2728.89 

1242.50|2046.67 

994  .111 

1637.33 

53 

4970.50 

8188.33 

2485.34 

4094.17 

1657.00 

2729.44 

1242.87 

2047.08 

994.404 

1037.07 

54 

4971.96 

8190.00 

2486.07 

4095.00 

1657.49 

2730  00 

1243.23 

2047.50 

994.690 

1038.00 

55 

4973.42 

8191.67 

2486.80 

4095.83 

10.VT.98 

2730.56 

1243.60,2047.92 

994  .  988 

1638.33 

56 

4974.88 

8193.35 

2487.53 

4096.07 

1658.47 

2731.11 

1243.90  2048.33 

995.  2«1 

1038.07 

57 

4976.34 

8195.00 

2488.20 

4097.50 

1058.95 

273  1.  67  1  1244.  33  !  2048.  7'5 

995.57'3 

1039.00 

58 

4977.81 

8196.67 

2488  99 

4098.33 

1659.44 

27  3.  '.22  1244.  09  !  2049.  17 

995.865 

1039.33 

59 

4979.27 

8198.33 

2489.72 

4099.17 

1659.93 

2732  .  78  1  245  .  06  1  2049  .  58  996  .  1  57 

1039.07 

208 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

81° 

^T 

Tan. 

Arc. 

Tan.   |   Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.      Arc. 

815.98-2 

1350.00 

699.509:1157.14 

612.187  1012.50 

544.280900.000 

489.977810.000 

o 

816.301 

1350.28 

699.7131157.38 

612.3671012.71 

544.439900.185 

490.121  810.167 

i 

816.440 

1350.56 

699.918 

1157.62 

612.540  1012.92 

544.598:900.370 

490.264810.333 

2 

816.084 

1350.83 

700.127 

1157.86 

612.729  1013.13 

544.  761  1900.556 

490.410810.500 

3 

816.927 

1351.11 

700.336 

1158.10 

612.911  1013.33 

544.  923  1900.741 

490.557810.067 

4 

817.166  1351.39 

700.511 

1158.33 

613  0911013.  54 

545.082 

900.926 

490.700810  833 

5 

817.405  1351.67 

700.745 

1158.57 

613.270  1013.  75 

545.242 

901.111 

490.843811.OtK) 

6 

817.644  1351.94 

700.950 

1158.81 

613.4491013.9(5 

545.401 

901.296 

490.987811.107 

7 

817.883  1352.24 

701.155 

1159.05 

613.628  1014.17 

545.560 

901.481 

491.130811.333 

8 

818.126,1352.50 

701.364 

1159.29 

613.811 

1014.38 

545.723 

901.667 

491.277811.500 

9 

818.370-1352.78 

701.572 

1159.52 

613.994 

1014.58 

545.885 

901.852 

491.423811  667 

1O 

818.609  1353.06 

701.777 

1159.76 

614.173 

1014.79 

546.045 

902.037 

491.506811.833 

11 

818,8481353.33 

701.982 

1160.00 

614.352 

1015.00 

546.204 

902.222 

491.710812.000 

12 

819.091  1353.61 

702.191 

1160.24 

614.535 

1015.21 

546.367 

902.407 

491.850812.107 

13 

819.335  1353.  89 

702.400 

1160.48 

614.718 

1015.42 

546.529 

902.593 

492.002812.333 

14 

819.574  1354.17 

702.604 

1160.71 

614.897 

1015.63 

546.688 

902.778 

492.140812.500 

15 

819.813  1354.44 

702.809 

1160.95 

615.076 

1015.83 

546.848 

902.963 

492.289812.667 

16 

820.0561354.72 

703.018 

1161.19 

615.259 

1016.04 

547.010 

903.148 

492.435812.833 

17 

820  300  '  1355.01' 

703.227 

1161.43 

615.442 

1016.25 

547.173 

903.333 

492.582 

813.000 

18 

820.539  1355.28 

703.432 

1161.67 

615.621 

1016.46 

547.332 

903.519 

492.725 

813.167 

19 

820.777  1355.56 

703.636 

1161.90 

615.800 

1016.67 

547.491 

903.704 

492.869 

813.333 

20 

821.021  1355.83 

703.845 

1162.14 

615.983 

1016.88 

547  654 

903  889 

493.015 

813.500 

21 

821.265  1356.11 

704.054 

1102.38 

6J6.166 

1017.08 

547.810 

904.074 

493.161 

813.667 

22 

821.508  1356.3C 

704.263 

1162.62 

616.348 

1017.29 

547.979 

904.259 

493.307 

813.833 

23 

821.752:1356.67 

704.472 

1162.86 

616.531 

101  7.  5< 

548.141 

904.444 

493.454 

814.000 

24 

821.  991  11356.94 

704  .  677 

1163.10 

616.710 

1017.71 

548.301 

904  63( 

493.597 

814.167 

25 

822.230 

1357.22 

704.881 

1163.33 

616.889 

1017.92 

548.460 

904.815 

493.741 

814.333 

26 

822.473 

1357.50 

705.090 

1163.57 

617.072 

1018.13 

548.623 

905.000 

493.887 

814.501 

27 

822.717 

1357.78 

705  299 

11(53.81 

617.225 

1018.33 

548.785 

905.185 

494.033 

814.667 

28 

822.960 

1358.06 

705.508 

1164.05 

617.438 

1018.54 

548.948 

905.370 

494.179 

814.833 

29 

823.204 

1358.33 

705.717 

1164.29 

617.621 

1018.75 

549.110 

905.550 

493.326 

815.000 

30 

823.443 

1358.61 

705.9-21 

1164  5'. 

017.800 

1018.9C 

549.269 

905.741 

494.409 

815.167 

31 

823.682 

1358.89 

706.126 

1104.70 

617.979 

1019.17 

549.429 

905.926 

494.613 

815.333 

32 

823.925 

1359.17 

706.335 

1105.00 

618.102 

1019.38 

549.591 

906.111 

494.759 

815.500 

33 

824.169 

1359.44 

7'06.544 

1165.24 

618.345 

1019.58 

549.754 

906.296 

494.905 

815.667 

34 

824.413 

1859.72 

706.758 

1165.48 

018.527 

1019.79 

549  916 

906.481 

495.051 

815.833 

35 

824.656 

1360.(K 

7'06.962 

1165.71 

618.710 

1020.00 

550.079 

9  6.667 

495  198 

816.000 

36 

824.895 

1360.28 

707.166 

1165.95 

018.889 

1020.21 

550.238 

906.852 

495.341 

816.167 

37 

825.134 

1360.56 

707.371 

1166.19 

019.009 

1020.42 

550.397 

907.037 

495.485 

816.333 

38 

825.313 

1360.83 

707.580 

1166.43 

619.251 

1020.63 

550.560 

907.222 

495.631 

816.501 

39 

825.621 

1361.11 

707.789 

1166.67 

619.434 

1020.83 

550.722 

907.407 

495.777 

816.667 

40 

825.865 

1361.39 

707.998 

1106.90 

619  617 

1021.04 

550.885 

907.593 

495.923 

810.833 

41 

82(5.1081361.67 

708.207 

1167.14 

619.800 

1021.25 

551.047 

907.778 

496.070 

817.  OtX 

42 

826.  352  11361.  94 

708.415 

1107.38 

619.982 

1021.46 

551.210 

907.963 

496.216 

817.107 

43 

826.596  1362.22 

708.  624  '11  67.  62 

620  165 

1021.67 

551.372 

908.148 

496.362 

817.333 

44 

826.839  1362.  5( 

708.833  1  167.  86 

020.348 

1021.88 

551.535 

908.333 

496.509 

817.500 

45 

827.  OS3  1362.78 

709.042  1168.10 

620.531 

1022.08 

551.697 

908.519 

496.655 

817.667 

46 

827.326  1363.  Cf 

709.251  1168.33 

620.714 

1022.29 

551  .860 

908.704 

496.801 

817.833 

47 

827.570  1303.33 

709.400  1168  57 

0-20.896 

1022.50 

552.022 

908.889 

496.947 

818.00< 

48 

827.814  1363.61 

709.668  1168.81 

621.079 

1022.71 

552.185 

909.074 

497.094 

818.167 

49 

828.057 

1303.89 

709.8771169.05 

621.20-2 

1022.92 

552.347 

909.259 

497.240 

818.333 

50 

828.301  1364.17 

710.086  1169.29621.445 

1023.13 

552  510 

909.444 

497.386 

818.50< 

51 

828.  545  11364.4-1 

710.  295  11  69.  52  62  1.627 

1023.33 

552.672 

909.630 

497.533 

818.66; 

52 

828.788  1364.72 

710.504  1169.766-21.810  .1023.  54 

552.  835:909.  81  r 

497.679 

818.83 

53 

8-29.  (32  1365.00 

710.713  1170.00  621  .993  1023.^5 

552.997910.000 

497.825 

819.001 

54 

829.275  1365.28 

710.922 

1170.24622.176  H'23.90 

553.160910.185 

497.971 

819.167 

55 

8-9.5191365.56 

711.130 

1170.48022.3591024.17 

553.322i910.  370 

498.118 

819.333 

56 

82!).  763  13(55.83 

711.339 

1170.71  622.541  1024.38 

553.485  910.  6« 

498.264 

819.500 

57 

830.006  13(56.11 

711.548 

1170.95622.724  1024.58 

553.647910.741 

498.410 

819.667 

58 

830.2501366.39 

711.  7571  1171.  19  622.  907  1024  79 

553.  8101910.  926 

498.557819.833 

59 

200 


TABLE   XIV.— ACTUAL   TANGENTS,    ETC. 


$2° 
M. 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan.    |  Arc. 

Tan.   I    Arc. 

O 

4980.73 

8200.00 

2490.45 

4100.00 

1660.41:2733.33 

1245.42  2050.00  996.450  1610.00 

1 

498*.  19 

8201.67 

2491.19 

4100.83 

1660.90!  2733.  89 

1  245  .  79  2050  .  42  ]  996  .  742  J  640  .  33 

3 

4983.65 

8203.33 

2491.92 

4101.67 

166  1.39:  2734.  44 

1246.15  2050.83  997.034  1640.67 

3 

4985.11 

8205.00 

2492.65 

4102.50 

1661  87  i  2735.  00 

1246.522051.25997  327  1641.00 

4 

4986.57 

8206.67 

2493.38 

4103.33 

1662.362735.56 

1246  88  2051.67  £97.  619  1641.33 

5 

1988.03 

8208.33 

2494.11 

4104.17 

1662.85 

2736.11 

1247  .  25  2052  .  08  997  .  91  1  !  1641  .  67 

6 

4989.49 

8210.00 

2494.84 

4105.00 

1663.34 

2736.67 

1247.62  2052.50  9'J8.  204  (1642.00 

7 

4990.95 

8211.67 

2495.57 

4105.83 

1663.82 

2737.22 

1247.98  2052.92  998.496  1642.33 

8 

4993.42 

8213.33 

2496.30 

4106.67 

1664.31 

2737.78 

1248.352053.331998.788 

1642.67 

9 

4993.88 

8215.00 

2497.03 

4107.50 

1664.80 

2738.33 

1248.71 

2053.75 

999.080 

1643.00 

10 

4995.34 

8216.67 

2497.76 

4108.33 

1665.28 

2738.89 

1249.08 

2054.17 

999.373 

1643.33 

11 

4996.83 

8218.33 

2498.51 

4109.17 

1665.78 

2739.44 

1249.45 

2054.58 

999.671 

1643.67 

13 

1998.33 

8220.00 

2499.25 

4110.00 

1666.28 

2740.00 

1249.82 

2055.00999  969 

1644.00 

13 

4999.78 

8221.67 

2499.98 

4110.83 

1666.76 

2740.56 

1250.19 

2055.42 

1000.26 

1644.33 

14 

5001.24 

8223.33 

2500.71 

4111.67 

1667.25 

2741.11 

1250.55 

2055.83 

1000.55 

1644.67 

15 

5002  70 

8225.00 

2501.44 

4112.50 

1667.74 

2741.6; 

1250.92 

2056.25 

1000.85 

1645.00 

16 

5004.16 

8226.67 

2502.17 

4113.33 

1668.23 

2742.22 

1251.28 

2056.67 

1001.14 

1645.33 

17 

5005.6-2 

8228.33 

2502.90 

4114.17 

1668.71 

2742.78 

1251.65 

2057.08 

1001.43 

1645.67 

18 

5007.08 

8230.00 

2503.63 

4115.00 

1669.20 

2743.33 

12.V2.01 

2057.50 

1001.72 

1646.00 

19 

5008.57 

8231.67 

2504.38 

4115.83 

1669.70 

2743.89 

1252.39 

2057.92 

1002.02 

1646.33 

2O 

5010.06 

8233.33 

2505.12 

4116.67 

1670.19 

2744.44 

1252.76 

2058.33 

1002.32 

1646.67 

31 

5011.52 

8235.00 

2505.85 

4117.50 

1670.68 

2745.00 

1253.12 

2058.75 

1002.61 

1647.00 

33 

5012.99 

8236.67 

2506  58 

4118.33 

1671.17 

2745.56 

1253.49 

2059.17 

1002.90 

1647.33 

33 

5014.45 

8238.33 

2507  32 

4119.17 

1671.65 

2746.11 

1253.85 

2059.58 

1003.20 

1647.67 

34 

5015.91 

8240.00 

2508.05 

4120.00 

1672.14 

2746.67 

1254.22 

2060.00 

1003.49 

1648.00 

35 

5017.40 

8241.67 

2508.79 

4120.83 

1672.64 

2747  2  •' 

1254.59 

2060.42 

1003.79 

1648.33 

36 

5018.89 

8243.33 

2509.54 

4121.67 

1673.13 

2747  .'78 

(254.96 

2060.83 

1004.08 

1648.67 

37 

5020  35 

8245.00 

2510.27 

4122.50 

1673.62 

2748.33 

1255.33 

2061.25 

1004.38 

1649.00 

38 

5021.81 

8246.67 

2511.00 

4123.33 

1674.11 

2748.89 

1255.70 

2061.67 

1004.67 

1649.33 

39 

5023.30 

8248.33 

2511.74 

4124.17 

1674.61 

2749.44 

1256.07 

2062.08 

1004.97 

1649.67 

30 

5024.79 

8250.00 

2512.49 

4125.00 

1675.10 

2750.00 

1256.44 

2062.50 

1005.26 

1650.00 

31 

5026.25 

8251.67 

2513.22 

4125.83 

1675.59 

2750.56 

1256.81 

2062.  92 

1005.56 

1650.33 

33 

5027.71 

8253.33 

2513.95 

4126.67 

1676.08 

2751.11 

1257.17 

2063.  33  !  1005.  85 

1650.67 

33 

5029.20 

8255.00 

2514.69 

4127.50 

1676.57 

2751.67 

1257.54 

2063.75 

1006.15 

1651.00 

34 

5030.69 

S256.67 

2515.44 

4128.33 

1677.07 

2752.22 

1257.92 

2064.17 

1006.45 

1651.33 

35 

5032.18 

825S.33 

2516.17 

4129.17 

1677.56 

2752.78 

1258.28 

2064.58 

1006.74 

1651.67 

36 

5033.07 

S260.00 

2516.90 

4130.00 

1678.04 

2753.33 

1258.65 

2065.00 

1007.03 

1652.00 

37 

5035.13 

8261.67 

2517.64 

4130.83 

1678.54 

2753.89 

1259.02 

2065.42 

1007.3311652.33 

38 

5H36.59 

S263.33 

2518.39 

4131.67 

1679.04 

2754.41 

1259.39 

2065.83 

1007.63  1652.67 

39 

5038.05 

8265.00 

2519.12 

4132.50 

1679.52 

2755.00 

1259.76 

2066.25 

1007.92 

1653.00 

40 

5039.51 

8266.67 

2519.85 

4133.33 

1680.01 

2755.56 

1260.12 

2066.67 

1008.21 

1653.33 

41 

43 

5041.00 
5012.49 

8268.33 
8270.00 

2520.59 
2521.34 

4134.17 
4135.00 

1680.51 
1681.00 

2756.11 
2756.67 

1260.49 
1260.87 

2067.08 
2067.50 

1008.51  1653.67 
1008.81  1654.00 

43 

5043.98 

8271.67 

2522.08 

4135.83 

1681.50 

2757.22 

1261.24 

2067.92 

1009.10  1654.33 

44 

5015.47 

8273.33 

2522.83 

4136.67 

1682.00 

2757.78 

1261.61 

2068.33 

1009.40  1654.67 

45 

5046.93 

8275.00 

2523.56 

4137.50 

1682.48 

2758.33 

1261.98 

2068.75 

1009.70  1655.00 

46 

47 

5048.398276.67 
5019.888278.33 

2524.29 
2525.03 

4138.33 
4139.  11; 

16S2.97 
16S3.47 

2758.89 
2759.44 

1  262.  34  !  2069.  17 
1262.722069.58 

1009.99  1655.33 
1010.29'l655.67 

48 

5051.378280.00 

2525.78 

4110.00 

16S3.96 

2760.00 

1263.092070.00 

1010.58  1656.00 

49 

5052  .  86  8281  .  67 

2526.52 

4140.83 

1684.46 

2760.56 

1263.46 

2070.42 

1010.881650.33 

50 

5054.35:8283.33 

2527.27 

4141.67 

1684.96 

2761.11 

1263.83 

2070.83 

1011.18  1656.67 

51 

5055.81 

8285.00 

2528.00 

4142.50 

1685.45 

2761.67 

1264.202071.25 

1011.47  1657.00 

52 

5057.288286.67 

2528.73 

4143.33 

1685.93 

2762.22 

1264.5621)71.67 

1011.76  1657.33 

5:? 

5058.778288.33 

2529.48 

4144.17 

1686.43 

2762.  7S 

1264.91  2072.08 

1012.06  1657.  07 

54 

5060  25  '  8290.  00 

2530.22 

4145.00 

16S6.93 

2763.33 

1  265.  3  1  2072.  50 

1012.36  1658.00 

55 

506  1.74  '829  1.67 

2530.97 

4145.83 

1687.42 

2763.89 

1265.682072.92 

1012.66  1658.33 

56 

5063.  23  8293.  33 

2531.71 

4146.6? 

1687.92 

2764.44 

1266.052073.33 

1012.96  1058.67 

57 

5064.72i8295.00 

2532.45 

4147.50 

1688  42 

2765  .  00 

1266.432073.75 

1013.251659.00 

58 

5066.21  8296.  67 

2533.20 

4148.33 

1688.91 

2765.56 

1266.802074.17 

1013.55  1659.33 

59 

5067.678298,33 

2533.94 

4149.17 

1689.41 

2766.11 

1267.17.2074  58 

1013.85:1659.67 

210 


TABLE   XIV. — ACTUAL   TANGENTS,  ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve.       1O°  Curve. 

82° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc.      Tan. 

Arc. 

M. 

830.494 

1366.67 

711.966 

1171.43623.090 

1025.00 

553.972 

911.111498.703 

820.000 

O 

830.787  1366.94 

712.175 

1171.67623.272 

1025.21 

554.135911.296498.849 

820.167 

1 

880.981 

1367.22 

712.3S4 

1171  90  623.455 

1025.42 

554.  297  1  911.  481  49S.  996 

820.333 

2 

831.224 

1367.50 

712  592 

1172.14:623.638 

1025.63 

554.460 

911.667499.142820.500 

9 

881.408 

1367.78 

712.801 

1172.38623.821 

1025.83 

554.622 

911.852499.288 

820.667 

4 

881.712 

1368.06 

713.010 

1172.62624.004 

1026.04 

554.785 

912.037499.434 

820.833 

5 

831.856 

1368.33 

713.219 

1172.86  624  186 

1026.25 

554.947  912.222499.581 

821.0TK) 

6 

832.199 

1368.61 

713.428 

1173.10624.369 

1026.46 

555.110 

912.407J499.72; 

821  167 

7 

832  442 

1368.89 

713.637 

1173.33624.552 

1026.67 

555.272 

912.593i499.873 

821.333 

8 

832.686 

1369.17 

713.845 

1173.57 

624.735 

1026.88 

555,435 

912.778500  020 

821.500 

9 

832.930 

1369.44 

714.054 

11.73.81 

624.917 

1027.08 

555.597 

912.963500.166 

821.667 

10 

833.178 

1369.72 

714.267 

1174.05625.104 

1027.29 

555  763 

913.148500.315 

821.83:) 

11 

833.427 

1370.00 

714.480 

1174.29625.290 

1027.50 

55^.929 

913.333:500.464 

822.00L 

12 

833  670 

1370.28 

714.689 

1174.52625.473 

1027.71 

556.091 

913.519:500.610 

822.1(57 

13 

833.914 

1370.56 

714.898  1174.76625.656 

1027.92 

556.254 

913.704  500.757 

822.  3:  W 

14 

834.157 

1370.83 

715  10711175.00625.838 

102S.13 

556.416 

913.889500.903 

822.500 

15 

831.401 

1371.11 

715.316 

1175.24  626.021 

102S.33 

556.579 

914.074  501  049 

822.667 

16 

834.645 

1371.39 

715.524 

1175.48626.204 

1028.54 

556.741 

914.259501.196 

822.833 

17 

834.888 

1371.67 

715.733 

1175.71 

626.387 

1028.75 

556.904 

914.444  501.342 

823.000 

18 

835.137 

1371.94 

715.946 

1175.95 

626.573 

1028.96 

557.070 

914.630501.491 

823.167 

19 

835.385 

1  372  22 

716.159 

1176.19 

626.760 

1029.17 

557.235 

914.815501.640 

823.333 

2O 

.835.629 

1372!  50 

716.368 

1176.43 

62(5.942 

1029.38 

557.398 

915.000501.787 

823.500 

21 

835.872 

1372.78 

7  16.  '577 

1176.67 

627.125 

1029.58 

557.560 

9  i  5.  185  501.  933 

823.667 

22 

836.116 

1373.06 

716.786 

1176.90 

627.308 

1029.79 

557.723 

915.370502  079 

823.833 

2'3 

836.360 

1373.33 

716.995 

1177.  14^627.  491 

1030.00 

557.885 

915.556502.225 

824.000 

24 

836.608 

1373.61 

717.208 

1177.38627.677 

1030.21 

558.051 

915.741  502.375 

824.167 

25 

836  .  H56 

1373.89 

717.421 

1177.62627.803 

1030.42 

558.217 

915.926502.524 

824.333 

26 

837.100  1374.17 

717.629 

1177.86628.046 

1030.63 

558.379 

916.111  502.670 

824.500 

21 

837.344 

1374.44 

717.83S 

1178.10 

628.229 

1030.83 

558.542 

916.296502.816 

824.667 

28 

837.592 

1374.72 

718.051 

1178.33 

628.415 

1031.04 

558.707 

916.481^02.965 

824.833 

29 

837.840 

1375.00 

718  264 

1178.57 

628.602 

1031.25 

558.873 

9l6.667Wl15 

825.000 

30 

838.084 

1375.28 

718.473 

1178.81 

628.784 

1031.46 

559.035 

916.852503.261 

825.167 

31 

838.328 

1375.5.6 

718.682 

1179.05 

628.967 

1031.6; 

559.198 

917.037503.407 

825.333 

32 

838.576 

1375.83 

718.895 

1179.29 

629.154 

1031.88 

559.364 

917.222503.556 

825  500 

33 

838  824 

1376.11 

719.108 

1179.52 

629.340 

1032.  OS 

559.529 

917.407503.706 

825.667 

34 

839  068 

1376.39 

719.317 

1179.76 

629.523 

1032.29 

559.692 

917.593503.852 

825.833 

35 

839  312 

1376.67 

719.525 

1180.00 

629  706 

1032.5(1 

559.854 

917.778503.998 

826.000 

36 

839.560  1376.94 

719.738 

1180.24 

629.892 

1032.71 

560.020 

917.963504.147 

826.167 

37 

839.  808  1  1377.  22 

719.951 

1180.48 

630.078 

1032.92 

560.186 

918.148504.296 

826.333 

38 

840.052 

1377.50 

720.160 

1180.71 

630.261 

1033.13 

560.348 

918.333504.443 

826.500 

39 

840.296 

1377.78 

720.369 

1180.95 

630.444 

1033.33 

560.511 

918.519504  589 

826.667 

40 

8Mh544 

1378.06 

720.582 

1181.19 

630.630 

1033.54 

5(50  676 

918.704  504.738 

82(5  833 

41 

840.792 

1378.33 

720.795 

1181.43 

630.817 

1033.75 

560.842 

918.889504.887 

827.000 

42 

841.041 

1378.61 

721.008 

1181.67 

631.003 

1033.SH5 

5(51.008 

919.074505.036 

827.167 

43 

841.289 

1378.89 

721.221 

1181.90 

631.189 

1034.17 

561.17'4 

919.259505.186 

827.333 

44 

841  533 

1379.17 

721.430 

1182.14 

631.372 

1034.3s 

561.336 

919.444505.332 

827.501: 

45 

841  .  776 

1379.44 

721.638 

1182.38 

631.555 

1034.5* 

561  499 

919.630505.478 

827.66; 

46 

842.025 

1379.72 

721.851 

1182.62 

631  .  74  1 

1034.79 

561.664 

919.815505.627 

827.833 

47 

812.273 

1380.00 

722.064 

1182.86 

631.928 

1035.00 

561.830 

920.000505.777 

828.000 

48 

812.522 

1380.28 

722  277 

1183.10 

632  114 

1035.21 

561.996 

920.185505.926 

828.167 

49 

842  770 

1380.56 

722.490 

1183.33 

63.2.300 

1035.42 

562.161 

920.370506.075 

828.333 

50 

843.014:1380.83 

722.699 

1183.57 

632.483 

1035.63 

562  324 

920.556506.221 

828.500 

51 

843.25711381.11 

722.908 

1183.81 

632.666 

1035.83 

562.486 

920.741  506.367 

828.667 

52 

843.506  1381.3'.) 

723.121 

1184.05 

632.852 

1036.04 

562.652 

920.926506.517 

828.833 

53 

843.75-1  !l3Sl.f)7 

723.834 

1184.29 

633.039 

1036.25 

562.818 

921.111  506.666 

829.000 

54 

844.002 

1381.94 

723  547 

1184.52 

633.225 

1036.46 

562.983 

921.296506.815 

829.167 

55 

844  251 

1382.2',! 

723.760 

1184.76 

033.411 

1036.67 

563.149 

921.481  506.964 

829.333 

56 

844.499 

1382.50 

523.973 

1185.00 

633.598 

1036.88 

563.315 

921.667507  113 

829.500 

57 

844  .  748 

1382.78 

724  186 

1185.24 

633.784 

1037.08 

563.480 

921  .  852  507  .  262  1  829  .  667 

58 

844.996  1383.06 

724.399 

1185.48 

623.970 

1037.29 

563.646 

922.037  507.  4121  829.  833 

59 

211 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


83° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

~o~ 

Tan. 

5069714 

Arc. 

8300.00 

Tan. 

2534.69 

Arc. 

4150.00 

Tan. 

Arc. 

Tau. 

T267.54 

Arc. 

2075.00 

Tan. 

Arc. 

1689.91 

2766.67 

1014.15 

1660.00 

i 

5070.63 

8301.67 

2535  42 

4150.831690.39 

2767.22 

1267.91 

2075.42 

1014.44 

1660.33 

2 

5072.12 

8303.33 

2536.15 

4151.67 

1690.88 

2767.78 

1268.27 

2075.83 

1014.73 

1660.67 

3 

5073.61 

8305.00 

2536.90 

4152.50  1691.38 

2768.33 

1268.65 

2076.25 

1015.03 

1661.00 

4 

5075.09 

8306.67 

2537.64 

4153.33!1691.87 

2768.89 

1269.02 

2076.67 

1015.33 

1661.33 

5 

5070.58 

8308.33 

2538.39 

4154.17:1692.  37 

2769.44 

1269.39 

2077.08 

1015.63 

1661.67 

6 

5078  07 

8310.00 

2539.13 

4155.00  1692.87 

2770.00 

1269.76 

2077.50 

1015.93 

1662.00 

7 

5079.56 

8311.67 

2539.88 

4155.83  1693.36 

2770.56 

1270.14 

2077.92 

1016.22 

1662.33 

8 

5081.05 

8313.33 

2540.62 

4156.67 

1693.86 

2771.11 

1270.51 

2078.33 

1016.52 

1662.67 

0 

5082.54 

8315.00 

2541.36 

4157.50 

1694.36 

2771.67 

1270.88 

2078.75 

1016.82 

1663.00 

10 

5084.03 

8316.67 

2542.11 

4158.33 

1694.85 

2772.22 

1271.25 

2079.17 

1017.12 

1663.33 

11 

5085.52 

8318.33 

2542.85 

4159.17 

1695.35 

2772.78 

1271.63 

2079.58 

1017.42 

1663.67 

12 

5087.01 

8320.00 

2543.60 

4160.00 

1695.85 

2773.33 

1272.00 

2080.00 

1017.71 

1664.00 

13 

5088.50 

8321.67 

2544.34 

4160.83 

1696.34 

2773.89 

1272.37 

2080.42 

1018.01 

1664.33 

14 

5089.99 

8323.33 

2545.09 

4161.67  1696.84 

2774.44 

1272.74 

2080.83 

1018.31 

1664.67 

15 

5091.48 

8325.00 

2545.83 

4162.50  1697.34 

2775.00 

1273.12 

2081.25 

1018.61 

1665.00 

16 

501)2.97 

8326.67 

2546.58 

4163.3311697.83 

2775.56 

1273.49 

2081.67 

1018.91 

1665.33 

17 

5094.46 

8328.33 

2547.32 

4164.17 

1698.33 

2776.11 

1273.86 

2082.08 

1019.20 

1665.67 

18 

5095.95 

8330.00 

2548.07 

4165.00 

1698.83 

2776.67 

1274.23 

2082.50 

1019.50 

1666.00 

19 

5097.44 

8331.67 

2548.81 

4165.83 

1699.32 

2777.22 

1274.61 

2082.92 

1019.80 

1666.33 

20 

5098.93 

8333.33 

2519.56 

4166.67 

1699.82 

2777.78 

1274.98 

2083.33 

1020.10 

1666.67 

21 

5100.45 

8335.00 

2550.32 

4167.50 

700.32 

2778.33 

1275.36 

2083.75 

1020.40 

1667.00 

22 

5101.97 

8336.67 

2551  08 

4168.33 

1700.83 

2778.89 

1275.74 

2084.17 

1020.71 

1667.33 

23 

5103.46 

8338.33 

2551.82 

4169.17 

701.33 

2779.44 

1276.11 

2084.58 

1021.00 

1667.67 

24 

5104.95 

8340.00 

2552.57 

4170.00 

701.82 

2780.00 

1276.48 

2085.00 

1021.30 

1668.00 

25 

5106.44 

8341  .  67 

2553.31 

4170.83 

702.32 

2780.56 

1276.86 

2085.42 

1021.60 

1668.33 

26 

5107.93 

8343.33 

2554.06 

4171.67 

702  82 

2781.  11 

1277.23 

2085.83 

1021.90 

1668.67 

27 

5109:43 

8345.00 

2554.80 

4172.50 

703  31 

2781.67 

1277.60 

2086.25 

1022.20 

1669.00 

28 

5110.91 

8346.67 

2555  55 

4173.33 

703.81 

2782.22 

1277.97 

2086  67 

1022.49 

1669.33 

29 

5112.39 

8348.33 

2556.29 

4174.17 

1704.31 

2782.78 

127'8.35 

2087.08 

1022.79 

1669.67 

3O 

5113.88 

8350.00 

2557.04 

4175.00 

1704.80 

2783.33 

1278.72 

2087.50 

1023.09 

1670.00 

31 

5115  40 

8351.67 

2557.80 

4175.83 

1705.31 

2783.89 

1279.10 

2087.92 

1023.39 

1670.33 

32 

5116.92 

8353.33 

2558.55 

4176.67 

1705.82 

2784.44 

1279.48 

2088.33 

1023.70 

167'0.67 

33 

5118.41 

8355.00 

2559.30 

4177.50 

17'06.31 

2785.00 

1279.85 

2088.75 

1023.99 

1671.00 

34 

5119.90 

83.-)6.67 

2560.04 

4178.33 

1706.81 

2785.56 

1280.22 

2089.17 

1024.29 

1671.33 

35 

5121.39 

8358.33 

2560.79 

4179.17 

1707.31 

2786.11 

1280.60 

2089.58 

1024.59 

1671.67 

36 

5122.88 

8360.00 

2561.53 

4180.  (X) 

1707.80 

2786.67 

1280.97 

2090.00 

1024.89 

1672.00 

37 

5124.40 

f^GI.67 

2562.29 

4180.83 

1708.31 

2787.22 

1281.35 

2090.42 

1025.19 

1672.33 

38 

5125.92 

K303.33 

2563.05 

4181.67 

17'08.81 

2787.78 

1281.73 

2090.83 

1025  50 

1672.67 

39 

5127.41 

8365.00 

2563.80 

4182.50 

1709.31 

2788.33 

1282.10 

2091.25 

1025.79 

1673.00 

40 

5128.90 

8366.67 

2564.54 

4183.33 

1709.81 

2788.89 

1282.47 

2091.67 

1026.09 

1673.33 

41 

5180.39 

8368.33 

2565.29 

4184.  17[1710.  3012789.  41 

1282.84 

2092.08 

1026.31) 

1673.67 

42 

5131.88 

8370.00 

2566.03 

4  1  85.  OOi  1710.  80  2790.  00 

1283.22 

2092.50 

1026.69 

1674.00 

43 

5133.39 

8371.67 

2566.79 

4185.83  1711.31 

2790.56 

1283.60 

2092.92 

1026.99 

1674.33 

44 

5131.91 

8373.33 

2567.55 

4186.671711.81 

2791.11 

1283.98 

2093  33 

1027.30 

1674.67 

45 

5136.40 

8375.00 

2568.30 

4187.50  1712.31 

2791.67 

1284.35 

2093.75 

1027.59 

1675.00 

46 

5137.89 

8376.67 

2569.04 

4188.331712.81 

2792.22 

1284.72 

2094.17 

1027.89 

1675.33 

47 

5139.41 

8378.33 

2569.80 

4189.17  1713.31 

2792.78 

1285.10 

2094.58 

1028.20 

1675.67 

48 

5140.93 

8380.00 

2570.56 

4190.001713.82 

2793.33 

1285.48 

2095.00 

1028.50 

1676  00 

49 

5142.42 

8381.67 

2571.30 

4190.83 

1714.32 

2793.89 

1285.85 

2095.42 

1028  80 

1676.33 

50 

5143.91 

83S3.33 

2572.05 

4191  67 

1714.81 

2794.44 

1286.23 

•2005  .  83 

1029.10 

1676.67 

51 

5145.43 

8385.00 

2572.81 

4192.50  1715.32 

2795.00 

1286.61 

2096.25 

1029.40 

1677.00 

52 

5146.94 

8386  .  67 

2573  57 

1193.33  1715.82 

2795.55 

1286.98 

2096.67 

1029.70 

1677.33 

53 

5148.46 

8388.33 

2574.33 

4194.17  1716.33 

2796.11 

1287.37 

2097.08 

1030.01 

1677.67 

54 

5149.98 

8390.00 

2575.09 

4195.001716.84i2796.67 

1287.74 

2097.50 

1030.31 

1678.00 

55 

5151.47 

8391.67 

2575.83 

4195.83  1717.33  2797.22 

1288.12 

2097.92 

1030  61 

1678.33 

56 

5152.96 

8393.33 

2576.57 

4196.671717.832797.78 

1288.49 

2098.  S3 

1030.91 

1678.07 

57 

5154.48 

8335.00 

2577.33 

4197.  50  1718.  3412798.  33 

1288.87 

2098.75 

1031.21 

1679.00 

58 

5156.00 

8396.67 

2578.09 

4198.33  1718  84:2798.89 

1289.25 

2099.17 

1031.51 

1679.33 

59 

5157.49 

8398.33 

3578.8* 

4199  17  1719.34|2799  44 

1289.622099.58 

1031.81 

1679.67 

212 


TABLE  XIV. — ACTUAL  TANGENTS,   ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

83° 
M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

845.244 

1383.33 

724.612 

1185.71 

534.157 

1037.50 

563.812 

922.222 

507.561 

830.000 

O 

845.488 

1383.61 

724.820 

1185.95 

J34.339 

1037.71 

563.974 

922.407 

507.707 

830.167 

1 

845.  73^ 

1383.89 

725.029 

1186.19 

634.522 

1037.92 

564.137 

922.593 

507.853 

830.333 

2 

845.980 

1384.1? 

725.242 

1186.43 

634.709 

1038.13 

564.303922.778 

508.002 

830.500 

3 

846.228 

1384.44 

725.455 

1186.67 

634.895 

1038.33 

564.468 

922.963 

508.152 

830.66? 

4 

846.47? 

1884.72 

725.668 

1186.90 

635.081 

1038.54 

564.634 

923.148 

508.301 

830.833 

5 

846.725 

1385.00 

725.881 

1187.14 

635  268 

1038.75 

564.800 

923.333 

508.450 

831.000 

6 

84(5.974 

1385.28 

726.094 

1187.38 

635.454 

1038.96 

564.965 

923  519 

508.599 

831.16? 

7 

847.222 

1385.56 

726.307 

1187.62 

(535.640 

1039.17 

565.131 

923.704 

508.748 

831.333 

8 

847.470 

1385.83 

726.520 

1187.86 

635.827 

1039.38 

565.297 

923.889 

508.897 

831.500 

9 

847.719 

1386.11 

726.733 

1188.10 

636.013 

1039.58 

565.462 

924.074 

509.047 

831.667 

1O 

847.967 

1386.39 

726.946  1188.33 

636.200 

1039.79 

565.628 

924.259 

509.196 

831.833 

11 

848.216 

1386.67 

727.159  1188.5? 

636.386 

1040.00 

565.794 

924.444 

509.345 

832.000 

12 

848.464 

1386.94 

727.3721188.81 

636.572 

1040.21 

565.959 

924.630 

509.494 

832.167 

13 

848.712 

1387.22 

727.5851189.05 

636.759 

1040.42 

566.125 

924.815 

509.643 

832.333 

14 

848.961 

1387.50 

727.798  1189.29 

636.945 

1040.63 

566.291 

925.000 

509.792 

832.500 

15 

849.209 

1387.78 

728  0101189.52 

63?  .  131 

1040.  83 

566.457 

925.185 

509.942 

832.667 

16 

849.458 

1388.06 

728.223  1189.76 

637.318 

1041.04 

566.622 

925.370 

510.091 

832.833 

17 

849.706 

1388.33 

728.4361190.00 

637.504 

1041.25 

566.788 

925.556 

510.240 

833.000 

18 

849.954 

1388.61 

728.649 

1190.24 

637.690 

1041.46 

566.954 

925.741 

510.389 

833.16? 

19 

850.203 

1388.89 

728.862 

1190.48 

637.87? 

1041.67 

567.119 

925.926 

510.538 

833.333 

20 

850.456 

1389.17 

729.079  1190.71 

633.067 

1041.88 

567.288 

926.111 

510.690 

833.500 

21 

850.709 

1389.44 

729.  296  ;  11  90.  95 

638.257 

1042.08 

567.457 

926.296 

510.842 

833.667 

22 

850.958 

1389.72 

729.509  1191.  1<J 

638.443 

1042.29 

567.623 

926.481 

510.991 

833.  a33 

23 

851.206 

1390.00 

729.722  1191.43 

638.629 

1042.50 

567.788 

926.66? 

511.141 

834.  00( 

24 

851  .  454 

1390.28 

729.9351191.67 

(538.816 

1042.71 

567.954 

926.852 

511.290 

834.16? 

25 

851.703 

1390.56 

730.  148;  1191.  9( 

639.002 

1042.92 

568.120 

927.03? 

511.439 

834.333 

2C> 

851.951 

1390.83 

730.361  1192.14 

639.189 

1043.13 

568.285 

927.222 

511.588 

834.500 

27 

852.200 

1391.11 

730  574  1192.38 

639.475 

1043.33 

568.451 

927.407 

511.73? 

834.667 

28 

852.448 

1391.39 

730.787 

1192.6L 

639.561 

1043.54 

568.617 

927.593 

511.886 

834.833 

29 

852.696 

1391.6? 

731.000 

1192.86 

C39.748 

1043.75 

568.783 

927.778 

512.035 

835.  00( 

3O 

852.950 

1391.94 

731.217 

1193.10 

639.938 

1043.96 

568.951 

927.963 

512.188 

835.167 

31 

853.203 

1392.22 

731.434 

1193.33 

640.12? 

1044.17 

569.120 

928.148 

512.340 

835.333 

32 

853.451 

1392.50 

731.647 

1193.57 

640.314 

1044.36 

569.286 

928.333 

512.489 

835.500 

33 

853.699 

1392.78 

731.860 

1193.81 

640.500 

1044.58 

569.452 

928.519 

512.638 

835.667 

34 

853.948 

1393.06 

732.073 

1194.05 

640.687 

1044.79 

569.61? 

928.704 

512.787 

835.833 

35 

854.196 

1893.33 

732.286 

1191.29 

640.873 

1045.00 

569.783 

928.889 

512.936 

836.000 

36 

854.449 

1393.61 

732.503 

1194.52 

641.063 

1045.21 

569  .  952 

929.074 

513  088 

836.167 

37 

854.703 

1393.89 

732.720 

1194.76 

641.253 

1045.42 

570.121 

929.259 

513.240 

836.  33:3 

38 

854.951 

1394.17 

732.933 

1195.00 

641.439 

1045.63 

570.28? 

929.444 

513.389 

836.500 

39 

855.199 

1394.44 

733.146 

1195.24 

641.626 

1045.83 

570.452 

929.630 

513.539 

836.66? 

4O 

855.448 

1394.72 

733.359 

1195.48 

641.812 

1046.04 

57'0.618 

929.815 

513.688 

836.833 

41 

855.696 

1395.00 

733.572 

1195.71 

641.998 

1046.25 

570.784 

930.000 

513.837 

837.000 

42 

865.949 

1395.28 

733  789  1195.95 

642.  18S 

1046.46 

570.952 

930.185 

513.989 

837.167 

43 

856.203 

1395.56 

734.006  1196.19 

642.378  1046.6? 

571.121 

9?0.370 

514.141 

837.333 

44 

856.451 

1395.83 

734.219  1196.43 

642.565  1046.88 

571  .287 

930.556 

514.290 

837.500 

45 

856.699 

1396.11 

734.4321196.67 

642.751 

1047.08 

571.453 

930.741 

514.439 

837.667 

46 

856.953 

1396.39 

734.649  1196.90 

642.941 

1047.29 

571.622 

930.926 

514.591 

837.833 

47 

857.206 

1396.67 

734.8661197.14 

643.131  1047.50 

571.790 

931.111 

514.7'43 

838.000 

48 

857.454 

1396.94 

735.079  1197.38 

643.317 

1047.71 

571.956 

931.296 

514.892 

838.167 

49 

857.702 

1397.22 

735  202  1197.62 

613.501 

1047.92 

572.122 

931.481 

515.042 

838.333 

5O 

857.956 

1397.50 

735.50!)  1197.86 

643  .  693 

1048.13 

572.291 

931.66? 

515.1941838.500 

51 

858.209 

1397.78 

735.726  1198.10 

643  8S:J, 

1048  33 

572.460 

931.852 

515.346838.667 

52 

858.462 

1398.06 

735  .  943  1  1  98  .  33  644  .  073 

1043.54 

572  628 

932.037 

515.498838.833 

53 

858.715 

1398.33 

736.1601198.57644.263 

104>  .75 

572.79? 

932.222 

515.  650  839.  00( 

54 

858.964 

1398.61 

736.373  1198.81  644.450 

1048  96 

572.963 

932.407 

515.799:839.16? 

55 

859.212 

1398.89 

736.5861199.05644.636 

1049.17 

573.129 

932.593 

515.948839.333 

56 

859.465 

1399.17 

736.803  1199.29644  826 

1049.38 

573.298 

932.778 

516.100839.500 

57 

859.718 

1399.44 

737.020  1199.52645.016 

1049.58 

573.466 

932.963 

516.252839.66? 

58 

859  967 

1399  .  72;  737  .  233  1  1  99  .  76  645  .  202 

1049.79 

573.632 

933.148 

516.401  839.833 

59 

213 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


84° 
M. 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

5158.9SS400.00 

2579.58 

4200.00 

1719.84 

2800.00 

1289.99 

2100.00 

1032.11 

680.00 

1 

5100.50 

S401.67 

2580.34 

4200.83 

17'20.34 

2800.56 

1290.37 

2100.42 

1032.41 

1680.33 

2 

5162.01 

8403  33 

2581.10 

4201.67 

1720.85 

2801.11 

1290.75 

2100.83 

1032.72 

080.  (17 

3 

5108.53 

S405.00 

2581.86 

4202.50 

1721.35 

2801.67 

1291.13 

2101.25 

1033.02 

1681.00 

4 

5165.05 

8406.67 

2582.62 

4203.33 

1721.86 

2802.22 

291.51 

2101.67 

1033.38 

681.33 

5 

5166.57 

840S.33 

2583.38 

4204.17 

1722.37 

2802.78 

291.89 

2102.08 

1038.63 

681.67 

6 

5168.09 

8410.00 

,1584.14 

4205.00 

1722  87 

2803.33 

292.27 

2102.50 

1083.93 

082.00 

7 

5169.  58 

8411.67 

2584.88 

4205.83 

1723.37 

2803.89 

292.64 

2102.92 

1034.28 

1082.38 

8 

5171.07 

8413.33 

2585.63 

4206.67 

1723.87 

^804.44 

1293.02 

2103.33 

1034.53 

1682.67 

9 

5172.58 

8415.00 

2586.39 

4207  50 

1724.37 

2805.00 

1293.40 

2103.75 

1034.8:3 

1683.00 

1O 

5174.10 

8416  67 

2587.15 

4208.33 

1724.88 

2805  56 

1293.78 

2104.17 

1035.14 

16S3.33 

11 

5175.62 

8418.33 

2587.91 

1209.17 

1  725  .  38 

2806.11 

1294.  1C. 

2104.58 

1035.44 

1683.67 

13 

5177.14 

8420.00 

2588.66 

4210.00 

1725.89 

,806.67 

1294.54 

2105.00 

1035.74 

1084.00 

13 

5178.66 

8121.67 

2589.42 

4210.83 

1726.4U 

2807.22 

1294.92 

2105.42 

1036.05 

1684.33 

14 

5180.18 

8423.33 

2590.18 

4211.67 

1726.90 

2807.78 

1295.30 

2105.83 

1036.35 

1684.67 

15 

5181.69 

8425.00 

2590.94 

4212.50 

1727.41 

2808.33 

i295.67 

2106.25 

1036.66 

1685.00 

10 

5183.  21 

8426.67 

58301.7(1 

4213.33 

1727.92 

2808.89 

1296.05 

2106.67 

1036.96 

1685.33 

17 

5184.73 

8428.33 

2592.46 

4214.17 

1728.42 

2809.44 

1296  43 

2107.08 

1037.y(i 

1685.67 

18 

5186.25 

8430.00 

25U.-J.22 

4215  00 

1728.93 

2810.00 

1206.  81 

2107.50 

1037.57 

1686.00 

19 

5187.77 

8431.67 

2593.98 

4215.83 

1729.43 

2810.56 

1297.19 

2107.92 

1037.87 

1686.33 

20 

5189.29 

8433.33 

2594.74 

4216.67 

729.94 

2^11.11 

1297.57 

2108.33 

10:38.17 

1686.67 

21 

5190.78 

8485.00 

2595.48 

4217.50 

1730  44 

2811.67 

1297.95 

2108.75 

1038.47 

1687.00 

22 

5192.27 

8436.67 

£598.88 

4218.33 

1730.93 

2812.22 

1298.32 

2109.17 

103S  77 

1687.33 

23 

5193.78 

8498.83 

2596.99 

4219.17 

1731.44 

2812.78 

1298.70 

2109.58 

1039.07 

1687.67 

24 

5195.30 

8440.00 

2597.75 

4220.00 

1731.95 

2813.33 

1299.08 

2110.00!  1039.  38 

1688.00 

ft  FJ 

5196.82 

8441.67 

2598.51 

4220.  8S 

1732.45 

2813.89 

1299.46 

21  10.  42!  1039.  68 

1688.  33 

3<i 

5198.34 

SI  43.  33 

2599.27 

4221.67 

1732.96 

2814.44 

1299.84 

21  10.  83|1  039.  99 

1688.67 

37 

5199.89 

S445.002600.04 

4222.50 

1733.47 

2815.00 

1300.22 

2111  25 

1040.29 

1689.00 

28 

5201.43 

8446.6712600.81 

4223.33 

1733.99 

2815.56 

1300.61 

2111.67 

1040.60 

1689.33 

29 

5202.95 

8448.33 

2601  57 

4224.17 

1734.50 

2816.11 

1300.99 

2112.08 

1040.91 

1689.67 

30 

5204.47 

8450.00 

2602.33 

4225.00 

1735.00 

2816.67 

1301.37 

2112.50 

1041.21 

1690.00 

31 

5205.99 

8451.67 

2603.09 

4225.83 

1735.51 

2S17.22 

1301.75 

2112.92 

1041.52 

1690.33 

33 

•>207.51 

845:}  .  33 

2ii03.85 

4226.67 

1736.01 

2817.78 

1302.13 

2113.33 

1041.82 

1690.67 

33 

5209.03 

8455.00 

2604.61 

4227.50 

1736  52 

2818.33 

1302.51 

2113.75 

1042.12 

1691.00 

34 

>2!0.54 

8456.67 

2605.37 

1228.33 

17S7.03 

2818.89 

1302.89 

2114.17 

1042.43 

1691.33 

35 

5212  06 

8458.33 

2606.13 

1229.17 

1737.53 

2819.44 

1303.27 

2114.58 

1042.73 

1691.67 

36 

5213.58 

8460.00 

2606.89 

4230.00 

1738.04 

2820.00 

1303.65 

2115.00 

1043.03 

1692.00 

37 

5215.10 

8461.67 

2607.64 

4230.83 

1738.55 

2820.56 

1304.03 

2115.42 

1043  34 

1692.33 

38 

5216.62 

8463.33 

2608.40 

4231.67 

1739.05 

2821.11 

1304.41 

2115.83 

1043.64 

1692.67 

39 

5218.14 

8465.00 

2609.16 

4232.50 

1739.56 

2821.67 

1304.79 

2116.25 

1043.95 

1693.00 

40 

5219.65 

8466.67 

2609.92 

4233.33 

1740.06 

2822.22 

1305.17 

2116.67 

1044.25 

1693.33 

41 

5221.20 

8408.33 

2610.70 

4234.17 

1740.58 

2822.78 

1805.55 

2117.08 

1044.56 

1693.67 

42 

5222.75 

8470.002511.47 

4235.00 

1741.10 

2823.33 

1305.94 

2117.50 

1044.87 

1694.00 

43 

5224.27 

8471.672612.23 

4235.83 

1741.60 

2823.89 

1306.32 

2117.92 

1045.17 

1694.33 

44 

5225.  78  j  84;  3.  33  !  26  12.  99 

4236.67 

1742.11 

2824.44 

1306.70 

•2118.33 

1045.48 

1694.67 

45 

5227.30 

8475.002613.75 

4237.50 

1742.61 

2825.00 

1307.08 

2118.75 

1045.78 

1695.00 

46 

5228.82 

8476.672614.51 

4238.33 

1743.12 

2825.56 

1307.46 

2119.17 

10  46.  OS 

1695.33 

47 

5230.37 

847S.332<il5.28 

4239.17 

1743.64 

2826.11 

1307.85 

2119.58 

1046.31 

161)5.67 

48 

5231.92 

8480.00  2616  05 

1240.00 

1744.15 

2826.67 

130S.23 

2120.00 

1046.70 

1696.00 

49 

1233.43 

8481.67 

2616.81 

4240.83 

1744.66 

2827.22 

1308.61 

2120.42 

1047.01 

1696.33 

50 

5234.95 

8483  33 

2617.57 

4241  67 

1745.16 

2827.78 

1308.99 

2120.83 

1047.31 

1696.67 

51 

5236.47 

8485.002618.33 

4242.50 

1745.67 

2828.33 

1309.37 

2121.251047.61 

1697.00 

53 

5237.99 

S486  672619.09 

4243.33 

1746.18 

2828.89 

1309.75 

21  21.67;  1047.  92 

1697.33 

53 

5259.54 

84S8.33  2619  86 

4244.17 

1746.69 

2829.44 

1310  14 

2122.08  104S.23 

1697.67 

54 

5241.08 

8490.002620.64 

4245.00 

1747.21 

2830.00 

1310.52 

2122.50  1048.54 

1698.00 

55 

5242.60 

8491.672621.40 

4245.83 

1747.71 

2830.56 

1310.90 

2122.92  1048.84 

169S.33 

5(> 

5244.12 

8493  332622  16 

4246.67 

1748.22 

2831.11 

1311.  2^ 

2123.33  1049.14 

1698  C.7 

57 

5245  6718495.  00  2622.  93 

4247.50 

1748.74 

2831.67 

1311.67 

2123.75  1049.45 

1699.00 

58 

5247.21  8496.67  26-23.70 

4248.  3:j 

1749.25 

2832.2-. 

1312.06 

2124.17  1049.71* 

1699.33 

59 

5248  .  73  1  8498  .  33  2624  .  4b 

4249.17 

1749.  7b 

2832.78 

1312.44 

2124.581050.07 

1699.67 

214 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

84° 

Tan.       Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

800.215  1400.00 

737.446 

1200.00 

645.389 

1050.00573.798:933.333 

516.550 

840.000 

O 

800.408  1400.28 

737.003  1200.24 

045.579 

1050.21  573.907  933.519 

516.702 

840.167 

1 

800.721  1400.50 

737.880  1200.  4H 

045.709 

1050.42574.136 

J33.704 

516.854 

840.333 

2 

800.  975  1400.% 

738.097 

1200.71 

045.959 

1050.  63  (574.304 

J33.889 

517.007 

840.500 

3 

801.228  1401.11 

738.314 

1200.95 

640.148 

1050.83 

574.473 

934.074 

517.159 

840.667 

4 

861.481 

1401.39 

738  531 

1201  19 

640.338 

1051.04 

574.642 

934.259 

517.311 

840.833 

5 

801.734 

1401.07 

738.748 

1201.43 

046.528 

1051.25 

574.811 

134.444 

517.463 

841.000 

G 

861.983 

1401.94 

738.901 

1201.07 

040.715 

1051.46 

574.977 

934.630 

517.612 

841.167 

7 

802.231 

1402.2;.' 

739.174 

1^01  90 

046.901 

1051.67 

575.142 

934.815 

517.761 

841.333 

8 

802.484 

1402.50 

739.391 

1202.14 

647.091 

1051.88 

575.311 

J35.000 

517.913 

841.500 

9 

862.737 

1402.78 

739.008 

1202.38 

647.281 

1052.08 

575.480 

935.185 

518.065 

841.667 

10 

862.900 

1403.00 

739.825 

1202.62 

647.471 

1052.29 

575.649 

)35.370 

518.217 

841.  833 

11 

883.244 

1403.33 

740.042 

1202.86 

617.661 

1052.50 

575.818 

935.556 

518.369 

842.000 

13 

803.497 

1403.61 

740.259 

1203.10 

647.851 

1052.71 

575.987 

935.741 

518.521 

842.167 

13 

863.750 

1103.89 

740.476 

1203.33 

648.041 

1052.92 

576.156 

935.92(5 

518.673 

842.333 

14 

864.003 

1404.17 

740.693 

1203.57 

048.231 

1053.13 

576.325 

J36.111 

518.825 

842.500 

15 

804.256 

1404.44 

740.910 

1203.81 

048.421 

1053.33 

576.494 

936.296 

518.977 

842.667 

1O 

804.509 

1404.72 

741.127 

1201.05 

048.611 

1053.54 

576.662 

936.481 

519.129 

842.833 

17 

864.763 

1405.00 

741.344 

1204.29 

648.801 

1053.75 

576.831 

936.667 

519.281 

843.000 

18 

865.010 

1405.2b 

741.561 

1204.52 

648.990 

1053.96 

577.000 

930.852 

519.433 

843.167 

19 

865.269 

1405.56 

741.778 

1204.76 

649.180 

1054.17 

577.  1G9 

937.037 

519.585 

843.333 

3O 

865.517 

1405.83 

741.991 

1205.00 

049.307 

1054.38 

577.335 

937.222 

519.734 

843.500 

31 

805.  7C6 

1406.11 

742.204 

1205.24 

ti49  553 

1054.58 

577.500 

937.407 

519.884 

843.667 

33 

800.019 

1400.39 

742.421 

1205.48 

04!)  .  743 

1054.7U 

577.669 

937.593 

520.030 

843.833 

33 

800.272 

1406.07 

742.638 

1205.71 

049.933 

1055.00 

577.838 

937.778 

520.188 

844.000 

34 

800.525 

1400.94 

742.855 

12-J5.95 

050.  123 

1055.21 

578.007 

937.903 

520.340 

844.167 

35 

806.778 

1407.22 

743.072 

200.19 

050.313 

1055.42 

578.176 

938.148 

520.492 

844.333 

36 

867.036 

1407.50 

743.293 

1206.43 

050.500 

1055.63 

578.348 

J38.333 

520.047 

844.500 

37 

807.294 

1407.78 

743.514 

1206.67 

050.  7XX) 

1055.83 

578.520 

938.519 

520.801 

844.667 

38 

807.548 

1408.00 

743.  73  •> 

1206.90 

650.890 

1056.04 

578.089 

938.704 

520.953 

844.8:33 

39 

887.801 

1408  33 

743.949 

1207.14 

651  .080 

1056.25 

578.858 

938.889 

521.106 

845.000 

3O 

868.054 

1408  0] 

744.160 

1207.38 

(55  1.270 

1056.46 

579.027 

939.074 

521.258 

845.167 

31 

868.307 

1408  89 

744.383 

1207.62 

651.400 

105(5.67 

579.196 

939.259 

521.410 

845.333 

33 

688.600 

868.813 

1409.17 
1409.44 

744.  600  j  1207.  86 
744.817  1208.10 

051.050 
051.840 

1056.88 
1057.08 

579.304 
579.533 

939.444 
939.030 

521.562 
521.714 

845.500 
845.667 

33 
34 

809.067 

1409.72 

745.  034  11208.  33 

052.030 

1057.29 

579.702 

939.815 

521.806 

845.833 

35 

869.320 

1410.00 

745.251  1208.57 

052.220 

1057.50 

579.871 

940.000 

522.018 

846.000 

36 

869.573 

1410.28 

745.468 

1208.81 

052.410 

1057.71 

580.040 

940.185 

522.170 

84(5.167 

37 

869.826 

1410.56 

745.  685  |1209.  05 

052.599 

1057.92 

580.209 

940.370 

522.322 

846.333 

38 

870.079 

1410.83 

745.902 

1209.29 

052.789 

1058.13 

580.378 

940.550 

522.474 

846.500 

39 

870.332 

1411.11 

746.119 

1209.52 

052.979 

1058.33 

580.547 

940.741 

522.626 

846.667 

4O 

870.590 

1411.39 

746.340 

1209.70 

053.173 

1058.54 

580.719 

940.920 

522.781 

846.833 

41 

870.848 

1411.67 

746.501 

1210.00 

653.366 

1058.75 

580.891 

941.111 

522.936 

847.000 

43 

8  VI.  102 

1411.91 

746.778 

1210.24 

653.550 

1058.96 

581.060 

941.296 

523.088 

847.167 

43 

871..  355 

1412.22 

740.995  1210.48 

653.746 

1059.17 

581.228 

941.481 

523.240 

847.333 

44 

871.608 

1412.50 

747.212  1210.71 

653.936 

1059.38 

581.397 

941.667 

523.392 

847.500 

45 

871.861 

1412.78 

747.429 

1210.95 

661.1:36 

1059.58 

581.566 

941.852 

523.544 

847.667 

46 

872.119 

1413.  00 

747.651 

1211.19 

654.320 

1059.79 

581.738 

942.037 

523.699 

847.833 

47 

872.377 

1413.  33 

747.872  1211.43 

054.513 

1060.00 

581.910 

942.222 

523.853 

848.000 

48 

872.630 

1413.61 

748.  OS9  1211.67 

654.703 

1060.21 

582.079 

942.407 

524.006 

848.167 

49 

872.883 

1413.89 

748.  3061  1211.  90 

654.893 

1060.42 

582.248942.593 

524.158848.333 

5O 

873.130 

1414.17 

748.523  1212.14 

655.083 

1060.  63^2.417  942.  778 

524.310848  500 

51 

873.390 

1414.44 

748.740  1212.38 

055.273 

1060.  831582.  586  942.  %3 

524.462848.667 

53 

873.048 

1414.72 

748.961 

1212.62 

055.407 

106  1.04  582.  758  943.148 

524.617848.838 

53 

873.906 

1415  00 

749.18", 

1^12.80 

055.000 

106  1.25  582.  930  943.  333 

524.771!  849.(KK) 

54 

874.  159  14T,.  28 

749.391 

1213.10 

055.  S50 

10(51.46 

583.099913.519 

524.923  849  167 

55 

874.412  1415.50 

749.616 

1213.33 

05«*.  040 

1001.07 

583.208943.704 

525.075849.333 

56 

874.070  1415.83 

149.837 

1213.57 

650  234 

1061.88 

583.440 

943.889 

525.  230  849.  500  1  57 

874.928  1410.11 

750.058 

1213.81 

656  427 

IOftJ.08J588.6l2 

944.074 

525.385849.667  58 

875.181  I4l6.39750.27fa 

1214.05 

656.017 

1062.  29:583.781(944.  259 

525.  537  849.833|  59 

215 


TABLE  XIV. — ACTUAL  TANGENTS,   ETC. 


85° 

1°  Curve. 

3*  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

Ivi7 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

o 

9350.25 

8500.00 

2625.22 

4250.00 

1750.2(5 

2833.  Jtt 

1312.82 

2  125.  a) 

1050.37 

1700.00 

i 

5251.80 

8501.67 

2625.99 

4250.83 

1750.78 

2833.89 

1313.20 

2125.42 

1050.68 

1700.33 

<£ 

5253.34 

8503.33 

2626.77 

4251.67 

1751.30 

2834.44 

1818.59 

2125.83 

1050.99 

1700.0? 

3 

5254.86 

8505.00 

2627.53 

4252.50 

1751.80 

2835.00 

1313.97 

2126.25 

1051.29 

1701.00 

4 

5256.38 

8506.67 

2628.29 

4253.33 

1752.31 

2835.56 

1314.35 

2126.67 

1051.60 

1701.33 

5 

5257.93 

8508.33 

2629.06 

4254.17 

1752.82 

2836.11 

1314.74 

2127.08 

1051.91 

1701.07 

6 

5259.47 

8510.00 

2629.83 

4255.00 

1753.34 

2836  67 

1315.12 

2127.50 

1052.22 

1702.00 

7 

5260.99 

8511.67 

2630.59 

4255.83 

1753.85 

2837.22 

1315.50 

2127.92 

1052.52 

1702.33 

8 

5262.51 

8513.33 

2631.35 

4256.67 

1754.3.5 

2837.78 

1315.88 

2128.33 

1052.82 

1702.67 

9 

5264.06 

8515.00 

2632.13 

4257.50 

1754.87 

2838.33 

1316.27 

2128.75 

1053.13 

1703.0J 

10 

5265.61 

8516.67 

2632.90 

4258.33 

1755.38 

2838.89 

1316.66 

2129.17 

1053.44 

1703  33 

11 

5267.15 

8518.33 

2633.67 

4259.17 

1755.90 

2839.44 

1317.04 

2129.58 

1053.75 

1703  67 

13 

5268.70 

8520.00 

2634.45 

4260.00 

1756.41 

2840.00 

1317.43 

2130.00 

1054.06 

1704.00 

13 

5270.22 

8521.67 

2635.21 

4260.83 

1756.92 

2840.56 

1317.81 

2130.42 

1054.37 

1704.  3'} 

14 

5271.74 

8523.33 

2635.96 

4261.67 

1757.43 

2841.11 

1318.19 

2130.83 

1054.67 

1704.07 

15 

5273.28 

8525.00 

2636.74 

4262.50 

1757.94 

2841.67 

1318.58 

2131.25 

1054.98 

1705.00 

16 

5274.83 

8526.67 

2637.51 

4263  33  1758.46 

2842.22 

1318.96 

2131.67 

1055.29 

1705.33 

17 

5276.38 

8528.33 

2638.29 

4264.17 

1758.97 

2842.78 

1319.35 

2132  08 

1055.60 

1705.07 

18 

5277.92 

8530.00 

2639.06 

4265.00 

1759.49 

2843.33 

1319.74 

2132.50 

1055.91 

1706.00 

19 

5279.47 

8531.67 

2639.83 

4265.83 

1760.01 

2843.89 

1320.12 

2132.92 

1056.22 

1706.33 

20 

5281.02 

8533.33 

2640.61 

4266.67 

1760.52 

2844.44 

1320.51 

2133.33 

1056.53 

1708.67 

31 

5282.57 

85&5.00 

2641.38 

4267.50 

1761.04 

2845.00 

13-30.90 

2133.75 

1056.84 

1707.00 

33 

5284.11 

8536.67 

2642.15 

4268.33 

1761.55 

2845.56 

1321.28 

2134.17 

1057.15 

1707.33 

33 

5285.63 

8538.33 

2642.91 

4269.17 

1762.06 

2846.11 

1321.66 

2134.58 

1057.45 

1707.67 

34 

5287.15 

8540.00 

2643  67 

4270.00 

1762.56 

2846.67 

1322.04 

2135.00 

1057.75 

1708.00 

35 

5288.70 

8541.67 

26-14.44 

4270.83 

1763.08 

2847.22 

1322.43 

2135.42 

1058.06 

1708.33 

36 

5290.24 

8543.33 

2645.22 

4271.67 

1763.60 

2847  .  78 

1322.82 

2135.83 

1058.37 

1708.67 

37 

5291.79 

8545.00 

2645.99 

4272.50 

1764.11 

2848.33 

1323.20 

2136.25 

1058.68 

1709.00 

38 

5293.34 

H546.67 

2646.77 

4273.33 

1764.63 

2848.89 

1323.59 

2136.67 

1058.99 

1709.33 

39 

5294.88 

8548.33 

2647.54 

4274.17 

1765.14 

2849.44 

1323.98 

2137.08 

1059.30 

1709.67 

30 

5296.43 

8550.00 

2648.31 

4275.00 

1765.66 

2850  00 

1324.36 

2137.50 

1059.61 

1710.00 

31 

5297.98 

8551.67 

2649.  01) 

4275.83 

1766.17 

2850.56 

1324.75 

2137.92 

1059.92 

1710.33 

33 

5299.53 

8553.33 

2649.86 

4276.67 

1766.69 

2851.11 

1325.14 

2138.33 

1000.23 

1710.67 

33 

5301.07 

H555.00 

2650.63 

4277.50 

1767.21 

2851.67 

1325.52 

2138.75 

1060.54 

1711.00 

34 

5302.62 

ci5.56.67 

2651.41 

4278.33 

1767.72 

2852.22 

1325.91 

2139.17 

1060.  85 

1711.33 

35 

5304.17 

8558.33 

2652.18 

4279.17 

1768.24 

2852.78 

1326.30 

2139.58 

1061.16 

1711.67 

36 

5305.71 

8560.00 

2652.95 

4280.00 

1768.7.5 

2853.33 

1326.69 

2140.00 

1061.47 

1712.00 

37 

5307.26 

8561.67 

2653.73 

4280.831769.27 

2853  89 

1327.07 

2140.42 

1061.78 

1712.33 

38 

5308.81 

8563.33 

3654.50 

4281.67  1769.78 

2854.44 

1327.46 

2140.83 

1062  09 

1712.67 

39 

5310.35 

8565.00 

3655.27 

4282.50 

1770.30 

2855.00 

1327.85 

2141.25 

1062.40 

1713.00 

4O 

5311.90 

8566.67 

2656.05 

4283.33 

1770.82 

2855.56 

1328.23 

2141.67 

1062.70 

1713.33 

41 

5313.45 

8568.33 

2656.82 

4284.171771.33 

2856.11 

1328.62 

2142.08 

1063.01 

1713.07 

43 

5315.00 

8570.00 

2657.60 

4285.00  1771.85 

2856.67 

1329.01 

2142  50 

1063.32 

1714.00 

43 

5316.54 

8571.67 

2658.37 

4285.  83  |1772.  36 

2857.22 

13-29.39 

2142.92 

1063.63 

1714.33 

44 

5318.09 

8573.33 

2659.14 

4286.67 

1772.88 

2857.  78  !  1329.  7  8 

2143.33 

1063.94 

1714.67 

45 

5319.66 

8575.00 

2659.93 

4287.50 

1773.40 

2858.331330.17 

2143.75 

1064.26 

1715.00 

46 

5321.24 

8576.67 

2660.72 

4288.33 

1773.93 

•3858.89  1330.57 

2144.17 

1061.57 

1715.33 

47 

5322.79 

8578.33 

2661.49 

4289.17 

1774.44 

2859.44  1330.95 

2144.58 

1064.88 

1715.67 

48 

5324.33 

8580.00 

2662.26 

4290.00 

1774.96 

2860.00  1331.34 

2145.00 

1065.19 

1716.00 

49 

5325.88 

8581.67 

3(563.04 

4290.83 

1775.48 

2860.56 

1331.73 

2145.42 

1065.50 

1716.33 

50 

5327.43 

8583.33 

2663.81 

4201.67 

1775.99 

2801.11 

1332.122145.83 

1065.81 

1710  07 

51 

5328.98 

8585.00 

3664.59 

4292.50 

1776.51 

2861.67i  1332.  50  2  146.  25 

1006.12 

1717.00 

53 

5330.52 

8586.67 

3665.36 

4293.33 

1777.02 

3862.22  1332.89  2146.67 

1006.43 

1717.33 

53 

5332.07 

8588.33 

2666.13 

4294  17 

1777.54 

2862  78  1333.282147.08 

1000.74 

1717.07 

54 

5333.62 

8590.00 

3666  91 

4295.00 

1778.06 

2863.33  1333.60  2147.50 

1067.05 

1718.00 

55 

5335.19 

8.591  .  67 

2667.69 

4295.83  1778.58 

2803.89  1334.015  2147.92 

1067.36 

1718.33 

56 

5&36.77 

8593.33 

2668.48 

4296  .  07 

1779.11 

2864.44  1334.452148.33 

1067  68 

1718.67 

57 

5338  31 

8595.00 

2069.26 

4297  50177'9.62 

2865.00  1334.842148.75 

1007.99 

1719.00 

58 

5339.86 

8596.67 

2070.03 

4298.331780.14 

2805.56  1335.222149.17 

1068  30 

1719.33 

59 

5341.44 

8598.33 

2670.82 

4299.  17I1780.  6612866.  11  1335.62  2149.58 

1068.01 

719.07 

216 


TABLE  XTV.— ACTUAL  TANGENTS,  ETC 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

85° 

Tan. 

Arc. 
1416.67 

Tan. 

Arc. 

Tan. 

Am 

1062.50 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

875.434 

750.493 

1214.29 

656.807 

583.950944.444 

525.689850.000 

O 

875.692 

1416.94 

750.714 

1214.52 

657.000 

1062.71 

584.122944.630 

525.  844  i  850.  167 

1 

875.950 

1417.22 

750.935 

1214.76 

657.194 

1062.92 

584.294:944.815 

525.999 

850.333 

2 

87(5.203 

1417.50 

751.152 

1215.00 

657.384 

1063.13 

584.463945.000 

520.151 

850.500 

3 

876.450 

1417.78 

751.369 

1215.24 

657.574 

1063.33 

584.631 

945.185 

526.303 

850.667 

4 

876.714 

1418.06 

751.590 

1215.48 

657.767 

1063.54 

584.804 

945.370 

526.458 

850.833 

5 

876.972 

1418.33 

751.811 

1215.71 

657.961 

1063.75 

584.976 

945.556 

526.613 

851.000 

6 

877.225 

1418.61 

752.028 

1215.95 

658.151 

1063.96 

585.144 

945.741 

526.765 

851.167 

7 

877.479 

1418.89 

752.245 

1216.19 

658.341 

1064.17 

585.313 

945.926 

526.917 

851.333 

8 

877.737 

1419.17 

752.466 

1216.43 

658.534 

1064.  08 

585.485 

946.111 

527.072 

851.500 

9 

877.995 

1419.44 

752.688 

1216.67 

658.728 

1064.58 

585  657 

946.296 

527.227 

851.667 

10 

878.252 

1419.72 

752.909 

1216.90 

658.921 

1064.79 

585.830 

946.481 

527.382 

851.833 

11 

878.510 

1420.00 

753.130 

1217.14 

659.115 

1065.00 

586.002 

946.667 

527.537 

852.000 

12 

878.764 

1420.28 

753.347 

1217.38 

659.305 

1005.21 

586.170 

946.852 

527.689 

852.167 

13 

879.017 

1420.56 

753.564 

1217.62 

659.495 

1065.42 

586.339 

947.037 

527.841 

852.333 

14 

879.275 

1420.83 

753.785 

1217.80 

659.688 

1065.03 

586.511 

947.222 

527.996 

852.500 

15 

879.5:33 

1421.11 

754.000 

1218.10 

659.882 

1005  83 

586.683 

947.407 

528.150 

852.667 

16 

879.791 

1421.39 

754.227 

1218.33 

660.075 

1000.04 

586.856 

947.593 

528.305 

852.833 

17 

880.049 

1421  .  67 

754.448 

1218.57 

600.269 

1066.25 

587.0^8 

947.778 

528.460 

853.000 

18 

880.307 

1421.94 

754.670 

1218.81 

660.463 

1066.46 

587.200 

947.963 

528.615 

853.167 

19 

880.  5G4 

1422.22 

754.891 

1219.05 

660.656 

1066.67 

587.372 

948.148 

528.770 

853.333 

2O 

860.822 

1422.50 

755.112 

1219.21 

660.850 

1066.88 

587.544 

948.333 

528.925 

853.500 

21 

881.080 

1422.78 

755.333 

1219.52 

661.043 

1067.08 

587.716 

948.51'. 

529.080 

853.  £67 

22 

881.334 

1423.00 

755.550 

1219.76 

001.233 

1067.29 

587.885 

948.704 

529.232 

853.833 

23 

881.587 

1423.33 

755.767 

1220.00 

661.423 

1067.50 

588.054 

948.889 

529.384 

854.000 

24 

881  '.845 

1423.61 

755.988 

1220.24 

661.617 

1067.71 

588.226 

949.074 

529.539 

854.167 

25 

882.103 

1423.89 

756.209 

1220.48 

601.810 

1067.92 

588.398 

949.259 

529.694 

854.333 

26 

882.301 

1424.17 

756.430 

1220.71 

602.004 

1068.13 

588.570 

949.444 

529.849 

&54.500 

21 

882.619 

1424.44 

i  56.  652 

1220.95 

662.197 

1068.33 

588.742 

949.630 

530.003 

854.667 

28 

882.876 

1424.72 

756.873 

1221.19 

662.391 

1068.54 

588.914 

949.815 

530.158 

854.833 

29 

883.134 

1425.00 

757.094 

1221.43 

662.584 

1068.75 

589.086 

950.000 

530.313 

855.000 

30 

883.392 

1425.2b 

757.315 

1221.67 

662.778 

1068.96 

589.258 

950.185 

530.468 

855.167 

31 

883.650 

1425.56 

757.536 

1221.90 

662.971 

1069.17 

589.430 

950.370 

530.623 

855.333 

32 

883.908 

1425.83 

757.757 

1222.14 

663.165 

1009.38 

589.602 

950.  55t 

530.77'8 

855.500 

33 

884.160 

1426.11 

757.97'8 

1222.38 

663.358 

1069.58 

589.774 

950.741 

530.933 

855.667 

34 

884.424 

1426.  3U 

758.200 

1222.62 

603.552 

1069.79 

589.946 

950.  92f 

531.088 

855.833 

35 

884.682 

1426.67 

758.421 

1222.86 

663.745 

1070.00 

590.118 

951.111 

531.243 

856.000 

36 

884.940 
885.198 

1426.94 
1427.22 

758.64-J 
758.863 

1223.10 
1223.33 

663.939 
664.132 

1070.21 
1070.42 

590.290951.291 
590.462951.481 

531.398 
531.552 

856.167 
856.333 

37 

38 

885.456 

1427.50 

759.084 

1223.57 

664.326 

1070.63 

590.635 

951.667 

531.707 

856.500 

39 

885.714 

1427.78 

759.305 

1223.81 

664.520 

1070.83 

590.807 

951.852 

531.862 

856.667 

40 

885.972 

1428.06 

759.526 

1224.05 

664.713  1071.04 

590.979 

952.037 

532.017 

856.833 

41 

886.230 

1428.33 

759.747 

1224.29664.907  1071.25 

591.151 

952.222 

532.172 

857.000 

42 

886.488 

1428.61 

759.969 

1224.52 

665.  100  1  1071.  46 

501.828 

952.407 

532.327 

857.167 

43 

886.746 

1428.89 

760.190 

1224  76 

665.294  1071.67 

591.495 

952.593 

532.482 

S57  333 

44 

887.008 

1429.17 

760.415 

1225.00665.491  1071.H8 

591.670952.778 

532.640 

857.500 

45 

887.271 

1429.44 

700.640 

1225.24  665.688  1072.08 

591.845952.963 

f  32.  797 

857.667 

46 

887.  529  11429.  72 

760.801 

1225.48665.881  1072.29 

592.017953.148 

532.952 

857.833 

47 

887.787 

1430.00 

761.082 

1225.71 

606.075  1072.50 

592.189953.333 

533.107 

858.000 

48 

888.045 

1430.28 

761.304 

1225.95 

666.268 

1072.71 

592.362 

953.519 

533.262 

858.167 

49 

888  303 

1430.56 

761.525 

1226.19 

666.462 

1072.92 

592.534 

953.704 

533.417 

858.333 

50 

888.561 

1430.83 

761.746 

1226.43666.656  1073.13 

592.706  1953.  889 

533.572 

858.500 

51 

888.819 

1431.11 

761.967 

1226  67660.849  1073.33 

592.8781954.074 

533.727 

858.667 

52 

889.077 

1431.39 

762  .  1  88  1  226  .  90  667  .  043  1  0?  3  .  54 

593.050954.259 

533.  8S2'  858.  833 

53 

889.335 

1431.67 

702.409  1227.14  607  236  1073.75 

593.222954.444 

534.036859.000 

54 

889.598 

1431.94 

702  035  1227.38  667.433  1073.96 

593.397  954.030 

534.194859.167 

55 

889  860 

1432.22 

702.800  1227.62  067  630  1074.17 

593.572954.815 

534.352859.333 

56 

890.118 

1432.50 

763.081  1227.80  667.824  1074.38 

593.  74  4  :  955.  000 

534.507859.500 

57 

890.376 

1432.78 

763  .  302  1  228  .  1  0  008  .  01  7  1074  58 

593  916955.185 

534.662859.667 

58 

890.639 

1433.06 

703.527  1228.33  608.215  1074.79 

594.092955.370 

534.8201859.833 

59 

217 


TABLE   XIV. — ACTUAL   TANGENTS,    ETC. 


86° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan.    j    Arc. 

Tan. 

Arc. 

Tan. 

Are. 

Tan. 

Arc. 

Tan. 

Arc. 

0 

5343.01  8600.00 

2671.604300.00 

1781.19 

2806.67 

1336.01 

2150.00  1068.  93  S  720.00 

1 

5344.  56  8001.  07' 

2672.384300.83 

781.70 

2867.22 

1330.40 

2150.421069.24    720.33 

2 

5340.11  8603.33 

2673.154301.67 

782.22 

2867.78 

1336.79 

2150.83  1069.55!  720.07 

3 

5347.658605.00 

2673.934302.50 

782.  73 

2868.33 

1337.17 

2151.25  1069.  S6,  721.00 

4 

5349.208606.07 

.'674.70  4303.  33 

783.25 

2868.89 

1337.56 

2151  6711070.17 

721.33 

5 

5350.788608  33 

2075.494304.17 

783.78 

2869.44 

1337.95 

2152.08  1070.48 

721.67 

6 

5352.358610.00 

2  '.76.  27  4305.  00 

1784.30 

2870.00 

1338  35 

2152.50 

1070.80 

722.00 

7 

5353.5)0 

8611.67 

2077  05  4305  83 

1784  82 

28?'0.56 

1338.73 

2152.92 

1071.11 

722  33 

8 

5355.45 

8613.33 

2677.824306.67 

1785.33 

2871.11 

1339.12 

2158.88 

1071.42 

1722.67 

9 

5857.02 

8615.00 

2678.61 

4307.50 

1785.86 

2871.67 

1339.52 

2153.75 

1071.73 

1723.00 

1O 

5358.60 

8616.67 

2679  40 

4308.33 

1786.38 

2872.22 

1339.91 

2154.17 

1072.05 

1723.33 

li 

5360.14 

8618.33 

2680.17 

4309.17 

1786.90 

2872.78 

1340  30 

2154.58 

1072.36 

723.67 

12 

5361.698620.00 

2680.94 

4310.00 

1787.41  2873.33 

1340.68 

2155.00 

1072.67 

1724  00 

13 

5363.2786:21.67 

2681.73 

4310.83 

1787.942873  89 

1341.08 

2155.42 

1072.98 

1724.33 

14 

5364.84 

8623.33 

2682.52 

4311.67 

1788.47;2874.44 

1341.47 

2155.83 

1073.30 

1724.67 

15 

5366.4-2 

862500 

2683.31 

4312.50 

1788.992875.00 

1341.86 

2156.25 

1073.61 

1725  00 

16 

5367.99 

8626.67 

2684.10 

4313.33 

1789.522875  56 

1342.26 

2156.67 

1073.93 

1725.33 

17 

5369.54 

8628.33 

2684.87 

4814.1; 

1790.032876.11 

1342.65 

2157.08 

1074.24 

1725.67 

18 

5371.09 

8630.00 

2685.64 

4315.00 

1790.552876.6? 

1343  03 

2157.50 

1074.55 

1726.00 

19 

5372.66 

8631.67 

2686.43 

4315.83 

1791.07 

2877.22 

1343.43 

2157.92 

1074.86 

1720.33 

2O 

5374.24 

8633  33 

2687.22 

4316.67 

1791.602877.78 

1343.82 

2158.33 

1075.18 

1726.67 

21 

5375.82 

8635  00 

2688.01 

4317.50 

1792.122878.33 

1344.21 

2158.75 

1075.49 

1727.00 

22 

5377.39 

8636  67 

26^8  79 

4318  33 

1  792.  65  !  287  8.  89 

1344.61 

2159.17 

1075.81 

1727.33 

23 

5378.91 

8638.33 

2689.57 

4319.17 

1793.  16|  2879.  44 

1345.00 

215!)  5S 

1076.12 

1727  67 

34 

5380.49 

8640.00 

2690.34 

4320.00 

1793.682S80.00 

1345.38 

2160.00 

1076.43 

1728.00 

25 

5382.06 

8641.67 

2691.13 

4320.83 

1794.202880.56 

1345.78 

2160  42 

1076.74 

1728.33 

26 

538  i.  64 

8643.33 

2691.92 

4321.6? 

1794.732881.11 

1346.17 

2160.83 

1077.06 

1728.67 

27 

5385.21 

8645.00 

2693.70 

4322.50 

1795.262881.6? 

1346.56 

2161.25 

1077.37 

1729.00 

28 

5386.79 

8616.67 

2093.49 

4323.33 

1795.782882.22 

1346.96 

2161.67 

1077.69 

1729.33 

39 

5388.36 

8648.33 

2094.28 

4324.17 

1796.31 

2882.78 

1347.35 

2162.08 

1078.00 

1729.67 

3O 

5389.94 

8650.00 

2695.07 

4325.00 

1796.832883.33 

1347.75 

2162  50 

1078.32 

1730.00 

31 

5391.49 

8051  or 

2695.84 

4325.83 

1797.  35;  2883.  89 

1348.13 

2162.92 

1078.03 

7'30.33 

32 

5393.03 

S053  33 

2096.62 

4326.67 

1797'.  86  2884.  44 

1348.52 

2103.33 

1078.94 

1730.67 

33 

5394.61 

8655.00 

v!697.40 

4327.50 

1798.392885.00 

1348.91 

2163.75 

1079.25 

1731.00 

34 

5396.18 

8656  67 

2698.19 

4328.33 

1798.91  2885.56 

1349.31 

2164.17 

1079.57 

1  731.33 

35 

5397.76 

8658.33 

2698.98 

4329.17 

1799.44 

2886.11 

1319.70 

2164.58 

1079.88 

1731.07 

36 

5399.34 

8660.00 

2699.77 

4330.00 

1799.96 

2886.6? 

1350.10 

2165.00 

1080.20 

1732  00 

37 

5100.91 

8661.67 

2700.55 

4330.83 

1800.49 

2887.22 

1350.40 

2165.42 

1080.51 

1732.33 

38 

5402.49 

S663.33 

-!701.34 

4331.67 

1801  01 

2887.78 

1350.88 

2105.83 

1080.83 

1732.07 

39 

5404.06 

8665.00 

2702.13 

4332.50 

1801.54 

2888.33 

1351.28 

2166.25 

1081.14 

1733.00 

4O 

5405.64 

8666.67 

2702.92 

4333.33 

1802  00 

2888.89 

1351.67 

2166.67 

1081.40 

1733.33 

41 

5107.21 

8668.33 

2703  71 

4334  17 

180;.  59  2889.  44 

1352.07 

2167.08 

1081.77 

1733.67 

42 

5408.79 

8670.00 

2704.49 

4335.00 

1803.122890.00 

1352.40 

2167.50 

1082.09 

1734.00 

43 

5110.37 

8671.67 

2705.28 

4335.83 

1803.642890.56 

13  -.2.85 

2167.92 

1082.40 

1734.33 

44 

5411  94 

8673.33 

2706.07 

4336  67 

1804.172891.11 

1353.25 

2168.33 

1082.72 

1734.67 

45 

5413.52 

8675.00 

2706.86 

4337.50 

1804.692891.67 

1358.04 

2168.75 

1083.03 

1735.00 

46 

5415.09 

8676.67 

2707.65 

1338.33 

1805.222892.22 

1354.04 

2169.17 

1083  35 

1735.33 

47 

5416.67 

8678.33 

2708.43 

4339.17 

1805.74  2892.78 

1354.43 

2169.58 

1083.66 

1735.67 

48 

5418.24 

80SO  00 

2709.22 

4340.00 

1806.272893.33 

1354.82 

2170.00 

1083.98 

1736.00 

49 

5419.82 

8681.67 

2710.01 

4310.83 

1806.792893.89 

1355.22 

2170.42 

1084.29 

1736.33 

5O 

5421.39 

8083.33 

2710.80 

4341.67 

1807.322894  44 

1355.01 

2170.83 

1084.61 

1736.67 

51 

5423.00 

8685.00 

2711.60 

4342.50 

1807.85  2895.  00 

1356.01 

2171.25 

1084.93 

1737.00 

52 

5424.60 

8686.67 

2712.40 

4343.33 

1808.392895.56 

1350.41 

2171.67 

1085.25 

1737.33 

53 

5426.18 

8688  33 

2713.19 

4344.17 

1808.91  2896.11 

1356.81 

2172.08 

1085.57 

IT87.67 

54 

5427.75 

8090.00 

2713.98 

4345.00 

1809.442S90  67 

1357.20 

2172.50 

1085.88 

738.00 

55 

5429.33 

8691.67 

2714.71; 

4345.83 

1809.962S97.22 

1357  60 

2172.92 

1086.20 

738.33 

56 

5430.91 

H693  33 

2715.55 

-1346.67 

1810.492S97.7S 

1357.99 

2173.33 

1086.51 

7-58.67 

57 

5432.48 

8695.00 

2716.34 

4347.50 

1811.01  2898.33 

1358.3S 

2173.75 

1080.83 

1739.00 

58 

5434  06 

8096.67 

2717.13 

4348.33 

191  1.54  '2898.  89 

1358.78 

2174.17 

1087.14 

1739.33 

59 

5435.638698.33 

2717.92 

43  19.  1?  11812.06  2899  44 

1359.17 

2(74.58 

1087.46 

1739.67 

218 


TABLE  XIV. — ACTUAL  TANGENTS,  ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

86° 

Tan. 

Arc. 

Tan.      Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

890.90-4 

1433.  33  1763.  752  '1228.57 

668  412 

1075.00 

594.267 

955.556 

534.977 

860.000 

O 

891.160;  1433.  61  |763.  97'4|1228.  81 

608.605 

1075.21 

594.439 

955.741 

535.132 

800.167 

1 

891.41711433.89764.195 

1229.05 

668.799 

1075.  42  594.01; 

955.920 

535.287 

860.333 

2 

89i.ti75  1434.1?  764.413 

l'J'H)  >>() 

668.992 

1075.63 

594  .  783 

956.111 

535.442 

800.500 

3 

891.  9:33;  1434.44764.  03? 

1229.52 

009.180 

1075.83 

591.955 

956.290 

535.597 

860.607 

4 

892.196  1434.72764.862 

1229.70 

009.383 

1076.04 

595.130 

956.481 

535.755 

860.833 

5 

892.459  1435.00  765.087 

1230.00 

009.580 

1076.25 

595,300 

950.667 

535.912 

861.000 

6 

K92.717  1435.28  765.309 

1230.24 

669.774 

1076.46 

595.478 

956.852 

536.067 

861.167 

7 

892.9751435.50705.530 

1230.48 

009.967 

1076.67 

595.650 

957.037 

536.222 

861.333 

8 

893.237 

1435.83 

765.755 

1230.71 

070.164 

1076.88 

595.825 

957.222 

536.380 

861.500 

9 

893.500 

1436.11 

765.980 

1-230.95 

670.361 

1077.08 

596.000 

957.407 

536.538 

861.667 

1O 

893.758 

1430.39 

766  201 

1231.19 

670.555 

1077.29 

596.172 

957.593 

536.693 

861.833 

11 

894.010 

1436.67 

766.422 

1231.43 

670.748 

1077.50 

590.344 

957.778 

536.848 

862.000 

12 

894.279 

1436.94 

766  648 

1231.67 

670.945 

1077.71 

596.520 

957.963 

537.005 

862.167 

13 

894.542 

1437.22 

766.873 

1231.90 

671.143 

1077.92 

596.695 

958.148 

537.163 

862.333 

14 

894.804 

1437.50 

767.098 

1232.14 

671.340 

1078.13 

596.870 

958.333 

537.321 

862.500 

15 

895.067 

1437.78 

767.323 

1232.38 

671.537 

1078  33 

597.045 

958.519 

537.479 

862.667 

16 

895  .  325 

1438.06 

767  .  545 

1232.02 

071.730 

1078.54 

597.218 

958.704 

537.634 

862.833 

17 

895.583 

1438.33 

767.706 

1232.86 

671  .  924 

1078.75 

597.390 

958.889 

537.788 

803.000 

18 

895.846 

1438.61 

767.991 

1233.10 

672.121 

1078.90 

597.565 

959.074 

537.946 

863.167 

19 

896.108 

1438.89 

768.216 

1233.33 

672.318 

1079.17 

597.740 

959.259 

538.104 

863.333 

20 

896.  3U 

1439.17 

768.441 

1233.57 

672.515 

1079.38 

597.915 

959.444 

538.262 

803.500 

21 

890.634 

1439.44 

768.667 

1233.81 

672.712 

1079.58 

598.091 

959.630 

538.419 

863.667 

22 

896.892 

1439.72 

768.888 

1234.05 

672.906 

1079.79 

598.263 

959.815 

538.574 

863.833 

23 

897.150 

1440.00 

769.109 

1234.29 

673.099 

1080.00 

598.435 

900.000 

538.729 

864.000 

24 

897.412 

1440.28 

769.334 

1234.52 

673  296 

1080.21 

598.610 

960.185 

538.887 

804.167 

25 

897.675 

1440.56 

769.559 

1234.76 

673.494 

1080.42 

598.785 

960  370 

539  045 

864.333 

26 

897.938 

1440.83 

769.785 

1235.00 

673.691 

1080.63 

598.960 

900  556 

539.203 

864.500 

2V 

898.201 

1441.11 

770.010 

1235.24 

073.888 

1080.83 

599.130 

960.741 

539.360 

864.667 

28 

898.463 

1441.39 

770.235 

1235.48 

674.085 

1081.04 

599.311 

960.926 

539.518 

864.833 

29 

898.726 

1441  67 

770.460 

1235.71 

674.282 

1081.25 

599.486 

961.111 

539.676 

865.000 

3O 

898.984 

1441.94 

770.081 

1235.95 

67'4.470 

1081.40 

599.658 

961.290 

539.831 

865.167 

31 

899.242 

1442.22 

770.903 

1236.19 

074.669 

1081.67 

599.830 

961.481 

539.986 

865.333 

32 

899.505 

1442.50 

771.128 

1236.43 

074.800 

1081.88 

000.006 

961.667 

540.143 

865.500 

33 

899.767 

1442.78 

771.353 

1236.67 

67'5.063 

1082.08 

600.181 

901.852 

540.301 

865.667 

34 

900.030 

1443.00 

771.578 

1236.90 

675.260 

1082.29 

600.356 

902.037 

540.459 

865.833 

35 

900.293 

1443.33 

771.803 

1237.14 

675.458 

1082.50 

000.531 

962.222 

540.617 

806.000 

36 

900.556 

1443.61 

772.029 

1237.38 

675.655 

1082.71 

600.707 

962.407 

540.774 

866.167 

37 

900.818 

1443.89 

772.254 

1237.62 

075.852 

1082.92 

600.88-.' 

902.593 

540.932 

806.333 

38 

901.081 

1444.17 

772.479 

1237.80 

076.049 

1083.13 

601.057 

962.778 

541.090 

866.500 

39 

901.344 

1444.44 

772.704 

1238.10 

676.246 

1083.33 

601.232 

962.963 

541.248 

866.667 

4O 

901.607 

1444.  72  1772.  930 

1238.33 

676.443 

1083.54 

601.408 

963.148 

541.400 

866.833 

41 

901.809 

1  445.  00  !  773.  155  1238.  57 

676.640 

1083.75 

601.583 

963.333 

541.563 

867.000 

43 

902.132 

1445.28773.380 

1238.81 

076.837 

1083.96 

001.758 

963.519 

541.721 

867.167 

43 

902.395 

1445.50  773.605 

1239.05 

677.034 

1084.17 

001.933 

963.704 

541.879 

867.333 

44 

902.657 

1445.8377'3.831  1239.29 

677.232 

1084.38 

602.109 

963.889 

542  037 

867.500 

45 

902  .  920  1446.11  774  .  050  !  1239  .  52 

677.429 

1084.58 

602.284 

964.074 

542.194 

867.667 

46 

903.  183  11446.  39  '774.  281 

1239.76 

677.626 

1084.79 

602.459 

964.259 

542.352 

867.833 

47 

903.446 

1446.67774.506 

1240.00 

677.823 

1085.00 

002.634 

964.444 

542.510 

868.000 

48 

903.708 

1446.94,774.731 

1240.24 

6i  8.  020 

1085.21 

602.810 

964.630 

542.668 

868.167 

49 

903.971 

1447.22774.957 

240.48 

078.217 

1085.42 

602  985  '964.  81  5 

542.825 

868.333 

50 

904.239 

1447.50775.180 

2J0.71 

678.418 

1085.63 

603.  163  1965.  000 

542.986 

868.500 

51 

904.500 

1447.78775.415 

240.95 

078.019 

1085.83 

603.342965.185 

543.147 

868.667 

52 

904.709 

1448.  00  775.  H41 

241.19078.810 

1086.04 

603.517905.370 

543.304 

808  833 

53 

905.032 

1448.33775.800 

241.43079.013 

1086.25 

603.692 

965.556 

543  402 

869.000 

54 

90.").  294 

1448.61  770.091 

241.07 

079.210 

1086.46 

603.867 

965.741 

543.620 

869.167 

55 

905  .  557 

1448.89770.310 

1241.90 

079.407 

1086.07 

604.043 

965.926 

543.778 

869.333 

56 

905.820 

1449.17770.541 

1242.14 

679.604 

1086.88 

604.218 

906.111 

543.936 

869.500 

57 

906.  082  1  1449.  44  776.  7  07 
906.  345  U449.  72  776.  992 

1242.3S679.cS01 
1242.621679.998 

1087.08 
1087.29 

604.393 
604.568 

966.296 
900.481 

544.093 
544.251 

809  007 
869.833 

58 
59 

219 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


87° 

1°  Curve. 

3°  Carve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

5437.21 

8700.00 

2718.70 

4350.00 

812.59 

2900.00 

1359.57 

2175.001087.77 

1740.00 

1 

5438.81 

8701.67 

2719.51 

4350.83 

1813.12 

2900.50 

1359.9712175.42  1088.09 

1740.33 

3 

5440.42 

8703.33 

2720.31 

4351.67 

1813.66 

2901.11 

1300.37 

2175.83  1088.42 

1740.67 

3 

o441.99 

8705.00 

2721.10 

4352.50 

814.18 

2901.67 

1360.70 

2176.25  1088.73 

1741.00 

4 

5443.57 

8706.67 

2721.88 

4353.33 

814.71 

2902.2:2 

1361.16 

2176.67  |1089.  05 

1741.33 

5 

5445  14 

8708.33 

2722.67 

4354.17 

1815.23 

2902.78 

301.55 

2177.08  1089.361741.67 

0 

5446.  7'2 

8710.00 

2723.46 

4355*.  00 

1815.76 

2903.33 

1361.94 

2177.50  1089.08 

1742.00 

7 

5448.32 

8711.67 

2724.26 

4355.83 

1816.30 

2903.89 

1362  34 

2177.92  1090.00 

1742.33 

8 

5449.93 

8713.33 

2725.06 

4356.67 

1816.83 

2904.44 

1362.75 

2178.331090.32 

1742.67 

9 

5451.50 

8715.00 

2725.85 

4357.50 

1817.36 

2905.00 

1363.14 

2178.75 

1090.63 

1743.00 

10 

5153.08 

8716.67 

2726.64 

4358.33 

1817.88 

2905.56 

1303.53 

2179.17 

1090.95 

1743.33 

11 

5454.68 

8718.33 

2727.44 

4359.17 

1818.42 

2906.11 

1363.94 

2179.581091.27 

1743.67 

13 

5456.29 

8720.00 

2728.24 

4360.00 

1818.952906.67 

1364.84 

2180.0011091  .5ft 

1744.00 

13 

5457.  80 

8721.67 

,2729.03 

4360.83 

1819.482907.22 

1304.73 

2180.42  1091.91 

1744.33 

14 

5459.44 

8723.33 

2729.82 

4361  .  67 

1820.00 

2907.78 

1305.12 

2180.  83!  1092.  22 

1744.67 

15 

5461.04 

8725.00 

2730.62 

4362.50 

1820.54 

2908.33 

1365.53 

2181.251092  54 

1745.00 

16 

5462.65 

8726.67 

2731.42 

4363.33 

1821.07 

2908.89 

13:55.93 

2181.67 

1092.86 

1745.33 

17 

5464.22 

S7'28.33 

2732.21 

4364.17 

1821  60 

2909.44 

1300.32 

2182.08 

1093.18 

1745.67 

18 

5465.80 

8730.00 

2733.00 

4365.00 

1822.12 

2910.00 

1300.71 

2182.50 

1093.49 

1746.00 

19 

5467.40 

8731.67 

2733.80 

4365.83 

1822.66 

2910.56 

1307.12 

2182.92 

1093.81 

1746.33 

3O 

5469.01 

8733.33 

2734.60 

4366.67 

1823.19 

2911.11 

1367.52 

2183.33 

1094.14 

1746.67 

31 

5470.58 

873.5.00 

2735.39 

4367.50 

1823.72 

2911.67 

1367.91 

2183.75 

1094.45 

1747.00 

33 

5472.16 

8736.67 

2736  18 

4368.33 

1824.24 

2912.22 

1368.30 

2184  17 

1094.77 

1747.33 

33 

5473.76 

8738.33 

2736.98 

4369.17 

1824.78 

2912.78 

1368.71 

2184.58 

1095.09 

1747.67 

34 

3475.37 

8740.00 

2737.78 

4370.00 

1825.  31  |2913.  33 

1369.11 

•2185.00 

1095.41 

1748.00 

35 

5476.97 

8741.67 

2738.59 

4370.83 

1825.  8512913.  89 

1309.51 

2185.42 

1095.73 

1748.33 

36 

5478.58 

8743.  33 

2739.39 

4371.67 

1826.38 

2914.44 

1309.91 

2185.83 

1096.05 

1748.07 

37 

5480.  15 

8745.00 

2740.18 

4372.50 

1826.91 

•2915.01. 

1370.30 

2186.25 

1090.37 

1749.00 

38 

5481.73 

8746.67 

2740.96 

4373.33 

1827.43 

2915.56 

1370.70 

2186.67 

1096.68 

1749.33 

39 

54^3.33 

8748.33 

2741.77 

4374.17 

1827.97 

2916.11 

1371.10 

2187.08 

1097.00 

1749.67 

3O 

5484.94 

8750.00 

2742.57 

4375.00 

1828.50 

2916.67 

1371.50 

2187.50 

1097.32 

1750.00 

31 

5486.54 

8751.67 

2743.37 

4375.83 

1829.04 

2917.22 

1371.90 

2187.92 

1097.64 

1750.33 

33 

5488.15 

8753.33 

2744.17 

4376.67 

1829.57 

2917.78 

1372  30 

2188.  33 

1097.90 

1750.67 

33 

5489.75 

8755.00 

2744  98 

4377.50 

1830  10 

2918.33 

1372.70 

2188.75 

1098.29 

1751.00 

34 

5491.35 

8756.67 

2745.78 

4378.33 

1830.64 

2918.89 

1373.10 

2189.17 

1098.61 

1751.33 

35 

5492.96 

8758.33 

2746.58 

4379.17 

1831.17 

2919.44 

1373.51 

2189.58 

1098.93 

1751.67 

36 

5494.50 

8760.00 

2747.38 

4380.00 

1831.71 

2920.00 

1373.91 

2190.00 

1099.25 

1752.00 

37 

5496.14 

8761.67 

2748.17 

4380.83 

1832.23 

2920.5e 

1374.30 

2190.42 

1099.56 

1752.33 

38 

5497.71 

8763.33 

2748.96 

4381.07 

1832.76 

2921.11 

1374.69 

2190.83 

1099.88 

1752.07 

39 

5499.32 

8765.00 

2749.76 

4382.50 

1833.29 

2021.67 

1375.10 

2191.25 

1100.20 

1753.00 

40 

5500.92 

8766.67 

2750.56 

4383.33 

1833.83 

2922.22 

1375.50 

2191.67 

1100.52 

1753.33 

41 

5502.53 

8768.33 

2751.36 

4384.17 

1834.36 

2922.78 

1375.90 

2192.08 

1100.84 

1753.67 

43 

5504.13 

8770.00 

2752.17 

4385.00 

1834  90 

2Q23.33 

1376.30 

2192.50 

1101.16 

1754.00 

43 

5505.74 

8771.67 

2752.97 

4385.83 

1835.43 

2923.89 

1376.70 

2192.92 

1101.48 

1754.33 

44 

5507.34 

8773.33 

2753.77 

4386.67 

1835.97 

2924.44 

1377.10 

2193.33 

1101.80 

1754.67 

45 

5508.94 

8775.00 

2754.57 

4387.50 

1836.50 

21)25.00 

1377.50 

2193.75 

1102.13 

1755.00 

46 

5510.55 

8776.67 

2755.38 

4388.33 

1837.04 

21)25.50 

1377.90 

2194.17 

1102.45 

1755.33 

47 

5512.15 

8778.33 

•2756.18 

4389.17 

1837.57 

2926.11 

1378.31 

2194.58 

1102.77 

1755.67 

48 

5513.76 

8780.00 

2756.98 

4390.00 

1838.11 

2926.67 

1378.71 

2195.00 

1103.09 

1756.00 

49 

5515.36 

8781.67 

2757.78 

4390.83 

1838.64 

•2927.2;. 

1379.11 

•2195.42 

1103.41 

1756.33 

50 

5516.97 

8783.33 

•2758.58 

4391.67 

1839.18 

29-27.78 

1379.51 

2195.83 

1103.73 

1756.67 

51 
53 

5518.57 
5520.17 

8785.00 
8786.67 

2759.39 
2760.19 

4392.50 
4393.33 

1839.71  2928.33 
1840.2529-28.89 

1379.91 
1380.31 

2196.25 
2196.67 

1104.05 
1104.37 

1757.00 
1757.33 

53 

5521.78 

8788.33 

2760.99 

4394.17 

1840.78 

2929.44 

1380.71 

2197.08 

1104.69 

1  757  .  67 

54 

5523.83 

8790.  (X 

•2761.79 

4395.  (X 

1841.32 

2930.  0( 

1381.11 

•2197.50 

1105.01 

1758.00 

55 

5525.02 

8791.67 

2762.61 

4395.83 

1841.86 

2930.  5( 

1881.62 

2197.9-2 

1105.34 

1758.33 

56 

5526.65 

8793.33 

•2763  43 

4396.67 

1842.41 

•2931.11 

1881.98 

2198.33 

1105.67 

1758.07 

57 

5528.2" 

879.5.  (X 

2764.23 

4397.51 

1842.912931.67 

1382.33 

2198.75 

1105.99 

1759.00 

58 

5529.80 

8796.6' 

2765.03 

4398  33 

1843.  48  21)32.  '2- 

1382.73 

2199.17 

1100.31 

1759.33 

59 

5531.40 

8798.33 

2765.83 

4399.17 

1844.  01  12932.  78 

1383  13 

2199.58 

1100.63 

1759.07 

220 


TABLE  XIV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

87° 

Tan. 

Arc. 

Tan. 

777.217 

Arc. 
1242  80 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 
544  409 

Arc. 

M. 

906.008  1450.00 

680.1951087  50 

004.744 

966.667 

870.000 

0 

900.  875  11450.  28 

777.446 

1243.10 

680.396  1087.71 

004.922 

906.  &52 

544.569 

870.167 

1 

907.143 

1450.56 

777.676 

1243.33 

680.59?  1087.9-2 

005.101 

967.037 

544.730 

870.333 

2 

907.406 

1450.83 

777.901 

1243.57 

680.794  1088.13 

005.270 

967.222 

544.888 

870.500 

3 

907.668 

1451  .  1  1 

778.126 

1243.81 

680.991  1088.33 

005.451 

967.407 

545.046 

870.667 

4 

907.931 

1451.39 

778.352 

1244.05 

681.188  1088.54 

605.626 

967.593 

545.203 

870.833 

5 

908.194 

1451.67 

778.577 

1244.29 

681.3851088.75 

605.802 

907.778 

545.361 

871.000 

6 

908.461 

1451.94 

778.806 

1244.52 

681.58(51088.96 

605.980 

967.963 

545.522 

871.167 

7 

908.729 

1452.22 

779.035 

1244.76 

681.787  1089.17 

606.158 

908.148 

545.682 

871.333 

8 

908.992 

1452.50 

779.261 

1245.00 

681.984 

1089.38 

606.334 

968.333 

545.840 

871.500 

9 

909.254 

1452.78 

779.486 

1245.24 

682.181 

1089.58 

606.500 

968.519 

545.998 

871.667 

10 

909.5ft! 

1453.06 

779.715 

1245.48 

682.3821089.79 

606.687 

068.704 

546.159 

871  .833 

11 

909.789 

1453.33 

779.945 

1245.71 

682.5821090.00 

606.866 

068.889 

546.310 

872.000 

13 

910.052 

1453.61 

780.170 

1245.95 

682.7791090.21 

607.041 

069.074 

546.477 

872.167 

13 

910.315 

1453.  89 

780.395 

1246.19 

682.977  1090.42 

607.216 

969.250 

546.635 

872.333 

14 

910.582 

1454.17 

780.624 

1246.43 

683.177 

1090.63 

607.395 

069.444 

546.795 

872.500 

15 

910.850 

1454.44 

780.854 

1246.67 

683.378 

1090.83 

607.573 

909.630 

546  956 

872.667 

16 

911.112 

1454.72 

781.079 

1246.90 

683.5751091.04 

607.748 

060.815 

547.114 

872.833 

17 

911.375 

1455.00 

781.304 

1247.14 

683.  772'  1091.  25 

607.924 

970.000 

547.272 

873.000 

18 

911.643 

1455.28 

781.533 

1247.38 

683.973 

1091.40 

008.102 

070.185 

547.432 

873.167 

19 

911.910 

1455.56 

781.763 

1247.62 

684.174 

1091.67 

60S.  281 

970.370 

547.593 

873.333 

20 

912.173 

1455.83 

781.988 

1247.86 

684.371 

1091.88 

608.456 

970.556 

547.  751 

873.500 

31 

912.436 

1456.11 

782.213 

1248.10 

684.568 

1092.08 

608.031 

070.741 

547.908 

873.667 

33 

912.703 

1456.39 

782.443 

1248.33 

684.769 

1092.29 

608.800 

970.926 

548.060 

873.833 

33 

912.971 

1456.67 

782.672 

1248.57 

084.909 

1092.50 

608.988 

971.111 

548.230 

874.000 

34 

913.238 

1456.94 

782.901 

1248.81 

685.170 

1092.71 

009.160 

971.296 

548.390 

874.167 

35 

913.506 

1457.  a.1 

783.130 

1249.05 

685.371 

1092  92 

609.345 

971.481 

548.551 

874.333 

36 

913.768 

1457.50 

783.356 

1249.29 

685.568 

1093.13 

609.520 

971.667 

548.700 

874.500 

37 

914.031 

1457.78 

783.581 

1249.52 

085.765 

1003.33 

609.695 

971.852 

548.860 

874.667 

38 

914.299 

1458.06 

783.810 

1249.76 

085.966 

1003.54 

609.874 

072.03? 

549.02? 

874.833 

39 

914.506 

1458.33 

784.040 

1250  00 

686.166 

1093.75 

610.052 

972.222 

549.188 

875.000 

30 

914.834 

1458.61 

784.269 

1250.24 

680.307 

1003.90 

610.231 

072.40? 

549.348 

875.167 

31 

915.101 

1458.89 

784.498 

1250.48 

686.568 

1094.17 

610.409 

972.593 

549.500 

875.333 

33 

915.369 

1459.17 

784.728 

1250.71 

086  .  768 

1094.38 

610.587 

972.778 

549.670 

875.500 

33 

915.636 

1459.44 

784.957 

1250.95 

686.969 

1094.58 

610.766 

972.963 

540.830 

*75.667 

34 

915.904 

1459.72 

785.180 

1251.19 

687.170 

1094.79 

010.044 

973.148 

549.991 

875.833 

35 

916.171 

1460.00 

785  410 

1251.43 

087.370 

1095.0(1 

011.123 

973.333 

550.151 

876.000 

36 

916.434 

1160.28 

785.641 

1251.6: 

687.  50S 

1095.21 

011.208 

973  519 

550.300 

876.167 

37 

916.697 

1460.56 

785.8(56 

1251.90 

087.705 

1005.42 

(511.473 

973.704 

550.46? 

876.333 

38 

916.964 

1460.83 

786.095 

1252.14 

087.965 

1095.63 

611.652 

973.880 

550.628 

876.500 

39 

917.232 

1461.11 

786.325 

1252.38 

688.166 

1095.83 

611.830 

974.074 

550.788 

876.66? 

40 

917.499 

1461.3'.) 

786.554 

1252.62 

688.367 

1096.04 

612.000 

074.259 

550.040 

876.833 

41 

917.76? 

1461.67 

786.783 

1252.86 

688.567 

1096.25 

612.187 

974.444 

551.110 

8?7.00(i 

43 

918.034 

1461.94 

787.013 

1253.10 

688.768 

1096.46 

612.365 

974.630 

551.270 

877.167 

43 

918.302 

1462.22 

787.242 

1253.33 

688.969 

1006.67 

612.544 

9  i  4.  815 

551.431 

877.333 

44 

918.569 

1462.50 

787.471 

1253  57 

689.170 

1096.88 

612.722 

075.000 

551.591 

877.500 

45 

918.837 

1462.78 

787.701 

1253.81 

689.370 

1097.08 

612.901 

075.185 

551.752 

877.667 

46 

919.104 

1463.06 

787.930 

1254.05 

089.571 

1097.29 

013.070 

075.370 

551  913 

877.833 

47 

919.8721463.33 

788.159 

1254.20 

689.772 

1097.50 

613  258 

075.556 

552.073 

878.000 

48 

919.639 

1463.61 

788.389 

1254.52 

689.972 

1007.71 

613.430 

075.741 

552.234 

878.16? 

49 

919.907 

1463.89 

788  618 

1254.76 

690.173 

1097.92 

613.614 

075.926 

552.395 

878.333 

5O 

920.174 

1464.17 

788.84? 

1255.00 

090.374 

1098.13 

613.793 

976.111 

552.555 

878.500 

51 

920.442 

1464.44 

789.077 

1255.24 

600.574 

1098.33 

013.971 

970.296 

552.716 

878.667 

53 

920.709  1404.72 

789.306 

1255.48 

090.775 

1098.54 

614.150 

076.481 

552.876 

878.833 

53 

920.  977  [1465.  Od 

789.535 

1255.71 

600.076 

1098.75 

614.328 

976.667 

553.037 

870.000 

54 

921.249  1405.28 

789.709 

1255.95 

601.180 

109".  90 

614.510 

976.a->2 

553.201 

879.167 

55 

921.521  1465.50 

790.002 

1256.19 

691.384 

1090.17 

614.601 

977.037 

553.364 

879.333 

56 

921.780  1465.83 

790.231 

1250.43 

601.585 

1090.38 

614.870 

977.222 

553.525 

879.500 

57 

922.056  1466.11 

790.461 

1256.67 

691.786 

1009.58 

615.048 

977.40? 

553.685 

879.607 

58 

922.324  1466.39 

790.690 

1256.90 

691.987 

1099.79 

6  15.  227  1977.593 

553  846 

8?'9.833 

59 

221 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


88° 

1°  Curve. 

3°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

O 

5533.07 

8800.00 

2766.63 

4400.00 

1844.55 

2933.33 

13*3.53 

2200.00:1106.95 

1760.00 

1 

5534.67 

8801.  67  12767.  44 

4400.83 

1845.08 

2933.89 

1383.94 

2200.42  1107.27 

1760.33 

2 

5536.27 

8803.332768.24 

4401.67 

1845.61 

21)34.44 

1384.34 

2200.  83  i  1107.  59  1760.67 

3 

5537.88 

8805.00 

2769.04 

4402.50 

1846.15 

2935.00 

1384.74 

2201.25 

1107.91 

761.00 

4 

5539.48 

8806.67 

2769.84 

4403.33 

1846.68 

2935.56 

1385.14 

2201.67 

1108.23 

761.33 

5 

5541.12 

8808.33 

2770.66 

4404.17 

1847.23 

2936.11 

1385.55 

2202.08 

1108.56 

761.67 

G 

5543.75 

8810.00 

2771.48 

4405.00 

1847.77 

2936.67 

1385.96 

2202.50 

1108.89 

762.00 

7 

5544.35 

8811.67 

2772.28 

4405.83 

1848.31 

2937.22 

1386.36 

2202.92 

1109.21 

762.33 

8 

5545.90 

8813.33 

2773.08 

4406.67 

1848.84 

2937.78 

1386.76 

2203.33 

1109.53 

762.67 

9 

5547.56 

8815.00 

2773.88 

4407.50 

1849.38 

2938.  33 

1387.16 

2203.75 

1109.85 

1763.00 

1O 

5519.17 

8816.67 

2774.68 

4408.33 

1849.91 

2938.89 

1387.56 

2204.17 

1110.17 

1763.33 

11 

5550.80 

8818.33 

2775.50 

4409.17 

1850.46 

2939.44 

1387.97 

2204.58 

1110.50 

1763  67 

12 

5553.43 

8820.00 

2776.32 

4410.00 

1851.00 

2940.00 

1388.38 

2205.00 

1110.83 

1764.00 

13 

5554.04 

8821.67 

2777.12 

4410.83 

1851.54 

2940.56 

1388.78 

2205.42 

1111.15 

1764.33 

Id- 

5555.64 

8823  33 

2777.92 

4411.67 

1852.07 

2941.11 

1389.182205.83 

1111.47 

1764.67 

lS 

5657.2; 

8825.00 

2778.74 

4412.50 

1852.62 

2941.67 

1389.59 

2206.25 

1111.79 

1765.00 

16 

5558.91 

8826.67 

2779.56 

4413.83 

1853.16 

2942.22 

1390.00 

2206.67 

1112.12 

1765.33 

17 

5560.51 

8828.33 

2780.36 

4414.17 

1853.69 

•J942.78 

1390.40 

2207.08 

1112.44 

1765.67 

18 

5562  12 

8830.00 

2781.16 

4415  .00 

1854.23 

2943.33 

1390.80 

2207.50 

1112.76 

17'66  00 

19 

5563.75 

8831.  67 

2781.98 

4415.83 

1854.77 

•J943.89 

1391.21 

2207.92 

1113.09 

1766.33 

20 

5565.38 

8833.33 

2782.79 

4416.67 

1855.32 

•J944.44 

1391.61 

2208.33 

1113.42 

1766.67 

21 

5566.99 

8835.00 

2783.59 

4417.50 

1855.85 

2945.00 

1392.02 

2208.75 

1113.74 

767.00 

22 

5568.59 

8836.67 

.2784.40 

4418.33 

1856.39 

J945.56 

1392.42 

$£09.17 

1114.06 

1767.33 

23 

5570.22 

8838.33 

2785.21 

4419.17 

1856.93 

2946.11 

1392.83 

2209.58 

1114.3S 

767.67 

34 

5571.86 

8840.00 

2786.03 

4420.00 

1857.48 

2946.67 

1393.23 

2210.00  1114.71 

1768.00 

25 

5573.46 

8841  67 

2786.83 

4420  83 

1858.01 

.'947.22 

1393.63 

2210.4'J 

1115.03 

1768.33 

a  a 

5575  .  06 

8813  33 

2787.63 

44-J1.67 

1858.55 

J947.7S 

1391.04 

22  10.  S3 

1115.35 

1768.67 

27 

5576.70 

8845.00 

2788.45 

4422.50 

IS.J9.Oi) 

2948.33 

1391.44 

2211  25 

1115.08 

1769.00 

28 

5578.33 

8846.67 

2J89.27 

4423.33 

1859.63 

,5948.89 

131)4.85 

221  1  .  67 

1116.01 

1769.33 

29 

5579.96 

8848.33 

2790.08 

4424.17 

1860.18 

2949.44 

1395.26 

2212.08 

1116.33 

1769.67 

30 

5581.60 

8S50.00 

2790.90 

4425.00 

1860.72 

;>950.00 

1395.67 

2212.50 

1116.66 

1770  00 

31 

5583.20 

8851.67 

2791.7d 

4425.83 

1861.26 

2950.56 

1396.07 

2212.92 

1116.98 

1770.33 

32 

5584.80 

8853.33 

2792.50 

4426.67 

1861  79 

2951.11 

1396.47 

2213.33 

1117.30 

1770.67 

33 

5586.44 

8855.00 

2793.32 

4427.50 

1862.34 

2951.67 

131)6.88 

2213.75 

1117.63 

1771.00 

34 

5588.07 

8856.67 

2794.14 

4428.33 

1862.88 

,'952.22 

1397.89 

2214.17 

1117.96 

1771.33 

35 

5589.70 

8858.33 

27'94.95 

4429.17 

1863.43 

2952.78 

1397.70 

2214.58 

1118.28 

1771.67 

36 

5591.34 

8860.00 

2795.77 

4430.00 

1863.97 

2953.33 

1398.10 

2215.00 

1118.61 

1772.00 

37 

5592.97 

8861.67 

2796.59 

4430.83 

1864.52 

2953.89 

1398.51 

2215.42 

1118.94 

1772.33 

38 

5594.60 

8803.83 

2797.40 

4431.67 

1865.06 

2954.44 

1398.92 

2215.83 

1119.26 

1772.67 

39 

5596.24 

8865.00 

2798.22 

4432.50 

1865  60 

2955.00 

1399.33 

2216.25 

1119.59 

1773.00 

40 

5597  87 

8866.67 

2799  04 

4433.33 

1866.15 

.J955.56 

1399.74 

2216.67 

1119.9* 

1773.33 

41 

5599.47 

8S68.33 

2799.84 

4434.17 

1866.68 

2956.  11 

1400.14 

2217.08 

1120.24 

1773.67 

42 

5601  08 

8870.  U() 

2800.64 

4435.00 

1867.22 

2956.67 

1400.54 

2217.50 

1120.56 

1774.00 

43 

5602.71 

8871.67 

2801.46 

4435.83 

1867.76 

2957.22 

1400.95 

2217.92 

1120.88 

1774.33 

44 

5604.31 

8873.33 

2802.27 

443(5.67 

1868.31 

2957  78 

1401.36 

2218.33 

1121.21 

1774.67 

45 

5605.98 

8875.00 

2803.01) 

4437.50 

1868.85 

2958.33 

1401.77 

2218.75 

1121.54 

1775.00 

40 

5607.61 

8876.67 

2803  91 

4438.33 

1869.40 

2958.89 

1402.17 

2-J19.17 

1121.86 

1775.33 

47 

5609.24 

8878.  33 

2804.72 

4439.17 

1809.94 

2959.44 

1402.58 

2211).  58 

1122.19 

1775.67 

48 

5610.87 

8880.00 

2805.54 

4140.00 

1870.48 

2960.00 

1402.99 

22-0.00 

1122.52 

1776.00 

49 

o6l2.51 

8881.67 

2806.36 

4440.83 

1871.03 

2960.56 

1403.40 

2220.42 

1122.84 

1776.33 

5O 

5614.14 

8883.33 

2807.17 

1441.67 

1871.57 

2901.11 

1403.81 

2220.83 

1123.17 

1776.67 

51 

5615.77 

8885.002807.99 

4442.5!: 

1872.12 

2961.67 

1404.22 

2221.25 

1123.50 

1777.00 

53 

06  17.  41 

8886.672808.81 

4443.33 

1872.66 

2962.22 

140  4.  62 

2221.67 

1123.82 

1777.33 

53 

5619.04 

88SS.332809.62 

4444.17 

1873  21  2962.78 

1405.03 

2-222.08 

1124.15 

1777.67 

54 

5020.67 

8890.002810.44 

1445.00 

1873.75 

2963.33 

1405.44 

2222.50 

1124.48 

1778.00 

55 

5622.  31 

8891.672811.26 

1445.83 

1874.29 

2963.89 

1405.85 

2222.92 

1124.80 

177'8.33 

5(> 

5623.94 

8893.332812.07 

4446.67 

1874.84 

2964.44 

1406.26 

2223.33 

1125.131778.67 

57 

5625.60 

8895.002812.90 

44*7.50 

1875.392965.00 

1406.67 

2223.75 

1125.46  1779.00 

58 

5627.26 

8896.672813.73 

4448.33 

1875.952965.56 

1407.0!)  2224.  17 

1125.80  1779.33 

59 

5628.89 

8898.332814.55 

4449.17 

1876.49,2966.11 

1407.50J2224  58  1126.12  1779.  C7 

TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

1O°  Curve. 

88° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

922.  591  '1466.  67 

790.919 

1257.14 

692.187 

1100.00 

015  .  405  977  .  778  554  .  007  880  .  000 

~O 

9:22.859  14(56.94 

791.149 

1257.38 

602.388 

1100.21 

015.  584;  977.  963  554.  167 

880.167 

1 

923.  126  1467.  2* 

791.378 

1257.052 

602.589 

1100.42 

615.762978.148 

554.328 

880.333 

2 

923.394  1407.50 

791  .  607 

1257.86 

692.789 

1100.63 

615.041  978.333 

554.489 

880.500 

3 

923.  001  -1407.78 

791.837 

1258.10 

692.990 

1100.83 

616.119978.519 

554.649 

880.667 

4 

923.  934  i  1408.  00 

792.070  1258  33 

603.194  1101.04 

616.301  978.704 

554.813 

880.833 

5 

924.200 

1468.33 

792.304  1258.57 

693.399 

1101.25 

616.482978.889 

554.976 

881.000 

0 

924.478 

1468.61 

792.533  1258.81 

603.599 

1101.46 

616.661 

979.074 

555.137 

881  167 

7 

924.741 

1468.80 

792.762  1259  .Of, 

693.800 

1101.07 

616.839 

979.259 

555.297 

881.333 

8 

925.008 

1469.1', 

702.  991  1  1259.  20 

694.001 

1101.88 

617.018 

979.444 

555.458 

881.500 

9 

925.276 

1469.44 

793.221  1259.52 

694.201 

1102  08 

617.196 

979.630 

555.619 

881  607 

10 

925.548 

1469.7*. 

793.454 

1259.76 

694.406 

1102  29 

617.378 

979.815 

555.782 

881.833 

11 

925.820 

1470.00 

793.688 

1260.00 

694.610 

1102.50 

617.559 

980.000 

555.046 

882.000 

12 

926.088 

1470.28 

793.917 

1260.24 

694.811 

1102.71 

017.738 

980.185 

556.106 

882  1(57 

13 

926.355 

1470.56 

794.146 

1200.48 

695.011 

1102.92 

617.910 

080.370 

556.267 

882.333 

14 

926.628 

1470.83 

794.380 

1200.71 

695.216 

1103.13 

018.098 

980.556 

556.430 

882.500 

15 

920  900 

1471.11 

794.613 

1200.95 

695.420 

1103.33 

618.279 

980.741 

556.594 

882  667 

16 

927.167  1  471.30 

794.842 

1261.10 

095.021 

1103.54 

618.458 

980.926 

556.755 

882.833 

17 

927.435 

14;  1.67 

795.072 

1201.43 

095.821 

1103.75 

618.636 

981.111 

556.915 

883.000 

18 

927.707 

1471.94 

795.305 

1201.67 

09(5.026 

1103.90 

618.818 

981.296 

557.079 

883.167 

19 

927.979 

1472.22 

795.539 

1261.90 

696.230 

1104.17 

618.999 

981.481 

557.242 

883.333 

2O 

928.247 

1472.51! 

705.768 

1262.14 

600.431 

1104.38 

619.178 

981.667 

557.403 

883.500 

31 

928.514 

1472.78 

795.997 

1262.38 

096.631 

1104.58 

619.350 

981.852 

557.564 

883.667 

33 

928.787 

1473.06 

706.231 

1262.62 

606.836 

1104.70 

019.538 

982.037 

557.727 

883.833 

23 

929.059 

1473  3:-j 

790.464 

1202.80 

607  040 

1105.00 

619.720 

082.222 

557.891 

884.000 

24 

H29.327 

1473.61 

79».  .  603 

1263.10 

697.241 

1105.21 

610.808 

982.407 

558.051 

884  167 

25 

929.594 

1473.89 

796.923 

1203.33 

697.441 

1105.42 

620.076 

982.593 

558.212 

884.333 

36 

929.866 

1474.17 

797.156 

1263.57 

697.046 

1105.03 

620.258 

982.778 

558.375 

884.500 

27 

930.139 

1474.44 

;  97.  390 

1263.81 

097.850 

1105.83 

620.440 

982.963 

558.539 

884.667 

28 

930.411 

1474.72 

797.623 

1264.05 

698.054 

1106.04 

620.621 

983.148 

558.702 

884.833 

29 

930.683 

1475.00 

797.856 

1264.29 

698.258 

1106.25 

620.803 

983.333 

558.866 

885.000 

30 

930.951 

1475.  28 

798.080 

1264.52 

608.459 

1100  40 

020.981 

983  5  '.$ 

559.026 

885.167 

31 

931.218 

1475.56 

798.315 

1204.70 

698.660 

1100.67 

621.160 

983,  704 

559.187 

885.333 

32 

931.490 

1475.83 

798.549 

1205.00 

698.864 

1106.88 

621.341 

983.889 

559.351 

885.500 

33 

931.763 

1476.11 

798.782 

1205.24 

699.068 

1107.08 

621.523 

984.074 

559.514 

885.667 

34 

932.035 

1476.39 

709.015 

1205.48 

600.273 

1107.29 

621.705 

984.259 

559.078 

885.833 

35 

932.307 

1476.67 

799.249 

1265.71 

699.477 

1107.50 

621.886 

984.444 

559.841 

886.000 

36 

932.580 

1476.94 

799.482 

1265.95 

699.681 

1107.71 

622.068 

984.630 

560.005 

886.167 

37 

932.852 

1477.22 

799.716 

1266.19 

699.885 

1107.92 

622.249 

984.815 

500.168 

886.333 

38 

033.124 

1477.50 

790.949 

1266.43 

700.090 

1108.13 

622.431 

985.000 

500.332 

886.500 

39 

933.396 

1477.78 

800.182 

1266.67 

700.294 

1108.33 

622.613 

985.185 

560.495 

886.667 

4O 

933.664 

1478.06 

800.412 

1266.90 

700.495 

1108.54 

622.791 

985.370 

500.056 

886.833 

41 

933.931 

1478.33 

800.041 

1267.14 

700.695 

1108.75 

622.970 

985.556 

500.810 

887.000 

42 

934.204 

1478.61 

800.875 

1267.38 

7(0.900 

1108  90 

623.151 

985.741 

500.980 

887.167 

43 

934.476 

1478.89 

801.108 

1267.62 

701.104 

1109.17 

623.333 

985.926 

501.143 

887.333 

44 

934.748 

1479.17 

801.341 

1267.86 

701.308 

1109.38 

623.514 

986.111 

561.307 

887.500 

45 

935.021 

1479.44 

801.575 

1268.10 

701.513 

1109.58 

023.696 

986.290 

561.470 

887.007 

46 

935.  291 

1479.72 

801.808 

1268.33 

701.717 

1109.79 

623.878 

986.481 

561.634 

887.833 

47 

935.565 

1480.00 

802.042 

1268.57 

701  921 

1110.00 

024.059 

986.667 

561.797 

888.000 

48 

935.837 

1480.28 

802.275)1268.81 

702.125 

1110.21 

024.241 

986.852 

561.961 

888.167 

49 

936.110 

1480.56 

802.509  1269.05 

708,880 

1110  42 

624.423 

987.037 

562.124 

888.333 

5O 

93(5.382 

1480.83 

802.  742  11269.  29 

702.534 

1110.03 

624.604 

987.222 

562.288 

888.500 

51 

936  .  654 

1181.11 

802.975  1269  52 

702.738 

1110.83 

624.786 

987.407 

562.451 

888.067 

52 

936.927 

1481.30 

803.209  1269.76 

702.943 

1111.04 

624.967 

987.593 

562.615 

888.833 

53 

937.199 
937.471 

1481.67 
1481.94 

803.4421270.00 
803.676  1210.24 

703.147 
703.351 

1111.25 
1111.40 

625.149 
625.331 

087.778562.778 
987.963562.942 

880.000)  54 
889.167   55 

037.743 

1482.22 

803.000  1270.48 

703.555 

1111.67 

625.512 

988.  148!  563.  105 

889.333   56 

938.020 

1482.50 

804.147  1270.71 

703.763 

1111.88 

625.697 

988.888568.878 

8H9.500 

57 

938.297 

1482.78 

804.3841270.95 

703.971 

1112.08 

625.882 

088.5191563.438 

889.667 

58 

938.570 

1483.06 

804.617  1271.19 

704.175 

1112.29 

026.  004  988.  704  1  503.  602 

880.833 

59 

223 


TABLE  XIV. — ACTUAL  TANGENTS,    ETC. 


89° 

1°  Curve. 

2°  Curve. 

3°  Curve. 

4°  Curve. 

5°  Curve. 

M. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

Arc. 

o 

5(530.53 

8900.  OC 

2>  15.  37!  4450.  00  1877.04 

2966.67 

1107.90 

2225.00 

1120.45 

1780.ni) 

1 

3033.10 

8901.07' 

2816.184450.83  1877.58 

2907.22 

1408.31 

2225.42 

1126.78 

1780.33 

2 

5633.71) 

8903.33 

28  17.  CO  4451.  67 

1878.12 

2967.78 

1408.72 

2225.83 

1127.10 

1780.07 

3 

5635.43 

8905.  DO 

2817.824452.50 

1878.67 

2908.33 

1409.13 

^226.25 

1127.43 

1781.00 

4 

5(537.  00 

8900.07 

2818.  63!  4453.  33 

1879.21 

2908.89 

1409.54 

^226.67 

1127.76 

1781.33 

5 

5638.69 

81)08.33 

2819.45 

4454.17 

1679.76 

2969.44 

1409.95 

2227.  Oh 

1128.08 

1781.67 

6 

5(540.32 

8910.00 

2820.27 

4455.00 

1880.30 

2970.00 

1410.35 

2227.50 

1128.  41  11782.  00 

7 

5641.99 

8911.07 

2821.10 

4455.83 

1880.86 

2970.50 

1410.77 

2227.92 

1128.74J1782.33 

8 

5643.65 

8913.33 

2821.93 

4450.07 

1881.41 

2971.11 

1411.19 

2228.33 

1129.07 

1782.07 

9 

5645.28 

891  5.  OU 

2822.74 

4457.50 

1881.952971.67 

1411.59 

2228.75 

1129.40 

1783.00 

1O 

5646.91 

8916.67 

2823.56 

4458.  33  j  1882.  50 

2972.22 

1412.00 

2229.17 

1129.73 

1783.33 

11 

5648.55 

8918.33 

2824.38 

4459.17 

1883.04 

2972.78 

1412.41 

2229.58 

1130.05 

1783.07 

12 

5650.18 

8920.00 

2825.19 

4400.00 

1883.59 

2973.33 

1412.82 

2230.00 

1130.38 

1784.00 

13 

5051.84  8921.6? 

2826.02 

4460.83 

1884.14 

2973.89 

1413.23 

2230.42 

1130.71 

1784.33 

14 

5663.60 

8923.33 

•2826.80 

4401.  67  1  1884.  70 

2974.44 

1413.65 

2230.83 

1131.05 

1784.67 

15 

56«5.14 

8925.00 

2827.07 

4402.  50!  1885.  24 

2975.00 

1414.00 

2231.25 

1131.37 

1785.00 

16 

5056.77 

8926.67 

2828.49 

4403.33 

1885.78 

2975.56 

1414.47 

2231.67 

1131.70 

1785.33 

17 

5658.43 

8928.33 

2829.32 

4404.17 

1886:34 

2976.11 

1414.88 

2-232.  OS 

1132.03 

1785.67 

18 

5060.09 

8930.00 

•2830.15 

4405.  OJ 

1886.89 

2976.67 

1415.30 

2232.50 

1132.36 

1786.00 

19 

5661.72 

8931.67 

2830.97 

4465.83 

1887.44 

2977.22 

1415.71 

2232.92 

1132.69 

1786.33 

20 

5663.36 

8933.33 

2831.78 

4466.67 

1887.98 

2977.78 

1416.11 

2233.33 

1133.02 

1786.67 

21 

5665.02 

8935.00 

2832.61 

4467.50 

1888.53 

2978.33 

1416.53 

2233.75 

1133.35 

1787.00 

22 

5606.68 

8936.07 

2833.44 

4408.33 

1889.09 

2978.89 

1416.94 

2-234.17 

1133.68 

1787.33 

23 

5668.31 

8938.33 

2834.20 

4409.17 

1889.63 

2979.44 

1417.35 

2234.58 

1134.01 

1787.67 

24 

5669.95 

8940.00 

2835.08 

1470.00 

1890.18 

2^80.00 

1417.76 

2235.00 

1134.34 

1788.00 

25 

5071.61 

8941.67 

•2835.91 

4470.83 

1890.73 

2980.56 

1418.18 

2235.42 

1134.67 

1788.33 

26 

5673.27 

8913.33 

2836.74 

4471.67 

1891.28 

2981.11 

1418.59 

2235.83 

1135.00 

1788.67 

27 

5074.90 

8945.00 

2837.50 

4472.50 

1891.83 

2981.67 

1419.00 

2236.25 

1135.33 

1789.00 

28 

5676.54 

H94G.07 

•2838.37 

1473.33 

1892.31 

2982.22 

1419.41 

2230.67 

1135.65 

1789.33 

29 

5678.20 

8948.33 

2839.20 

4474.17 

1892.93 

2982.78 

1419.82 

2237.08 

1135.99 

1789.67 

30 

5679.86 

8950.00 

2840.03 

4475.00 

1893.48 

2983.33 

1420.24 

2237.50 

1136.32 

1790.00 

31 

5081.52 

8951.67 

2840.80 

4475.83 

1894  04 

2983.89 

1420.60 

2-237.92 

1136.65 

1790.33 

32 

5683.18 

8953.33 

2841.70 

4476.67 

1894.59 

2984.44 

1421.07 

2238.33 

1136.98 

1790.67 

33 

5084  84 

8955.00 

2842.53 

4477.50 

1«95.14 

2985.00 

1421.49 

2238.75 

1137.32 

1791.00 

34 

5080.51 

8956.67 

2843.36 

4478.33 

1895.70 

2985.56 

1421.90 

2239.17 

1137.05 

1791.33 

35 

5088.14 

8958.33 

2844.17 

4479.17 

1896.24 

2986.11 

1422.31 

2239.58 

1137.98 

1791.67 

36 

5689.77 

8960.00 

2844.99 

4480.00 

1896.79 

2986.67 

1422.72 

2240.00 

1138.30 

1792.00 

37 

5691.43 

8961.67 

2845.82 

4480.83  1897.34 

2987.22 

1423.13 

2240.42 

1138.03 

1792.33 

38 

5693.09 

8963.33 

2846.65 

4481.67:1897.89 

2987.78 

1423.55 

2240.83 

1138.97 

1792  07 

39 

5694.76 

8965.00 

2847.48 

4482.50 

1898.45 

2988.33 

1423.96 

2241.25 

1139.30 

1793  00 

40 

5096.42 

8966.67 

2848.31 

4483.33 

1899.00 

2988.89 

1424.38 

2241.67 

1139.63 

1793.33 

41 

5698.08 

8908.33 

2849.14 

4484.17  1899.56 

2989.44 

1424.80 

2242.08 

1139.96 

1793.07 

42 

5699.74 

8970.00 

2849.98 

4485.001900.11 

2990.00 

1425.21 

2242.50 

1140.30 

1794.00 

43 

5701.40 

8971.67 

2850.81 

4485.83  1900.66 

2990.56 

1425.63 

2242.92 

1140.03 

1794.33 

44 

5703.06 

8973.33 

2851.64 

4486.6711901.22 

2991.11 

1426.04 

•2243.33 

1140.96  1794.07 

45 

5704.73 

8975.00 

2852.47 

4487.501901.77 

2991.67 

1426.46 

2243.75 

1141.29  1795.00 

46 

5706.39 

8976.67 

2853.30 

4488.33  1902.33 

2992.22 

1426.87 

2244.17 

1141.63ll795.33 

47 

5708.05 

8978.33 

2854.13 

4489.17,1902.88 

2992.78 

1427.29 

2244.58 

1141.96 

1795.07 

48 

5709.71 

8980.00 

2854.90 

4490.00  1903.43 

2993.33 

1427.70 

2245.00 

1142.29 

17!  '0.00 

49 

5711.37 

8981  .  67 

2855.79 

4490.83 

1903.99 

2993.89 

1428.12 

2245.42 

1142.62 

1796.33 

50 

5713.03 

8983.33 

2856.62 

4491.67 

1904.54 

2994.44 

1428.54 

•2245.83 

1142.96 

1796.67 

51 

5714.70 

8985.00 

2857.45 

4492.50  1905.09 

291)5.00 

1428.95 

2246.25 

1143.29 

1797.00 

52 

5716.36 

8986.67 

2858.28 

4493.331905.65 

201*5.56 

1429.37 

2246.67 

1143.62 

1797.33 

53 

5718.02 

8988.33 

2859.11 

4494.17  1906.20 

2996.11 

1429.78 

2247.08 

1143.95 

1797.67 

54 

5719.68 

8990.00 

2859.95 

4495.  001  906.  76 

2990.67 

1430.20 

2247.50 

1144.29 

1798.00 

55 

5721  .34 

8991.67 

2860.78 

4495.831907.31 

2997.22 

1430.61 

2247.  92  !  1144.  02 

1798.33 

56 

5723.00 

8993.33 

2861.61 

4490.67  1907.86 

2997.78 

1431.03  -2248.33  1144.95  1  71)8.07 

57 

5724.67 

8995.00 

2862.44 

4497.501908.42 

2998.33 

1  431  .  44  2248  .  75  1145.  28  1  7  1)9  .  00 

58 

5726.33 

8990.07 

2803.27 

4498.33  1908.97 

2998.89 

1431.80  2249.  1711145.  02J1799.  33 

59 

5727.998998.33 

2804.10 

4499.17  1909.53 

2999.44 

1432.2712249.58  1145.951  1799.  07 

224 


TABLE  XTV.— ACTUAL  TANGENTS,    ETC. 


6°  Curve. 

7°  Curve. 

8°  Curve. 

9°  Curve. 

10°  Curve. 

89° 

Tan. 

Arc. 

Tan. 

Arc. 

Tan. 

A  re. 

Tan. 

Arc. 

Tan. 

Arc. 

M. 

938.8-12  1483.33 

804.851 

1271.43 

704.380 

1112.50 

626.245 

988.889 

563  765 

890.000 

0 

939.114  1483.61 

805.084 

1271.67 

7'04.584 

1112.71 

626.  427  [989.074 

563.929 

890.167 

1 

939.387 

1483.89 

805.318 

1271.90 

704.  78H 

1112.92 

626.608 

989.259 

564.092 

890.333 

2 

939.659 

1484.17 

805.551 

1272.14 

704.993 

1113.13 

626.790 

989.444 

564.256 

890.500 

3 

939.931 

1484.44 

805.785 

1272.38 

705.197 

1113.33 

626.972 

989.630 

564.419 

890.667 

4 

940  203 

148-4.72 

806.018 

1272.62 

7'05.401 

1113.54 

627.153 

989.815 

564.583 

890.833 

5 

940.476 

1485.00 

806.251 

1272.86 

705.605  1113.75 

627.3:-55 

990.000 

564.746 

891.000 

6 

940.753 

1485.28 

806.489 

1273.10 

705.8131113.96 

627.520 

990.185 

564.912 

891.167 

7 

941.030 

1485.56 

806.726 

1-J73.33 

706.02111114.17 

627.705990.370 

565.079 

891.333 

8 

941  .  302 

1485.83 

806.  96U 

1273.57 

706.225 

1114.38 

627.886 

990.556 

565.242 

891.500 

9 

941.574 

1486.11 

807.193 

1273.81 

706.430 

1114.58 

628.068 

900.741 

565.406 

891.667 

10 

941.847 

1486.39 

807.427 

1274.05 

706.634 

1114.79 

628.249 

990.926 

565.569 

891.833 

11 

942  119 

1486.67 

807.660 

1274.29 

706.838 

1115.00 

628.431 

991.111 

565.733 

892.000 

13 

942.396 

1486.94 

807.898 

1274.52 

707.046 

1115.21 

628.616 

991.296 

565.899 

892.167 

13 

942.673 

1487.22 

808.135 

1274.76 

707.254 

1115.42 

i28.80l 

991.481 

566.066 

892.333 

14 

942.945 

1487.50 

808.369 

1275.00 

707.458 

1115.63 

628.982 

991.667 

566.229 

892.500 

15 

943.218 

1487.78 

S08.602 

1275.24 

707.663 

1115.83 

629.164 

991  852 

566  393 

892.667 

16 

943.495 

1488.06 

808.840 

1275.48 

707  870 

1116.04 

629.349 

992.037 

566.559 

892.833 

17 

943.772 

1488.33 

809.077 

1275.71 

708.078 

1116.25 

629.533 

992.222 

566.725 

893.000 

18 

944.044 

1488.61 

809.310 

1275.95 

708.283 

1116.46 

629.715 

992.407 

566.889 

893.167 

19 

944.316 

1488.89 

809.544 

1276.19 

708.487 

1116.67 

629.897 

992.593 

5G7.052 

893.333 

30 

944.593 

1489.17 

809.781 

1276.43 

708  695 

1116.88 

630.082 

992.  77b 

567.219 

893.500 

31 

944.870 

1489.44 

810.019 

1276.67 

708.903 

nr.08 

630.266 

992.963 

567.385 

893.667 

22 

945.143 

1489.72 

810.252 

1276.90 

709.107 

111"'.  29 

630.448 

993.148 

567.549 

893.833 

23 

945.415 

1490.00 

810.486 

1277.14 

709.311 

iir.no 

630.  030 

993.333 

567.712 

894.000 

34 

945.692 

1490.28 

8  1  0.  723  i  1277.  38 

709.519 

iir.7i 

630.814 

993.519 

567.878 

894.167 

35 

945.969 

1490.56 

810.961 

1277.62 

709.727 

iir.92 

630.999 

993.704 

568.045 

894.333 

26 

916.241 

1490.83 

811.194 

1277.86 

709.931 

1118.13 

031.181 

J)93.88J 

568.208 

894.500 

27 

940.514 

1491.11 

811.428 

1278.10 

710.135 

1118.33 

631.362 

994.074 

568.372 

894.667 

28 

946.791 

1491.39 

811.665 

1278.33 

710.343 

1118.54 

631.547 

994.259 

508.538 

894.833 

29 

947.068 

1491.67 

811.903 

1278.57 

710.551 

1118.75 

031.  7S2 

994.444 

5C8.705 

895.000 

30 

947.345 

1491.94 

M12.140 

1278.81 

710.759 

1118.96 

t»31.917 

994.631 

508.871 

895.167 

31 

947.622 

1492.22 

812.378 

1279.05 

710.967 

1119.17 

632.102 

994.815 

569.037 

b95.333 

32 

947.899 

1492.50 

812.615 

1279.29 

711.175 

1119.38 

632.286 

995.000 

569.204 

895.500 

33 

948.176 

1492.78 

812.853 

1279.52 

711.383 

1119.5h 

ti32.47! 

995  185 

569.370 

895.667 

34 

948.448 

1493.00 

813.086 

1279.76 

711.587 

1119.79 

632.653 

995.370 

569.534 

895.833 

35 

948.721 

1493.33 

813.320 

1280.00 

711.791 

1120.  (X 

632.835 

995.  55( 

569.697 

896.000 

36 

948.998 

1493.61 

813.557 

1280.24 

7  11.  999 

1120.21 

633.019 

995.741 

569.863 

896.167 

37 

949  275 

1493.89 

813.795 

1280.48 

712.207 

1120.4^ 

633.204 

995.920 

570.030 

896.333 

38 

949.552 

1494.17 

814.032 

1280.71 

712.415 

1120.63 

633.389 

996.111 

570.196 

S96.500 

39 

949.829 

1494.44 

814.270 

1280.95 

712.623 

1120.83 

633.574 

996.290 

570.303 

896.667 

40 

950.106 

1494.72 

814.507 

1281.19 

712.830 

1121.04 

633.759 

996.481 

57'0.529 

896.833 

41 

950.383 

1495.00 

814.745 

1281.43 

713.038 

1121.25 

633.943 

996.667 

570.695 

897.000 

42 

950.660 

1495.28 

SI  4.  982 

1281.67 

713.246 

1121.46 

634.128 

996.852 

570.862 

897.167 

43 

950.937 

1495.56 

815.220 

1281.90 

713.454 

1121.67 

r.34.313 

997.037 

571.028 

897.333 

44 

951.214 

1495>3 

815.457 

1282.14 

713.662 

1121.  8b 

634.498 

95)7.222 

571  .  1  94 

897.500 

45 

951.491 

1496.11 

815.695 

1282.38 

713.870 

1122.08 

634.683 

997.407 

571.361 

897.667 

46 

951.768 

1496.39 

815.932 

1282.62 

714.078 

1122.29 

634.  86V  1  997.  593 

571.527 

897.833 

47 

952.045 

1496.67 

816.170 

12.S2.86J  714  286 

1122.50 

635.  052  1997.778 

571.694 

898.000 

48 

952.322 

1496.94 

816.407 

1283.10 

714.493 

1122.71 

635.237 

997.963 

571.860 

898.167 

49 

95-2.599 

1497.22 

816.645 

1283.33 

714.701 

1122.92 

635.422 

998.148 

572.026 

898.333 

50 

952.876 
953.153 

1497.50 
1497.78 

816.88212?<3.57 
817.120  1:281.81 

714.909  1123.13 
715.1171123.33 

635.  607!  998.  333 
635  791  998.519 

572.193 
572.359 

898.500 
898.667 

51 

53 

953.431 

1498.06 

817.3571284.05 

715.325  1123.54 

635.976998.704 

572.525 

^98.833 

53 

953.708 

1498.33 

817.595  1284.29 

71?.5o3ill23.7'5 

(.36.161  998.889 

572.602 

899.  00( 

54 

953.985  149S.61 

817.8321284.52 

715.741  1123.  9( 

636.346  999.074 

572.858 

899.107 

55 

954.262  1498.89 

818  070  1284.  76:715.  948  1124.17 

636.531  999.259 

573.024 

899.333 

56 

954.531)  I49»,ll 

818.307  12S5.  00  716.  156!  1124.  oS 

036.716999.444 

573.191 

899.500 

57 

954.816  1499.44 

818.545  1285.24  716.364  1124.58 

036.9(0999.630 

573.357 

HIM).  (507 

58 

955.0931499.72 

818.782  1285.48  716  572  1124.79 

637.085999.815 

573.524 

899.833 

59 

225 


TABLE  XV.— NATURAL  SINES   AND  COSINES. 


0° 

1° 

2° 

3°    | 

4° 

Sine 

Cosin 

Sine 

Cosin 

Sine  j  Cosin 

Sine 

Cosin  1 

Sine 

Cosin 

0 

Tooooo 

One. 

.01745 

.99985 

.03490 

.  90039 

.05234 

.90803 

.06976 

.99750 

60 

1 

.C0029 

One. 

.01774 

.99984 

.03519 

.99938 

.05203 

.99801; 

.07005 

.99754 

59 

2 

.00058 

One. 

.01803 

.99984 

.03548 

.99937 

.05292 

.99800: 

.07034 

.99752 

58 

3 

.00087 

One. 

.01832 

.99983 

.03577 

.99930 

.05321 

.99858 

.07063 

.99750 

57 

4 

.00116:  One. 

.01862 

.90983 

.03000 

.  99935 

.05350 

.9UH57. 

.07092 

.997481  56 

5 

.00145  One. 

.01891 

.99982 

.03035 

.99934 

.05379 

.90855 

.07121 

.00740  55 

G 

.00175:  One. 

.01920 

.99982 

.03004 

.99933 

.05408 

.90854 

.07150 

.99744!  54 

7 

.00204!  One. 

.01949 

.99981 

.03093 

.99932 

.U5437 

.  99852  ! 

.07179 

.99742;  53 

8 

.0023.T  One. 

.01978 

.99980 

.03723 

.99931 

.05466!.  99851' 

.07208 

.99740  52 

9 

.00202  One. 

.02007 

.99980 

.03752 

.99930 

.05495  .99849 

.07237 

.99738  51 

10 

.00291 

One. 

.02036 

.99979 

.03781 

.99929 

.05524 

.99847 

.07266 

.99736 

50 

11 

.00320 

.99999 

.02065 

.99979 

.03810 

.99927 

.05553 

.99846 

.07295 

.99734 

49 

12 

.00349 

.99999 

.02094 

.99978 

.03839 

.99928 

.055821.99844 

.07324 

.99731 

48 

13 

.00378 

.99999 

.02123 

.99977 

.03808 

.99925 

.05011 

.99842 

.07353 

.99729 

47 

14 

.00407 

.99999 

.02152 

.99977 

.03897 

.99924 

.05640 

.99841 

.07382 

.99727 

46 

15 

.00436 

.99999 

.02181 

.99976 

.03926 

.99923 

.05669 

.99839 

.07411 

.99725 

45 

16 

.00465 

.99999 

.02211 

.99976 

.03955 

.99922 

.05698 

.99838 

.07440 

.99723 

44 

17 

.00495 

.99999 

.02240 

.99975 

.03984 

.99921 

.05727 

.99836 

.07409 

.99721 

43 

18 

.00524 

.99999 

.02269 

.99974 

.04013 

.99919 

.05756 

.99834 

.07408 

.99719 

42 

19 

.00553 

.99998 

.02298 

.99974 

.04042 

.99918 

.05785 

.99833  .07527 

.99716 

41 

20 

.00582 

.99998 

.02327 

.99973 

.04071 

.99917 

.05814 

.99831, 

.07556 

.99714 

40 

21 

.00611 

.99998 

.02356 

.99972 

.04100 

.99916 

.05S44 

.  99829  ; 

.07585 

.99712 

39 

22 

.00640 

.99998 

.02335 

.99972 

.04129 

.99015 

.058731.99827  .07614 

.99710 

38 

23 

.00669 

.99998 

.02414 

.99971 

.04159 

.99013 

.05092 

.99826  .(-7643 

.99708 

37 

24 

.00698 

.99998 

.02443 

.93970 

.04108 

.99012 

.05931 

.99824 

.07672 

.99705 

36 

25 

.00727 

.99997 

.02472 

.99969 

.04217 

.99911 

.059601.99822 

.07701 

.99703 

35 

26 

.00756 

.99997 

.02501 

.99909 

.04246 

.99010 

.05989 

.99821 

.07730 

.99701 

34 

27 

.00785 

.99997 

.02530 

.99968 

.04275 

.C9909 

.00018 

.99819  .07759 

.99099 

33 

28 

.00814 

.99997 

.02560 

.99967 

.04304 

.99907 

.CC047 

.99817  .07788  .99696 

32 

29 

.00844 

.99996 

.02589 

.99906 

.04333 

.99006 

.00076 

.99815  .07817  .99694 

31 

30 

.00873 

.99996 

.02618 

.99966 

.04302 

.99905 

.06105 

.99813 

.07846  .99692 

30 

31 

.00902 

.99998 

.02647 

.99965 

.04391 

.99904 

.06134 

.99812 

.07875  .99689 

29 

32 

.00931 

.99998 

.02670 

.99904 

.04420 

OQOQO 

.06163 

.99810 

.079041.99687 

28 

33 

.00960 

.99995 

.02705 

.S99G3 

.04449 

!  99901 

.06192 

.90808 

.079331.99685 

27 

34 

.00989 

.99995 

.02734 

.99903 

.04478 

.90900 

.06221 

.99806 

.079621.99683 

26 

35 

.01018 

.99995 

.02763 

.99902 

.04507 

.99898 

.06250 

.99804 

.07991|.99680;  25 

36 

.01047 

.99995 

.02792 

.99961 

.04536 

.99897 

.00279 

.90803 

.08020:  99678  j  24 

37 

.01076 

.99994 

.02821 

.99900 

.04505 

.99896 

.00308 

.99801 

.080491.99676:  23 

38 

.01105 

.99994 

.02850 

.99959 

.04594 

.99894 

.06337 

.99709 

.080781.99673  22 

39 

.01134 

.09994 

.02379 

.99959 

.04623 

.90893 

.00366 

.99797 

.08107 

.99671 

21 

40 

.011641.99993 

.02908 

.99958 

.04053 

.99892 

.06395 

.99795 

.08136 

.90008 

20 

41 

.01  193  !.  99993 

.02938 

.99957 

.04082 

.99890 

.06424 

.99793 

.08165 

.99666 

19 

42 

.01222  .99993 

.02967 

.99956 

.04711 

.99889 

.00453 

.9G792  .08194  .99664  18 

43 

.012511.99992 

.02996 

.99955 

.04740 

.99888 

.00482 

.99790  .08223;.  99661  17 

44 

.01280  '.99992 

.03025 

.99954 

.047C9 

.99886 

.00511 

.99788 

.08252  .00050  16 

45 

.01309  .99991 

.03054 

.99953 

.04798 

.90885 

.00540 

.99786 

.08281  .99657  15 

46 

.01338  .99991 

.03083 

.99952 

.04827 

.99883 

.00509 

.90784 

.08310  .99654  14 

47 

.  01367  j.  99991 

.03112 

.99952 

.04856 

.998821  .00598 

.90782 

.083391.90652!  13 

48 

.  01396  !.  99990 

.03141 

.99951 

.04885 

.998811  .06627 

.99780 

.08368  .99649:  12 

49 

.01425J.  99990 

.03170 

.99950 

.04914 

.99S79I  .06656 

.99778 

.08397  .99647  11 

50 

.01454  .99989 

.03199 

.99949 

.04943 

.99878  j  .06685 

.99776 

.08426  .90644 

10 

51 

.01483  .99989 

.03228 

.99948 

.04972 

.99876 

.06714 

.99774 

.08455 

.99642 

9 

52 

.01513L99989 

.03257 

.99947 

.05001 

.90875 

.00743:.  99772 

.08484 

.99639 

8 

53 

.01542  .99988 

.03236 

.999-16 

.05030 

.90873 

.00773 

.99770 

.08513 

.99037 

7 

54 

.01571  .99988 

.03316 

.99945s 

.05059 

.90872!  .06802 

.99708 

.08543 

.90635 

6 

55 

.01600  .99987 

.08345 

.99944 

.05088 

.09870  .00831 

.99706 

.08571 

.90632 

5 

56 

.01  629  ;.99987 

.03374 

.99943 

.05117 

.99869 

.06860  .99764 

.08000 

.90030 

4 

57 

.01  658  ',99986 

.03403 

.99942 

.05146 

.99867 

.00889  .99762 

.08029 

.90627 

3 

58 

.016871.99986 

.03432 

.99941 

.05175 

.  90806 

.00018  .99700 

.08058 

.90625 

2 

59 

.  01716  L  99985 

.03461 

.99940 

.05205 

.99864 

.06947  .99758 

.08687 

.99622 

1 

60 

.  01745  j.  99985 

.03490 

.99939 

.05234 

.99863 

.06976  .00756 

.08716  .99619 

0 

/ 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin  Sine 

Co^in  |  Sine 

/ 

89° 

88° 

87° 

86° 

85° 

226 


TABLE  XV. -NATURAL  SINES  AND  COSINES. 


5° 

6° 

7°    j|    8° 

9° 

' 

Sine 

Cosin 

Sine 

Cosin 

Sine  I  Cosin 

Sine 

Cosin 

Sine 

Cosin 

' 

o 

708716 

"99619 

.10453 

.99452 

.12187  799255 

713917 

.99027 

.15643 

798769 

60 

1 

.08745 

.99617 

.10482  .99449 

.12216 

.99251 

.13946  .99023 

.15672 

.98764;  59 

o 

.08774 

99614 

.10511 

.99446 

.12245 

.99248 

.13975  .99019 

.15701 

.  98760  i  58 

3 

.08803 

99612 

.10540 

.99443 

.12274 

.99244 

.14004 

.99015 

.15730 

.98755  57 

4 

.08831 

.99609 

.10569  .99440 

.12302 

.99240 

.14033 

.99011 

.15758 

.98751  56 

.08860 

.99607 

.105971.99437! 

.12331 

.99237 

.14061 

.99006 

.15787 

.98746!  55 

6 

.08889 

99604 

.10626  j.99434 

.12360 

.99233 

.14090 

.99002 

.15816 

.98741!  54 

7 

.08918 

99602 

.10655 

.99431 

.12389 

.99230! 

.14119 

.98998 

.15845 

.98737  53 

8 

.08947 

99599 

.  10684 

.99428 

.12418 

.99226 

.14148  .98994 

.15873 

.98732  52 

9 

.08976 

99596 

.10713 

.99424 

.12447  .99222 

.14177 

.98990 

.15902 

.98728!  51 

10 

.09005 

99594 

.10742 

.99421 

.12476 

.99219 

.14205 

.98986 

.15931 

.98723 

50 

11 

.09034 

99591 

.10771 

.99418 

.12504 

.99215 

.14234 

.98982 

.15959 

.98718 

49 

12 

.09063 

99588 

.10800 

.99415: 

.12533 

.99211  i 

.14263 

.98978 

;  .15988 

.98714  48 

13 

.09092 

99586 

.10329 

.99412! 

.12562 

.  99208  ! 

.14292  .98973 

.16017 

.98709  47 

14 

.09121 

99583 

.10858 

99403  i 

.12591 

.90204! 

.14320  .68969 

.16046 

.98704  46 

15 

.09150 

99580 

.10387 

99406 

.12620 

.99200 

.14349 

.98965 

.16074 

.98700!  45 

16 

.09179 

.99578 

.10916 

99402  j 

.12649 

.99197; 

.14378 

.98961 

1  .16103 

.98695  44 

17 

.09208 

.99575 

.10945 

99399 

.12678 

.  99193  i 

.14407 

.98957 

.16132  .98690J  43 

18 

.09237 

.99572 

.10973 

99390 

.12706 

.99189 

.14436 

.98953 

i  .16160 

.98686  42 

19 

.09266 

.99570 

.11002 

93393 

.12735 

.991C61 

.14464 

.98948 

i  .16189 

.98681!  41 

20 

.09295 

.99567 

.11031 

.99390 

.12764 

.99182! 

.14493 

.98944 

.16218 

.98676 

40 

21 

.09324 

.99564 

.11060 

99336 

.12793 

.99178 

.14522 

.98940 

!  .16246 

.98671  39 

22 

.09353 

.99562 

.11039 

.99333 

.12822 

.99175 

.14551 

.98936 

.16275 

.98667  38 

23 

.09382 

.99559 

.11118 

.93330 

.12851 

.99171 

.14580 

.98931 

!.  16304 

.98662  37 

24 

.09411 

.99556 

.11147 

.99377 

.12330 

.99167 

.14608 

.98927 

.16333 

.98657  36 

25 

.09440 

.99553 

.11176 

.93374 

.12908 

.99163 

.14637 

.98923 

.16361 

.986521  35 

26 

.09469 

.99551 

.11205 

.99370, 

.12937 

.99160 

.14666 

.98919 

.163901.98648  34 

27 

.09498 

.99548 

.11234 

.99367! 

.12966 

.99156 

.14695 

.98914 

.  16419 

.98643!  33 

28 

.09527 

.99545 

.11263 

.99364 

.12995 

.99152 

.14723 

.98910 

.16447 

.98638  32 

29 

.09556 

.99542 

.11291 

.93360 

.13024 

.99148 

.14752 

.98906 

!  .16476 

.98633  31 

30 

.09585 

.99540 

.11320 

.99357 

.13053 

.99144 

.14781 

.98902 

.16505 

.98629  30 

31 

.09614 

.99537 

.11349 

.99354 

.13031 

.99141 

.14810 

.98897 

.16533 

.98624 

29 

32 

.09642 

.99534 

.11378 

.99351  i 

.13110 

.99137 

.14838 

.98893 

.16562 

.98619  28 

33 

.09671 

.99531 

.11407 

.99347 

.13139 

.99133 

.14867 

.98889 

i  .16591 

.98614!  27 

34 

.09700 

.99528 

.11436 

.93344 

.13163 

.99129 

.14896 

.98884 

'.16620 

.98609!  26 

35 

.09729 

.99526 

.11465 

.99341 

.13197 

.99125 

.14925 

.98880 

.16648 

.98604;  25 

36 

.09758 

.99523 

.11494 

.99337 

.13226 

.99122 

.14954 

.98876 

.1C677 

.98600!  24 

37 

.09787 

.99520 

.11523 

.99334 

.13254 

.99118 

.14982 

.98871 

.16706 

.98595  23 

38 

.09816 

.99517 

.11552 

.  99331  j 

.13283 

.99114: 

.15011 

.98867 

.16734 

.98590!  22 

39 

.09845 

.99514 

.11580 

.99327 

.13312 

.99110 

.15040 

.98863 

.16763 

.98585  21 

40 

.09874 

.99511 

.11609 

.99324 

.13341 

.99106 

.15069 

.98858 

.16792 

.98580  20 

41 

.09903 

.99508 

.11638 

.99320' 

.13370 

.99102 

.15097 

.98854 

.16820 

.98575 

19 

42 

.09932 

.99506 

.11667 

.  93317  | 

.13339 

.99098! 

.15126 

.98849  .16849 

.98570  18 

43 

.09961 

.99503 

.11696 

.  99314  ! 

.13427 

.99094 

.15155 

.98845 

.16878 

.98565!  17 

44 

.09990 

.99500 

.11725 

.93310! 

.13456 

.99091 

.15184 

.98841  .16906 

.98561  16 

45 

.10019 

.99497 

.11754 

•99307 

.13485 

.99087 

.15212 

.98836 

.16935 

.98656  15 

46 

.10048 

.99494 

.11783 

.99303 

.13514 

.99083 

.15241 

.98832 

i  .16964 

.98551!  14 

47 

.10077 

.99491 

.11812 

.99300! 

.13543 

.99079 

.15270 

.98827  .16992 

.98546 

13 

48 

.10106 

.99488 

.11840 

.99297! 

.13572 

.99075 

.  15299  i.  98823  |i.  17021 

.98541 

12 

49 

.10135 

.99485 

.11869 

.99293 

.13600 

.99071 

.15327 

.98818 

1  .17050 

.98536 

11 

50 

.10164 

.99482 

.11898 

.93290 

.13629 

.99067 

.15356 

.98814 

.17078 

.98531 

10 

51 

.10192 

.99479 

.11927 

.99286 

.13658 

.99063 

.15385 

.98809 

.17107 

.98526 

9 

52 
53 

.10221 
.10250 

.99476 
.99473 

.11956 
.11985 

.99283 
.99279 

.13687 
.13716 

.99059 
.99055 

.15414 
.15442 

.98805 
.98800 

.171  36  j.  98521 
.17164!.  98516 

8 

7 

54 

.10279 

.99470 

.12014 

.99276 

.13744 

.99051 

.15471 

.98796 

.17193 

.98511 

6 

55 

.10308 

.99467 

.12043 

.99272 

.13773 

.99047 

.15500 

.98791 

.17222 

.98506 

5 

56 

.10337 

.99464 

.12071 

.99269 

.13802 

.99043 

.15529 

.98787 

.17250 

.98501 

4 

57 

10366 

.99461 

.12100 

.99265 

.13831 

.99039 

.15557 

.98782 

.17279 

.98496 

3 

58 

.10395 

.99458 

.12129 

.99262 

.13860 

.99035 

.15586 

.98778 

.17308 

.98491 

2 

59 

.10424 

.99455 

.12158 

.99258 

.13889 

.99031 

.15615 

.98773 

.17886 

.98486 

1 

60 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

.1  7365  j.  98481 

0 

f 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

t 

84° 

83° 

82° 

81° 

80° 

227 


TABLE  XV. -NATURAL  SINES  AND  COSINES. 


10° 

11° 

12° 

13°    ||    14° 

' 

Sine 

Cosin 

Sine 

Cosin 

Sine  ;  Cosin 

Sine 

Cosin  Sine 

Cosin 

' 

~0 

.17365 

.98481 

719081 

.98163 

720791  797815 

722495 

797437 

.24192  .97030 

60 

1 

.17393 

.98476 

.19109 

.  98157 

.208201.97809 

.  22523 

.97430 

.24220 

.97023  59 

2 

.17422 

.98471 

.19138 

.98152 

.20848  .97803 

.22552 

.97424 

.24249 

.97015  58 

3 

.  17451 

.98466 

.19167 

.98146 

.20877 

.97797 

.22580 

.97417 

.24277 

.97008  57 

4 

.  17479 

.98461 

.19195 

.98140 

.20905 

.97791 

.22608 

.97411 

.24305 

.970011  56 

5 

.17508 

.98455 

.19224 

.98135 

.20933 

.  97784  ; 

.22637 

.97404 

.24333 

.96994  55 

6 

.17537 

.98450 

.19252 

.98129 

.20962 

.97778 

.22665 

-97398 

.24362 

.96987  54 

7 

.17565 

.98445 

.19281 

.98124' 

.20990 

.97772 

.22693 

.97391 

.24390 

.96980 

53 

8 

.17594 

.98440 

.19309 

.98118 

.21019 

.97766! 

22722 

.97384 

.24418 

.96973 

52 

9 

.17623 

.98435 

.19338 

.98112 

.21047 

.97760 

.22750 

.97378 

.24446 

.96966 

51 

10 

.17651 

.98430 

.19306 

.98107 

.21076 

.97754 

.22778 

.97371 

.24474 

.96959 

50 

11 

.17680 

.98425 

.19395 

.98101 

.21104 

.97748 

.22807  .97365 

.24503 

.96952 

49 

12 

.17708 

.98420 

.19423 

.98096 

.21132 

.97742  .22835  .97358 

.24531 

.96945  48 

13 

.  17737 

.98414 

.  19452 

.98C90 

.21161 

.97735 

.22863  .97351 

.24559 

.96937!  47 

14 

.  17766 

.98409 

.19481 

.98084 

.21189 

.97729 

.228921.97345 

.24587 

.96930  46 

15 

.17794 

.98404 

.19509 

.98079 

.21218 

.97723! 

.229201.97338 

.24615 

.96923 

45 

16 
17 

.17823 
.17852 

.98399 
.98394 

.19538 
.  19566 

.98073 
.98067: 

.21246 
.21275 

.977171 
.97711  ! 

.22948  j.97331 
.22977  .97325 

.24644 
.24672 

.96916  44 
.96909  43 

18 

.17880 

.98339 

.19595 

.98061 

.21303 

.97705 

.23005 

.97318 

.24700 

.96902  42 

19 

.17909 

.98383 

.  19623 

.98056 

.21331 

.97698 

.23033 

.97311 

.24728 

.96894]  41 

20  .17937 

.98378 

.19352 

.  98050 

.21360 

.97692, 

.23062 

.97304 

.24756 

.96887  40 

21  .17966 

.98373 

.19680 

.98044 

.21388 

.97686 

.23090 

.97298 

.24784 

.96880 

39 

22 

.17995 

.98368 

.19709 

.98039 

.21417 

.97680 

.23118 

.97291 

.24813 

.96873  38 

23 

.18023 

.98362 

.19737 

.98033 

.21445 

.97673 

.23146 

.97284 

.24841 

.96866  37 

24 

.18052 

.98357 

.19766 

.  93027  : 

.21474 

.97667 

.23175 

.97278 

.24869 

.96858  36 

25 

.18081  .98352 

.19794 

.98021 

.21502 

.97661 

.23203 

.9?271 

.24897 

.96851 

35 

26 

.181091.98347 

.19833 

.98016 

.21530 

.97655 

.23231 

.97264 

.24925 

.96844  34 

27 

.18138 

.98341 

.19851 

.98010 

.21559 

.97348 

.23280 

.97057 

.24954 

.96837  33 

28 

.18166 

.98336 

.19880 

.98004 

.21587 

.97342 

.23283 

.97251 

.24982 

.96829  32 

29 

.18195 

.98331 

.19908 

97998 

.21616 

.97638 

.23316 

.97244 

.25010 

.96822  31 

30 

.18224 

.98325 

.19937 

.97992 

.21644 

.97630 

.23345 

.97237 

.25038 

.96815 

30 

31 

.182521.98320 

.19965 

.97987 

.21672 

.97623 

.23373 

.97230 

.25066 

.96807 

29 

32 

.18281 

.98315!!  .19994 

.97931 

.21701 

.97617: 

.23401 

.97223  .25094 

.96800  28 

33 

.18309 

.98310 

.20022 

.97975  .21729 

.97611 

.23423 

.97217  .25122 

.96793  27 

34 

.18338 

.98304 

.20051 

.97969 

.21758 

.97604 

.23453 

.972101  .25151 

.96786  26 

35 

.18367 

.98299 

.20079 

97933 

.21783 

.97593 

.23488 

.97203  .25179 

.96778 

25 

30 

.18395 

.93294 

.20108 

97958  !  .21814 

.97592 

.23514 

.971  96  i  .25207 

.96771 

24 

37 

.18424 

.98238 

.20136 

97952  1  .21843 

.97535 

.23542 

.97189!  .25235 

.967'64 

23 

38 

.18452 

.98233 

.20165 

97943  .21871 

.97579! 

.23571 

.97182;  .25263 

.967561  22 

39 

.18481 

.98277 

.20193 

97940  i  .21899 

.975731 

.23599 

.97176!  .25291 

.96749 

21 

40 

.18509 

.98272 

.2022.2 

.  97934  j 

.21928 

.97566! 

.23627 

.97169i 

.25320 

.96742 

20 

41 

.18538 

.98267 

.20250 

97933  ' 

.21956 

.97560 

.23656 

.97162 

.25348 

.96734 

19 

42 

.18567 

.98261 

.20279 

97922   21985 

.97553 

.23684 

.97155(1  .25376 

.96727 

18 

43 

.18595 

.98256  i  .20307 

!  97916 

.22013 

.97547; 

.23712 

.97148  .25404 

.96719 

17 

44 

.18624 

.98250 

.20335 

97910  .22041 

.97541 

.23740 

.971411  .25432 

.98712 

16 

45 

.18652 

.98245 

.20364 

.97905 

.22070 

.975341 

.23769 

.97134;!  .25460 

.96705 

15 

46 

.18681 

.98240 

.20393 

.97893 

.22098 

.97528! 

.23797 

.97127  !  .25488 

.96697 

14 

47 

.18710 

.98234  .20421 

.97893 

.22126 

.97521 

.23825 

.97120'  .25516 

.96690 

13 

48 

.18738!.  98229  ij  .20450 

.  97887  i 

.22155 

.97515 

.23853 

.97113!  .25545 

.96682 

12 

49 

.18767 

.98223  .20478 

.97881 

.22183 

.97508; 

.23882 

.97106!!  .25573 

.96675 

11 

50 

.18795 

.98218 

.20507 

.97875 

.22212  .97502 

.23910 

.97100!  .25601  .96667 

10 

51 

.188241.98212! 

.20535 

.97869 

.22240 

.97496 

.23938 

.97093  .25629  .96660 

9 

52 

.18852 

.98207  .20563 

.978631 

.22268  .97489! 

.23966 

.97086  .25657  .96653 

8 

53 

.18881J.98201!  .  20592  i  .  97857  j 

.22297  .97483; 

.23995 

.  97079  !  .25685  .96645 

7 

54 

.18910 

.98196| 

.206201.97851 

.2232o  .97476 

.24023 

.97072  !  .25713;.  96638 

6 

55 

.18938 

.98190 

.  20649  .  97845  .  22353  :  .  97470  ! 

.24051 

.97065  .25741  .96630 

5 

56 

.18967 

.98185 

.20677 

.97839!  .  22382  .  97463 

.24079  .97058  .25769  .96623 

4 

57 

.18995 

.98179 

.20706 

.  97833  M  .22410  .97457 

.241081.97051  .25798  .96615 

3 

58 

.19024 

.98174 

.  20734  1.  97827  .22438  .97450 

.241  36j.  97(44! 

.25826  .96608 

2 

59 

.19052 

.98168 

.20763  .97821  .22467  .97444! 

.24164  .  97037  i 

.25854  .96600 

1 

60 

.19081 

.98163 

.20791  .97815 

.22495|.  97437 

.24192 

.97030  .25882  .96593 

0 

/ 

Cosin 

Sine  !  Cosin 

Sine 

Cosin  1  Sine 

Cosin 

Sine 

Cosin  Sine 

- 

79°    II    78° 

77° 

76° 

75° 

228 


TABLE  XV. -NATURAL  SINES   AND  COSINES. 


15°    | 

16° 

17° 

18° 

19° 

;  / 

Sine  Cosinj 

Sine  ;  Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

0 

.25882  .96593  1 

.27564  .96126 

.29237 

.95630! 

.30902 

.95106 

.32557 

.94552 

60 

1 

.25910  .96585 

.27592  .9(5118  .2D265 

.95622.  .30929 

.95097 

.32584 

.94542 

59 

2 

.25938  .96578  .27620  .96110 

.29293 

.95613!  .30957 

.95088 

.32612 

.94533  58 

3 

.  25966  !.  96570 

.27648  .96102 

.29321 

.95605  .30985 

.95079 

.32639 

.945231  57 

4 

.25994  .96562 

.27676  .96094 

.29:348 

.95596  .31012 

.95070 

.32667 

.94514  56 

5 

.26022  .96555 

.27704  .96086 

.29376 

.95588  .31040 

.95061 

.32694 

.945041  55 

6 

.26050  .96547 

.27731  .96078 

.29404 

.95579  .31068 

.95052 

.32722 

.94495 

54 

7 

.26079  .96540 

.27759!  '96070 

.29432 

.95571 

.31095 

.95043 

.32749 

.94485 

53 

8 

.26107  .96532 

.27787  .96062 

.29460 

.95562 

.31123 

.95033 

.32777 

.94476 

52 

9 

.26135  .96524 

.27815  .96054 

.29487 

.95554 

.31151 

.95024 

!  .32804 

.94466 

51 

10 

.26163 

.96517 

.27843;.  96046 

.29515 

.95545 

.31178 

.95015 

.32832 

.94457 

50 

11 

.26191 

.96509 

.27871  .96037 

.29543 

.95536 

.31206 

.95006 

'  .32859 

.94447 

49 

12 

.26219 

.96502 

.27899  .96029 

.29571 

.95528 

.31233 

.94997 

.32887 

.94438 

48 

13 

.26247 

.96494 

.  27927  i.  96021 

.29599 

.95519 

.31261 

.94988 

i  .32914 

.9H2S 

47 

14 

.26275 

.96486 

.27955  .96013 

.29626 

.95511 

.31289J.94979 

1.32942!.  94418 

46 

15 

.26303 

.96479 

.27983  j.96005 

.29654 

.95502 

.31316!.  94970 

.32969 

.94409 

45 

1G 

.26331 

.96471 

.280111.95997 

.29682 

.95493; 

.31344  .94961 

!  .32997 

.94399 

44 

17 

.26359 

.96463 

.280391.95989 

.29710 

.95485! 

.31372 

.94952 

i  .33024 

.94390 

43 

18 

.26387 

.96456 

.28067 

.95981 

.29737 

.9.5476 

.31399 

.94943 

.33051 

.94380 

42 

19 

.26415  .96448 

.28095 

.95972 

.29765 

.85467 

.31427 

.94933 

.33079 

.94370 

41 

20 

.26443 

.96440 

.28123  .95964 

.29793 

.95459  .31454 

.94924 

.33106 

.94361 

40 

21 

.26471 

.96433 

.28150 

.95956 

.29821 

.95450!  .31482 

.94915 

.33134 

.94351 

39 

22 

.26500 

.96425 

.28178 

.95948 

.29849 

.95441! 

.31510 

.94906 

.33161 

.94342 

38 

23 

.26528 

.96417 

.28206 

.95940 

.29876 

.95433 

.31537 

.94897 

.33189 

.94332 

37 

24 

.26556 

.96410 

.28234 

.95931 

.29904 

.95424 

.31565 

.94888 

.33216 

.94322 

36 

25 

.26584 

.96402 

.28262 

.95923 

.29932 

.95415! 

.31593 

.94878 

.33244 

.94313 

35 

26 

.26612 

.96394 

.28290 

.95915 

.29960 

.95407 

.31620 

.94869 

.33271 

.94303 

34 

27 

.26640 

.96386 

.28318 

.95907 

.29987 

.95398 

.31648 

.94860 

.33298 

.94293 

33 

28 

.26668 

.96379 

.28346 

.95898 

.30015 

.95389 

.31675 

.94851 

.33326 

.94284 

32. 

29 

.26696 

.96371J 

.28374 

.95890 

.30043 

.95380' 

.31703 

.94842 

.33353 

.94274 

31 

30 

.26724 

.96363! 

.28402 

.95882 

.30071 

.95372 

.31730 

.94832 

.33381 

.94264 

30 

31 

.26752 

.96355 

.28429 

.95874 

.30090 

.95363 

.31758 

.94823 

.33408 

.94254 

29 

32 

.26780 

.96347 

.28457 

.95805 

.301£G 

.95354 

.81780 

.94814 

.33436 

.94245 

23 

33 

.26808 

.96340 

.28485 

.95857 

.30154 

.95345 

.31813 

.94805 

.33463 

.94235 

27 

34 

.26836 

.96332 

.23513 

.95849 

.30182 

.95337 

.31841 

.94795 

.33490 

.94225 

26 

35 

.26864 

.96324 

.28541 

.95841 

.30209 

.95323 

.31868 

.94786 

.33518 

.94215 

25 

36 

.26892 

.96316 

.28509 

.95832 

.30237 

.95319 

.31896 

.94777 

.33545 

.94206 

24 

37 

.26920 

.96308 

.28597 

.95824 

.30265 

.95310 

.31923 

.94768 

.33573 

.94196 

23 

38 

.26948 

.96301 

.28625 

.95816 

.30292 

.95301 

.31951 

.94758 

.33600 

.94186 

22 

39 

.26976 

.  98293 

.28652 

.95807 

.30320 

.95203 

.31979 

.94749 

.33627 

.94176 

21 

40 

.27004 

.96285 

.28680 

.95799 

.30348 

.95284 

.32006 

.94740 

.33655 

.94167 

20 

41 

.27032 

.9627?' 

.28708 

.95791 

.30376 

.95275 

.32034 

.94730 

.33682 

.94157 

19 

42 

.27060 

.96269 

.  28736  j.  95782 

.30403 

.952G6 

.32001 

.94721 

.33710 

.94147 

18 

43 

.27088 

.96261 

.287641.95774 

.30431 

.95257 

.32089 

.94712 

.33737 

.94137 

17 

44 

.27116 

.96253 

.28792 

.95766 

.30459 

.95248 

.32110 

.94702 

.33764 

.94127 

16 

45 

.27144 

.96246 

.28820 

.95757 

.30486 

.95240 

.32144 

.94693 

.33792 

.94118 

15 

46 

.27172 

.96238! 

.28347 

.95749 

.305141.952311 

.32171 

.94684 

.33819 

.94108  14 

47 

.27200 

.96230 

.28875 

.95740 

.30542 

.95222; 

.32199 

.94674 

.33846 

.94098 

13 

48 

.272281.96222 

.28903 

.95732 

.30570 

.95213 

.32227 

.94665 

.33874  .94088 

12 

49 

.27256  |.96214 

.28931  .95724 

.30597 

.95204 

.32254 

.94656 

33901  .94078 

11 

50 

.27284 

.96206 

.28959  .95715 

.30625 

.95195 

.32282 

.94640 

.33929 

.94068 

10 

51 

.27312 

.96198 

.28987  .95707 

.30653 

.95186 

.32309 

.94637 

.33956 

.94058 

9 

52 

.27340  .96190; 

.29015  .95698 

.30680 

.95177: 

.32337 

.94627 

i  .33983  .94049 

8 

53 

.27368  .96182 

.29042:.  95690 

.30708 

.95168- 

.32364 

.94618 

|.  34011  .94039 

7 

54 

.27396  .96174 

.290701.95681 

.30736 

.95159 

.32392 

.94609 

.34038  .94029 

6 

55 

.27424  .96166 

.29098  .95673 

.30763 

.95150 

.32-119 

.94599 

.34065  .94019 

5 

56 

.27452  .96158 

.291261.95664 

.30791 

.95142 

.32447 

.94590 

.34093  .94009 

4 

57 

.27480  .96150 

.291  54!.  95656 

.30819 

.95133 

.32474 

.93580 

.341201.93999 

3 

58  1.27508  .96142 

.291821.95647 

.30846 

.95124 

.32502 

.94571 

.34147 

.93989 

2 

59  .27536  .96134 

.29209!.  95639 

.30874 

.95115 

.32529 

.94561 

.34175 

.93979 

1 

60  .27564  .96126 

.29237  .95630 

.80908 

.95106 

.32557 

.94552 

.34202 

.93969 

0 

7 

Cosin  i  Sine  j 

Cosin  Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

/ 

74* 

73° 

72° 

71° 

70° 

229 


TABLE  XV.-NATURAL  SINES  AND  COSINES. 


20° 

21° 

22°    I 

23° 

24° 

Sine 

Cosin 

Sine  ,  Cosin 

Sine  Cosin 

Sine  Cosin 

Sine  Cosin 

0 

.34202 

^  93969 

.  35837  i.  93358 

.37461 

.92718 

.39073 

.92050 

".40674  .91355 

60 

1 

.34229 

.93959 

.35864  .93348 

.37488  .92707 

.39100  .92039 

.40700  .91343 

59 

2 

.34257 

.93949 

.35891 

.93337 

.37515  .92G97 

.39127  .92028 

.40727  .91331 

58 

3 

.34284 

.93939 

.35918  .93327 

.37542  .92686 

.39153 

.92016 

.40753  .91319 

5? 

4 

.34311 

.93929 

.35945  .93316 

.37569  .92675 

.39180 

.92005 

.40780  .91307 

56 

5 

.34339 

.93919 

.35973  .93306 

.37595  .92664 

.39207 

.91994 

.40806  .91295 

55 

6 

.313661.93909 

.36000  .93295 

.37622 

.92653 

.89234 

.91982 

.40833  .91283 

54 

7 

.34393 

.93899 

.36027  .93285 

.37649 

.92642 

.39260 

.91971 

.40860  .91272 

53 

8 

.34421 

.93889 

.36054  .93274 

.37676 

.92631 

.39287  .91959] 

.40886  .91260 

52 

9 

.34448 

.93879 

.360811.93264 

.37703 

.92620 

.39314  .91948 

.40913  .91248 

51 

10 

.34475 

.93869 

.36108  .93253 

.37730 

.92609 

.39341 

.91936 

.40939 

.91236 

50 

11 

.34503 

.93859 

.36135  .93243 

.  37757  !.  92598 

.39367 

.91925 

.40966 

.91224 

49 

12 

.84530 

.  93849 

.36162  .93232 

.  37784  i.  92587 

.39394 

.91914 

.40992 

.91212 

48 

13 

.34557 

.93839 

.361901.93222 

.37811!.  92576 

.39421 

.91902 

.41019 

.91200 

47 

14 

.34584 

.93829 

.36217 

.93211 

.37838  .92565 

.39448:.  91  891 

.41045 

.91188 

46 

15 

.34612 

.93819 

.36244 

.93201 

.37865  .92554 

.394741.91879 

.41072 

.91176 

45 

16  .34639 

.93809 

.  36271  !.  931  90 

.37892  .92543 

.395011.91868 

.41098 

.91164 

44 

17  |  .34666 

.93799 

.36298  .93180 

.37919  .92532 

.39528  .91856 

.41125 

.91152 

43 

18  !.  34694 

.93789 

.36325  .93169 

.37946  .92521 

.395551.91845 

.41151 

.91140 

42 

19  .34721 

.93779 

.36352  .93159 

.37973  .92510 

.39581 

.91833 

.41178 

.91128 

41 

20 

.34748 

.93769 

.36379 

.93148 

.37999  .92499 

.39608 

.91822 

.41204  .91116 

40 

21 

.34775 

.93759 

.36406 

.93137 

.38026 

.92488 

.39635 

.91810 

.41231 

.91104 

39 

22 

.34803 

.93748 

.36434 

.93127 

.38053  .92477 

.39661 

.91799 

.41257 

.91092 

38 

23 

.34830 

.93738 

.36461 

.93116 

.38080  .92466 

.39688 

.91787 

.41284 

.91080 

37 

24 

.34857 

.93728 

.36488 

.93106 

.38107  .92455 

.39715 

.91775 

.41310 

.91068 

36 

25 

.34884 

.93718 

.36515 

.93095 

.38134 

.92444 

.39741 

.91764 

.41337 

.91056 

35 

26 

.34912 

.93708 

.36542 

.93084 

.38161 

.92432 

.39768  .91752 

.41363 

.91044 

34 

27 

.34939 

.93698 

.36569 

.93074 

.381881.92421 

.39795J.91741 

.41390 

.91032 

33 

28 

.34966 

.93688 

.36596 

.93063 

.38215 

.92410 

.39822 

.91729 

.41416 

.91020 

32 

29 

.34993 

.93677 

.36623 

.93052 

..C8241  .92399 

.39848 

.91718 

.41443 

.91008 

31 

30 

.35021 

.93667 

.36650 

.93042 

.38268  .92388 

.39875 

.91706 

.41469 

.90996 

30 

31 

.35048  .9365? 

.36677 

.93031 

.38295 

.92377 

.39902 

.91694 

.41496 

.90984 

29 

32 

.350751.93647 

.  36704  i.  93020 

.38322  .S23C6 

.3S92S 

.91683 

.41522 

.90972 

28 

33 

.35102  ;.93637 

.36731  .93010 

.38349 

.92355 

.33955 

.91671 

.41549 

.90960 

27 

34 

.35130  .93626 

.36758  .92999 

.38376 

.92343 

.39982 

.91660 

.41575 

.90948 

26 

35 

.35157  .93616 

.36785 

.92988 

.38403 

.92332 

.40008 

.91648 

.41602 

.90936 

25 

36 

.35184  .93606 

.36812 

.92978 

.38430 

.92321 

.40035 

.91636 

.41628 

.90924 

24 

37 

.35211 

.93596 

.36839  '.92967 

.38456 

.92310 

.40062 

.91625 

.41655 

.90911 

23 

38 

.35239  .93585 

.36867  .92956 

.38483 

.92299 

.40088 

.91613 

.41681 

.90899 

22 

39 

.35266  .93575 

.368941.92945 

.38510 

.92287 

.40115 

.91601 

.41707  .90887 

21 

40 

.35293  .93565 

.36921  .92935 

.38537 

.92276 

.40141 

.91590 

.41734  .90875 

20 

41 

.35320  '.93555 

.36948  .92924 

.38564 

.92265 

.40168 

.91578 

.41760 

.90863 

19 

42 

.35347  .93544 

.36975  .92913 

.38591 

.92254 

.40195 

.91566 

.41787 

.90851 

18 

43 

.35375  .93534 

.37002  .929021 

.38617 

.92243 

.40221 

.91555 

.41813  .90839 

17 

44 

.35402  .93524 

.37029  .92892' 

.38(344 

.92231 

.40248 

.91543 

.41840  .90826 

16 

45 

.35429  .93514 

.37056  .92881 

.38671 

.92220 

.40275 

.91531 

.41866  .90814 

15 

46 

.35456  .93503 

.37083 

.92870 

.38698 

.02209 

.40301 

.91519 

.41892  .90802 

14 

47 

.35484  .93493 

.37110 

.92859 

.38725 

.92198 

.40328 

.91508 

.41919  .90790 

13 

48 

.35511  .93483 

.37137 

.92849 

.38752 

.92186 

.40355 

.91496 

.41945;.  90778 

12 

49 

.35538  .93472 

.37164 

.92838 

.38778 

.92175 

.40381 

.91484 

.41972!.  907661  11 

50 

.35565  .93462 

.37191 

.92827 

.38805 

.92164 

.40408  .91472 

.  41998  r  90753 

10 

51 

.35592 

.93452 

.37218 

.92816 

.38832 

.92152 

.40434  .91461 

.42024  .90741 

9 

52 

.35619  .93441 

.37245 

.92805 

.  38859  j.  92141 

.40461!.  91449 

.42051 

.90729 

8 

53 

.35647 

.93431 

.37272 

.92794 

.38886  .92130 

.40488  .91437 

.42077 

.90717 

7 

54 

.35674 

.93420 

.37299 

.92784 

.38912  .92119 

.40514  .91425 

.42104 

.90704 

6 

55 

.35701 

.93410 

.37326 

.92773 

.389391.92107 

.40541  .91414 

.42130 

.90692 

5 

56 

.35728 

.93400 

.37353 

.92762 

.389661.92096 

.40567  .91402 

.42156 

.90680 

4 

57 

.35755 

.93389 

.37380 

.92751 

.38993!.  92085 

.40594  .91390 

.42183 

.90668 

3 

58 

.35782 

.93379 

.37407 

.92740 

.39020 

.92073' 

.40621  .91378 

.42209 

.90655 

2 

59 

.35810 

.93368 

.37434 

.92729 

.39046 

.92062 

.40647  .91366 

.42235 

.90643 

1 

CO 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674  '.91355 

.42262 

.90631 

0 

~ 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin  Sine 

Cosin 

Sine 

69° 

68° 

67° 

66° 

65° 

230 


TABLE  XV.— NATURAL  SINES  AND  COSINES. 


25° 

26° 

27° 

28° 

29° 

Sine  |Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine  '  Cosin 

Sine 

Cosin 

o 

.42262  .90631 

.43837 

.89879 

.45399 

.89101 

.  46947  i.  88295 

.48481 

.87462 

60 

1 

.42288  .90618 

.43863 

.89867 

.45425 

.89037 

.  46973  i.  88281 

.48506 

.87448 

59 

2 

.42315  .90606 

.43889 

.89854 

.45451 

.89074 

.46999 

.88267 

.48532 

.87434 

58 

3 

.42341  .90594 

.43916 

.89841 

.45477 

.89061 

.47024 

.88254 

.48557 

.87420 

57 

4 

.42367 

.90582 

.43942 

.89828 

.45503 

.89048 

.47050 

.88240 

.485831.87406 

56 

5 

.42394 

.90569 

.43968 

.89816 

.45529 

.89035 

.47076 

.88226 

.48608 

.87391 

55 

6 

.42420 

.90557 

.43994 

.89803 

.45554 

.89021 

.47101 

.88213 

.48634 

.87377 

54 

7 

.42446 

.90545 

.44020 

.89790 

.45580 

.89008 

.47127 

88199 

.48659 

.87363 

53 

8 

.42473 

.90532 

.44046 

.89777 

.45800 

.88995 

.47153 

.88185 

.48684 

.87349 

52 

9 

.42199 

.90520 

.4407'2 

.89764 

.45632 

.88981 

.47178 

.88172 

.48710 

.87335 

51 

10 

.42525 

.90507 

.44098 

.89752 

.45658 

.88968 

.47204 

.88158 

.48735 

.87321 

50 

11 

.42552 

.90495 

.44124 

.89739 

.45684 

.88955 

.47229 

.88144 

.48761 

.87306 

49 

12 

.42578 

.90483 

.44151 

.89726 

.45710 

.88942 

.47'255 

.88130 

.48786 

.87292 

48 

13 

.42604 

.90470 

.44177 

.89713 

.45738 

.88928 

.47281 

.88117 

.48811 

.87278 

47 

14 

.42631 

.90458 

.44203 

.89700 

.45762 

.88915 

.47306 

.88103 

.48837 

.87264 

46 

15 

.42657 

.90446 

.44229 

.89687 

.45787 

.88902 

.47332 

.88089 

.48862 

.87250 

45 

16 

.42683 

.90433 

.44255 

.89674 

.45813 

.88888 

.47358 

.88075 

.48888 

.87235 

44 

17 

.42709 

.90421 

.44281 

.89662! 

.45839 

.88875 

.47383 

.88062 

.48913 

.87221 

43 

18 

.42736 

.90408 

.44307 

.89649 

.45865 

.88862 

.47409 

.88048 

.48938 

.87207 

42 

19 

.42762 

.9C396 

.44333 

.89636 

.45891 

.88848 

.47434 

.88034 

.48964 

.87193 

41 

20 

.42788 

.90333 

.44359 

.89623 

.45917 

.88835 

.47460 

.88020 

.48989 

.87178 

40 

21 

.42815 

.90371 

.44385 

.89610 

.45942 

.88822 

47486 

.88006 

.49014 

.87164 

39 

22 

.42841 

.90338 

.44411 

.89597 

.45968 

.88808 

.475111.87993 

.49040 

.87150 

38 

23 

.42867 

.90346 

.44437 

.89584 

.45994 

.83795 

.47537 

.87979 

.49065 

.87136 

37 

24 

.42894 

.903U 

.44461 

.89571 

.46020 

.88782 

.47562 

.87965 

.49090 

.87121 

36 

23 

.42920 

.90321 

.44490 

.80558! 

.46046 

.88768 

.47588 

.87951 

.49116 

.87107 

35 

26 

.42946 

.90309 

.44516 

.89545 

.46072 

.88755 

.47614 

.87937 

.49141 

.87093 

34 

27 

.42972 

.90206 

.44542 

.89532 

.46097 

.88741 

.47639 

.87923 

.49166 

.87079 

33 

28 

.42999 

.90284 

.44568 

.89519 

.46123 

.88728 

.47665 

.87909 

.49192 

.87064 

32 

29 

.43025 

.9^271 

.44594 

.80506 

.46149 

.88715 

.47690 

.87896 

.49217 

.87050 

31 

30 

.43051 

.90259 

.44620 

.89493 

.46175 

.88701 

.47716 

.87882 

.49242 

.87036 

30 

31 

.43077 

.90246 

.44646 

.89480 

.46201 

.88688 

.47741 

.87868 

.49268 

.87021 

29 

32 

.43104 

.90233 

.44672 

.83467 

.46226 

.88674 

.47767 

.87854 

.49293 

.87007 

28 

33 

.43130 

.90221 

.44698 

.89454 

.46252 

.88661 

.47793 

.87840 

.49318 

.86993 

27 

34 

.43158 

.90203 

.44724 

.89441 

.46278 

.88647 

.47818 

.87826 

.49344 

.86978 

28 

35 

.43182 

.90196 

.44750 

.89428 

.46304 

.88634 

.47344 

.87812 

.49369 

.86964 

25 

36 

.43209 

.90183 

.44776 

.89415 

.46330 

.88620 

.47869 

.87798 

.49394 

.86949 

24 

37 

.43235 

.90171 

.44802 

.89402 

.46355 

.88607 

.47895 

.87784 

.49419 

.86935 

23 

38 

.43261 

.90153 

.44828 

.89389 

.46381 

.88593 

.47020 

.87770 

.49445 

.86921 

22 

39 

.43287 

.90146 

.44854 

.80376 

.46407 

.88580 

.47946 

.87756 

.49470 

.86906 

21 

40 

.43313 

.90133 

.44880 

.89363 

.46433 

.88566 

.47971 

.87743 

.49495 

.86892 

20 

41 

.43340 

.90120 

.44906 

.89350 

.46458 

.88553 

.47997 

.87729 

.49521 

.86878 

19 

42 

.43366 

.90108 

.44932 

.80337 

.46484 

.88539 

.48022 

.87715 

.49546 

.86863 

18 

43 

.43392 

.90095 

.44958 

.80324 

.46510 

.88526 

.48048 

.87701 

.49571 

.86849 

17 

44 

.43418 

.90082 

.44984 

.89311 

.46536 

.88512 

.48073 

.87687 

.49596 

.86834 

16 

45 

.43445 

.90070 

.45010 

.89298 

.46561 

.88499 

.48099 

.87673 

.49622 

.86820 

15 

46 

.43471 

.90057 

.45036 

.89285 

.46587 

.88485 

.48124 

.87659 

.49647 

.86805 

14 

47 

.43497 

.90045 

.45062 

.89272 

.46613 

.88472 

.48150 

.87645 

.49672 

.86791 

13 

48 

.43523 

.90032 

.45088 

.89259 

.46639 

.88458 

.48175 

.87631 

.49697 

.86777 

12 

49 

.43549 

.90019 

.45114 

.89245 

.46664 

.88445 

.48201 

.87617 

.49723 

.86762 

11 

50 

.43575 

.90007 

.45140 

.89232 

.46690 

.88431 

.48226 

.87603 

.49748 

.86748 

10 

51 

.43602 

.89994 

.45166 

.89219 

.46716 

.88417 

.48252 

.87589 

.49773 

.86733 

9 

52 

.43628 

.89981 

.45192 

.89206 

.46742 

.88404 

.48277 

.87575 

.49798 

.86719 

8 

53 

.43654 

.89968 

.45218 

.89193 

.46767 

.88390 

.48303 

.87561 

.49824 

.86704 

7 

54 

.43680 

.89956 

.45243 

.89180 

.46793 

.88377 

.4&S28 

.87546 

.49849 

.86690 

6 

55 

.43708 

.89943 

.45269 

.89167 

.46819 

.88363 

.48354 

.87532 

.49874 

.86675 

5 

56 

.437&S 

.89930 

.45295 

.89153 

.46844 

.88349 

.48379 

.87518 

.49899 

.86661 

4 

57 

.43759 

.89918 

.45321 

.89140 

.46870 

.88336 

.48405 

.87504 

.49924 

.86646 

3 

58 

.43785 

.89905 

.45347 

.89127 

.46896 

.88322 

.48430 

.87490 

.49950 

.86632 

2 

59 

.43811 

.89892 

.45373 

.89114 

.46921 

.88308 

.48456 

.87476 

.49975 

.86617 

1 

60 

.43837 

.89879 

.45399 

.89101 

.46947 

.88295 

.48481 

.87462 

.50000 

.86603 

_0 

/ 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine 

i  Cosin 

Sine 

Cosin 

Sine 

/ 

64° 

63° 

62° 

61° 

60° 

231 


TABLE  XV.— NATURAL   SINES  AND  COSINES. 


30° 

31° 

32°    | 

33° 

34° 

Sine 

Cosin 

Sine 

Cosin 

Sine 

Cosin 

Sine  !  Cosin 

Sine  Cosin 

~o 

.50000 

.86603 

751504 

785717 

752992  :  .84805 

754464  783867 

.55919 

.82904 

60 

l 

.50025 

.86588 

.51529 

.857'02 

.53017 

.84789 

.54488!.  83861 

.55943 

82887 

59 

2 

.50050 

.86573 

.51554 

.85687 

.53041 

.84774  .54513  .83835 

.55968 

.82871 

58 

3 

.50076 

.86559 

.51579 

.85672 

.53066  .84759 

.54537  .83819 

.55992 

.82855 

57 

4 

.50101 

.86544 

.51604 

.85657 

.530911.84743 

.  5450  l|.  83804 

.56016 

.82839 

56 

5 

.50126 

.86530 

.51628 

.85642 

.531  15  !.  84728 

.54586  .83788 

.56040 

.82822 

55 

6 

.50151 

.86515 

.51653 

.85627 

.531401.84712 

.54610i.83772 

.56064 

.82806 

54 

7 

.50176 

.86501 

.51678 

.85612 

.53164 

.84697 

.546351.83756 

.56088 

.827'90 

53 

8 

.50201 

.86486 

.51703 

.85597 

.53189 

.84681 

.54659  .83740 

.56112 

.82773 

52 

9 

.50227 

.86471 

.51728 

.85582; 

.53214 

.84666 

.54683  .83724 

.56136 

.82757 

51 

10 

.50252 

.86457 

.51753 

.85567 

.53238 

.84650 

.54708 

.837o8 

.56160 

.82741 

50 

11 

.50277 

.86442 

.51778 

.85551 

.53263 

.84635* 

.54732 

.83692 

.56184 

.82724 

49 

12 

.50302 

.86427 

.51803 

.85536 

.53288 

.84619 

.54756 

.83676 

.56208 

.82708 

48 

13 

.50327 

.86413 

.51823 

.85521 

.53312 

.84604 

.54781 

.83660 

.56232 

.82092 

47 

14 

.50352 

.86398 

.51852 

.85506 

.53337 

.84588 

.54805 

.83645 

.56256 

.82075 

46 

15 

.50377 

.86384 

.51877 

.85491 

.53361 

.84573 

.548291.83629 

.50280 

.82059 

45 

1G 

.50403 

.86369 

.51902 

.85476 

.53386 

.84557 

.54854  1.83613 

.56305 

.82043 

44 

17 

.50428 

.86354 

.51927 

.85461 

.53411 

.84542 

.54878  .83597 

!  .56329 

.82020 

43 

18 

.50453 

.86340 

.51952 

.85446 

.53435 

.84526 

.54902  .83581 

.56353 

.82610 

42 

19 

.50478 

.86325 

.51977 

.85431 

.53460 

.84511 

.M927  1.83565 

.56377 

.82593 

41 

20 

.50503 

.86310 

.52002 

.85416 

.53484 

.84495 

.54951 

.83549 

.56401 

.82577 

40 

21 

.50528 

.86295 

.52026 

.85401 

.53509 

.84480 

.54975 

.83533' 

.56425 

.82561 

39 

22 

.50553 

.86281 

.52051 

.85385 

.53534 

.84464! 

.54999 

.83517 

.56449 

.82544 

33 

23 

.50578 

.86206 

.52076 

.85370 

.53558 

.84448 

.55024 

.83501 

.56473 

.82528 

37 

24 

.50603 

.86251 

.52101 

.85355 

.53583 

.  84433  : 

.55048 

.83485 

.56497 

.82511 

36 

25 

.50628 

.86237 

.52126 

.85340 

.53607 

.84417 

.55072 

.83469 

.56521 

.82495 

35 

26 

.50654 

.86222 

.52151 

.85325 

.53632 

.84402 

.55097 

.83453 

.56545 

.82478 

34 

.50679 

.86207 

.52175 

.85310, 

.53656 

.84386 

.55121 

.83437 

.56569 

.82402 

33 

28 

.50704 

.86192 

.52200 

.85294 

.53681 

.84370 

.55145 

.83421 

.56593 

.82440 

32 

29 

.50729 

.86178 

.52225 

.85279 

.53705 

.84355 

.55169 

.83405 

.50617 

.82429 

31 

30 

.50754 

.86163 

.52250 

.85204 

.53730 

.84339 

.55194 

.83389 

.56041 

.82413 

30 

31 

.50779 

.86148 

.52275 

.  85249  ' 

.53754 

.  84324  ! 

.55218 

.83373 

.56665 

.82396 

29 

32 

.50804 

.86133 

.52299 

.85234 

.53779 

.84303 

.55242 

.83856 

.66689 

.82380 

28 

33 

.50829 

.86119 

.52324 

.85218 

.53804 

.84292 

.C52G6 

.83340 

.50713 

.82303 

27 

34 

.50854 

.86104 

.52349 

.85203 

.53828 

.84277, 

.55291 

.83324 

.56736 

.82347 

26 

35 

.50879 

.86089 

.52,374 

.85188 

.53853 

.84261  1 

.55315 

.8:3308 

.56760 

.82330 

25 

36 

.50904 

.86074 

.52399 

.85173 

.53877 

.84245 

.55339 

.83292 

.56784 

.82314 

24 

37 

.50929 

.86059 

.52423 

.85157 

.53902 

.84230 

.55363 

.83276 

.50808 

.82297 

23 

38 

.50954 

.86045 

.52448 

.85142 

.53926 

.84214 

.55388 

.83260 

.50832 

.82281  1  22 

39 

.50979 

.86030 

.52473 

.85127 

.53951 

.84198 

.55412 

.83244 

.50856 

.82264 

21 

40 

.51004 

.86015 

.52498 

.85112 

.53975 

.84182 

.55436 

.83228 

.50880 

.82248 

20 

41 

.51029 

.86000 

.52522 

.85090 

.54000 

.84167 

.55460 

.83212 

.56904 

.82231 

19 

42 

.51054 

.85985 

.52547 

.85081 

.54024 

.84151 

.55484 

.83195 

.56928 

.82214 

13 

43 

.51079 

.85970 

.52572 

.  85033  i 

.54049 

.84135 

.55509 

.83179 

.50952 

.82198 

17 

44 

.51104 

.85956 

.52597 

.85051  1 

.54073 

.84120 

.5o533  1.83163 

.50976  .82181 

16 

45 

.51129 

.85941 

.52621 

.85035! 

.54097 

.84104 

.55557 

.83147 

.57000  .82165 

15 

46 

.51154 

.85926 

.52646 

.85020: 

.54122 

.84088 

.55581 

.83131 

.57024 

.82148 

14 

47 

.51179 

.85911 

.53671 

.85005 

.54146 

.84072 

.55605 

.83115'  .57047 

!  82  132 

13 

48 

.51204 

.85896 

.52696 

.84989 

.54171 

.84057 

.55630 

.R3i)9S  .57071 

.82115 

12 

49 

.51229 

.85881 

.52?'20 

.8497'4 

.54195 

.84041 

.55654 

.83082  J  .57095 

.82098 

11 

50 

.51254 

.85866 

.52745 

.84959 

.54220 

.84025 

.55678 

.83066  .57119 

.82082 

10 

51 

.51279 

.85851 

.52770 

.84943 

.54244 

.84009 

.55702 

.&3050 

.57143 

.82065 

9 

52 

.51304 

.85,836 

.52794 

.84928 

.542691.83994 

.55726 

.83034 

.57167 

.82048 

8 

53 

.51329 

.85821 

.52819 

.84913 

.54293J.83978 

.55750 

.83017 

.57191 

.82032 

7 

54 

.51354 

.85806 

.52844 

.84897 

.54317 

.83962 

.55775 

.83001 

.57215 

.82015 

6 

55 

.51379 

.85792 

.52869 

.84882 

.54342 

.83946 

.55799 

.82985 

.57238 

.81999 

5 

56 

.51404 

.85777 

.52893 

.84866! 

.54366 

.83930 

.55823 

.82969 

.57262 

.81982 

4 

57 

.51429 

.85762 

.52918 

.84851  | 

.54391 

.83915 

.55847 

.82953 

.57286 

.81  965 

3 

58 

.51454 

.85747 

.52943 

.84836: 

.54415 

.83899 

.55871 

.82936 

.57310 

.81949 

2 

59 

.51479 

.85732 

.52967 

.84820 

.544401.83883  .55895 

.82920  .57334 

.81932 

i 

60 

.51504 

.85717 

.52992 

.84805 

.54464  .83867H  .55919 

.82904;  .57358 

.81915!  0 

/ 

Cosin 

~Sine^ 

Cosin 

Sine" 

Cosin  j  "Sine" 

Cosin 

Sine 

Cosin  Sii>e 

t 

59° 

58° 

57° 

56° 

55° 

232 


TABLE  XV.— NATURAL  SINES  AND  COSINES. 


35° 

36° 

37° 

38° 

39° 

' 

Sine  Cosin 

Sine  Cosin 

Sine  Cosin 

Sine 

Cosin 

Sine  |  Cosin 

~~0  !  757358  781915 

758779  780902  ! 

T60182 

.79864 

761566 

778801 

762932 

.77715 

60 

1  !  .573H1|.81899 

.58802 

.80885 

.60205 

.79846 

.61589 

.78783 

.62955 

.77690 

59 

2  !  .574051.81882 

.58826 

.80867 

.60228  .79829; 

.61612 

.78765 

.62977 

.77678 

58 

3  :  .57429  .81865; 

.58849 

.80850! 

.602511.  7981  li 

.61635 

.78747 

.63000 

.77'660 

57 

4  i  .57458 

.81848! 

.58873 

.80833; 

.60274!.  79793  i 

.61658 

.78729 

.63022 

.77641 

56 

5  !  .57477 

.81832: 

.58896 

.80816 

.  60298  L  79776 

.61681 

.78711 

.63045 

.77623 

55 

6  :  .57501 

.81815 

.58920 

.80799 

.60321  .79758' 

.61704 

.78694 

.63068 

.77605 

54 

7  I  .57524 

.81798 

.58943 

.80782 

.60344 

.797411 

.61726 

.78676! 

.63090 

.77586 

53 

8  i  .57548 

.81782 

.58967 

.80765 

.60367 

.79723 

.61749 

.78658 

.63113 

.77568 

52 

9  .57572 

.81765 

.58990 

.80748 

.60390 

.79706 

.61772 

.78640 

.63135 

.77550 

51 

10  j  .57596 

.81748 

.59014 

.80730 

.60414 

.79688 

.61795 

.78622 

.63158 

.77531 

50 

11  .57619 

.81731 

.59037 

.80713 

.60437 

.79671 

.61818 

.78604 

.63180 

.77513 

40 

12  i  .57643 

.81714 

.59061 

.80696 

.60460 

.79653 

.61841 

.78586 

.63203 

.77494 

48 

13  .57667 

.81698 

.59084 

.80679 

.60483 

.79635 

.€•1864  .78568 

.63225 

.77476 

47 

14 

.57691 

.81681 

.59108 

.80662 

.60506 

.79618 

.61887 

.78550 

.63248 

.77458 

46 

15 

.57715 

.81664 

.59131 

.80644! 

.60529 

.79600 

.61909 

.78532! 

.63271 

.77439 

45 

16 

.57738 

.81647 

.59154 

.80627 

.60553 

.79583 

.61932 

.78514! 

.63293 

.77421 

44 

17 

.57762 

.81631 

.59178 

.80610 

.60576 

.79565 

.619551.78496! 

.63316 

.77402  43 

18 

.57786 

.81614 

.59201 

.80593 

.60599 

.79547 

.61978  .78478! 

.63338 

.77384  42 

19 

.57810 

.81597 

.59225 

.  80576  j 

.60622 

.79520 

.62001 

.7'8460; 

.63361 

.77366 

41 

20 

.57833 

.81580 

.59248 

.80558 

.60645 

.79512 

.62024 

.78442 

.63383 

.77347 

40 

21 

.57857 

.81563 

.59272 

.80541 

.60668 

.79494 

.62046 

.78424 

.63406 

.77329 

39 

22 

.57881 

.81546 

.59205 

.80524: 

.60691 

.79477 

.62069 

.784051 

.63428 

.77310  38 

23 

.57904 

.81530 

.59318 

.80507 

.60714 

.79459 

.62092  .78387! 

.63451 

.77292  37 

24 

.57928 

.81513 

.59342 

.80489 

.60738 

.79441 

.62115  L78369J 

.63473 

.77273 

36 

25 

.57952 

.81496 

.59365 

.80472 

.60761 

.79424 

.621381.783511 

.63496 

.77255  35 

26 

.57976 

.81479 

.59389 

.80455 

.60784 

.79406'  .621601.78333! 

.63518 

.77236  34 

27 

.57999 

.81462 

.59412 

.80438! 

.60807 

.79388 

.62183!.  78315! 

.63540 

.77218  33 

28 

.58023 

.81445 

.59436 

.80420! 

.60830 

.79371 

.62206!.  78297 

.63563 

.77199 

32 

29 

.58047 

.81428 

.594591.80403 

60853 

.79353 

.622291.78279 

.63585 

.77181)  31 

30 

.58070 

.81412 

.59482 

.80386J 

.60876 

.79335 

.62251 

.78261 

.63608 

.77162 

30 

31 

.58094 

.81395 

.59506 

.80368 

.60899 

.79318 

.62274 

.78243 

.63630 

.77144 

29 

32  1  .58118 

.81378 

.59529  .80351 

.60922 

.79300 

.62297 

.78225 

.63653 

.77125 

28 

33 

.58141 

.81361 

.59552  .80334 

.60945 

.79282 

.62320  .78206 

.63675 

.77107 

27 

34 

.58165 

.81344: 

.59576  .80316! 

.6C968 

.79264 

.623421.78188 

.63698 

.77088  26 

35 
36 

.58189  .81327 
.58212  .81810 

.59599 

.59622 

.80299 
.80282 

.€0991 

.61015 

.79247 
.79229 

.62365  .78170 
.62388  .78152 

.63720 
.63742 

.77070!  25 
.77051124 

37  .58236J.81293 

.59646 

.80264 

.61038 

.79211 

.62411 

.78134! 

.63765!.  770331  23 

38  .58260 

.81276  .59669 

.80247 

.61061 

.79193 

.62433 

.78116 

.63787 

.7701  4  l  22 

39  .58283 

.81259! 

.59693 

.802301 

.61084 

.79176 

.62456 

.780981 

.63810 

.76996!  21 

40  .58307 

.81242 

.59716 

.80212 

.61107 

.791C8 

.62479 

.  78079  i 

.63832 

.76977 

20 

41  .58330 

.81225 

.59739  .80195 

.61130 

.79140 

.62502 

.  78061  • 

.63854 

.76959 

19 

42 

.58354  .81208 

.59763  .80178 

.61153 

.79122 

.62524 

.78043! 

.63877 

.76940!  18 

43 

.58378  .81191 

.59786  .80160 

.61176 

.79105 

.62547 

.78025 

.63899 

.76921!  17 

44 

.58401  .81174 

.59809  .80143 

.61199 

.79087 

.62570 

.78007 

.63922 

.769031  16 

45  i  .58425  .81157 

.59832  .80125 

.61222 

.79069 

.62592 

.77988 

.63944 

.76884  15 

46  1  .58449  .81140 

.59856 

.80108 

.61245 

.79051 

.62615  .77970 

.63966 

.76866!  14 

47 

.58472  81123 

.59879 

.80091 

.61268 

.79033 

.62638  .77'952! 

.63989 

.76847 

13 

48 

.58496 

.81106 

.59902 

.80073 

.61291  .79016 

.62660 

.77934 

.640111.76828 

12 

49 

.58519 

.81089 

.59926 

.80056 

.81814  .78006 

.62683 

.77916 

.64033 

.T6810 

11 

50 

.58543 

.81072 

.59949 

.80038 

.61337 

.78980 

.62706 

.77897 

.64056 

.76791 

10 

51 

.58567 

.81055 

.59972 

.80021 

.61360 

.78962 

.62728 

.77879 

.64078 

.76772 

9 

52 

.58590 

.81038 

.59995 

80003: 

.61383 

.78944 

.62751 

.778611 

.64100 

.76754 

8 

53 

.58614 

.81021 

.60019 

.79986; 

.61406 

.78926 

.62774 

.77843 

.64123 

.76735 

ft 

54 

.58637 

.81004 

.60042 

.79968 

.61429 

.78908 

.62796 

.77824 

.64145 

.76717 

6 

55 

.58661 

.80987 

.60065 

.79951; 

.61451 

.78891 

.62819 

.77806 

.64167 

.76698 

5 

56 

.58(584 

.H(M)7'() 

.60089 

.79934; 

.61474 

.78873 

.62842 

.77788 

.64190 

.76679 

4 

57 

.58708 

.80953 

.60112 

.79916, 

.61497 

.78855 

.62864 

.77769 

.64212 

.766611  3 

58 

.58731 

.80936 

.60135 

.79899 

.61520 

.78837 

.62887 

.77751 

.64234 

.76642;  2 

59 

.58755 

.80919 

.601581.79881 

.61543 

.78819 

.62909 

.77733 

.64256 

.76623  1 

60 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.  62932 

.77715 

.64279 

.76604  0 

| 

Cosin 

Sine" 

Cosin  Sine 

Cosin  j  Sine 

Cosin  Sine 

Cosin 

Sine 

/ 

54° 

53° 

52° 

51' 

50° 

233 


TABLE  XV.— NATURAL  SINES  AND  COSINES. 


40° 

41° 

42° 

43* 

44J 

Sine  ICosin 

Sine 

Cosin 

Sine 

1  Cosin 

Sine  !  Cosin 

Sine  Cosin 

0 

.64279 

.76604 

.65606 

.75471 

.00913 

.74314 

.68200  .73135 

769466  .71934  60 

1 

.64301 

.76586 

.65628 

.75452 

.60935 

.74295 

.68221 

.73116 

.69487  .71914  59 

2 

.64323 

.76567 

.65650 

.75433 

.60956 

.74276 

.68242 

.73090 

.69508  .71894  58 

3 

.61316 

.70548 

.65672 

.75414 

.60978 

.74256 

.68204 

.730?'6 

.  69529  !.  71873:  57 

4 

.04368 

.76530j 

.65694 

.75395 

.00399 

.74237 

.68285 

.73056 

.69549  .71853  56 

5 

.64390 

.76511 

.65716 

.75375 

.67021 

.74217 

.68306 

.73036 

.69570  .71833  55 

6 

.64412 

.76402 

.65738 

.75356 

.67043 

.74198 

.68327 

.73016 

.69591  .718131  54 

7 

.64435 

.76473 

.65759 

.75337 

.67064 

.74178 

.68349 

.72996 

.69012  .71792  53 

8 

.64457 

.76455 

.65781 

.75318 

.67083  .74159 

.68370 

.72976 

.696331.71772  52 

9 

.64479 

.78438 

.65803 

.  75299 

.  67107  !.  74139 

.68391 

72957 

.  69654  !.  71  752!  51 

10 

.64501 

.76417 

.65825 

.75280 

.67129 

.74120 

.68412 

!  72937  j 

.69675 

.71732 

50 

11 

.64524 

.76398 

.65847 

.75281 

.67151 

.74100 

.68434 

.72917 

.69696 

.71711 

49 

IS 

.64546  .76330 

.65363 

.75241 

.67172 

.74080 

.68455 

.72897 

.68717  .71  691  i  48 

13 

.64568  .76331 

.65891 

.75222 

.67194 

.74001 

.68476 

.72877 

.69737  .71671  47 

14 

.64590  76342 

.65913 

.75203 

.67215 

.74041 

.68497 

.72857 

.  69758  i.  71  650  46 

15 

.64612  .76323 

.65935 

.75184 

.67237 

.74022 

.68518 

.72837 

.69779  .71630!  45 

16 

.64635  .76304 

.65956 

.75165 

.67258 

.74002 

.68539 

.72817 

.69800 

.716101  44 

17 

.64857  .76236 

.65978 

.75146 

.67280 

.73983 

.68561 

.72797 

.69821 

.71590 

43 

18 

.646791.76207 

.66000 

.75128 

.67301 

.73963 

.68582 

.72777 

.69842 

.71569 

42 

19 

.64701 

.76248 

.65022 

.75107! 

.67323 

.73944 

.68603 

.72757 

.698621.71549 

41 

20 

.64723 

.76229 

.66044 

.  75088  ! 

.67344 

.73924 

.68624 

.72737 

.69883 

.71529 

40 

21 

.64746 

.76210 

.66066 

.  75039  ! 

.67386 

.73904 

.68645 

.72717 

.69904 

.71508 

39 

22 

.64768 

.7611)2 

.63333 

75350 

.67087 

.73885 

.68006 

.72697 

.69325 

.71488 

38 

23 

.64790 

.761731 

.68103 

75330 

.67409 

.7'3835 

.63G88 

.72677 

.69946 

.71468 

37 

24 

.64812  .761541 

.66131 

75011  i 

.67430 

.73848 

.637'09 

.7'2G57 

.69968 

.71447 

36 

25 

.64834  .  78135  | 

.66153 

74332  | 

.67452 

.73823 

.68730 

.72637 

.69987 

.71427 

35 

26 

.64856  1.761  16  ! 

.63175 

74373  ! 

.67473 

.73803 

.63751 

.72617! 

.70008 

.71407 

34 

27 

.64878  .76037! 

.65197 

74353 

.67435 

.73787 

.68772 

.72597; 

.70029 

.71386 

33 

28 

.64901 

.76078 

.63218 

74334 

.67516 

.73767 

.68793 

.  72577  ' 

.70049 

.71306 

32 

29 

.64923 

.76059! 

.68240 

74915 

.67533 

.73747 

.63814 

.72557 

.70070 

.71345 

31 

30 

.64945 

.76041! 

.68282 

74896 

.67559 

.73728 

.68835 

.72537; 

.7'0091 

.71325 

30 

31 

.61967 

.76022! 

.68284 

74876  ' 

.67580 

.73703 

.68857 

.72517 

.70112 

.71305 

29 

32 

.64989 

.76003' 

.66308 

74857! 

.67632 

.73383 

.63878 

.  72497  : 

70132 

.71284 

28 

33 

.65011 

.75934; 

.66327 

74838 

.67023 

.73633 

.63899 

.72-477! 

.70153 

.71264 

27 

34 

.65033 

.75985; 

.66349 

74818  ! 

.67645 

.73649 

.68920 

.72457 

.70174 

.71243 

26 

35 

.65055|.75946 

:  66371 

74799  ! 

.67666 

.73623 

.68341 

.72437 

.70195 

.71223 

35 

36 

.65077 

.75927 

.66393 

74780  ! 

.67688 

.73610 

.68982 

.724171 

.70215 

.71203 

24 

37 

.65100 

.759:38 

.6641  4  1.  74760  ! 

.67709 

.73590 

.68983 

.72397 

.70236 

.71182 

23 

38 

.651221.75889 

.66438 

.74741 

.67730 

7357'0 

.69004 

.72377 

.70257 

.71162 

22 

39 

.65144 

.75870 

.68458 

.74722; 

.67752 

.73551 

.69025 

.72357 

.70277 

.71141 

21 

40 

.65166 

.75851, 

.66480 

.74703 

.67773 

.73531 

.69046 

.72337 

.70238 

.71121 

20 

41 

.65188 

.75832 

.66501 

.74683 

.67795 

.73511 

.69067 

.72317 

.70319 

.71100 

19 

42 

.65210 

.75813 

.68523 

.74664! 

.67816 

.73491 

.63088 

.72297 

.70339 

.71080 

18 

43 

.65232 

.75794 

.68545 

.  74844 

.67837 

.73472 

.09109 

.72277 

.70360 

.71059 

17 

44 

.65254 

.75775: 

.66566 

.74325, 

.67859 

.73452 

.69130 

.  72257 

.70381 

.71039  16 

45 

.65276 

.75756 

.66588 

.74603 

.67880 

.73432 

.09151 

.72236 

.70401 

.71019  15 

46 

.65298  .75738: 

.66610 

.74586 

.67901 

.73413 

69172 

722:6 

.70422  .70998  14 

47 

.65320  .75719 

.66832 

.74567' 

.67923 

.73393 

.69193 

.72196 

.70443 

.70978!  13 

48 

.65342  .75700 

.66653 

.74548 

.67944 

.73373 

.69214 

.72176 

.70403 

.70957!  12 

49  1.65364  .75680 

.66675 

.74528 

.67965 

.73353 

.69235 

.72156  .70484 

.70937 

11 

50 

.65386 

.75661 

.66697 

.74509  .67987 

.73333 

.69256 

.72136 

.70505 

.70916 

10 

51 

.65408 

.75642 

.66718 

.74489  .68008 

.73314 

.69277 

.72116 

.70525 

.70896 

9 

52  1.65430  .75623 

.66740  .74470  .68029 

.73234 

.69298 

.72095 

.70540  .70375 

8 

53 

.65452  .75604 

.66762:.74451  .68051 

.73274 

.69319 

.72075  .70567  1.70855 

7 

54 

.65474  .75585: 

.66783  .74431  .68072 

.73254 

.69,340 

.  72055  i 

.70587  .70834 

6 

55 

.65496  '75566! 

.66805  .74412  .68093 

.73234 

.69361 

.72035! 

.70008  .70813 

5 

56 

.655181.75547 

.66827  .74392  1  .68115 

.73215 

.69382 

.72015 

.70628  .70793 

4 

57 

.65540 

.75528 

.66848  .74373  1  .68136 

.73195 

.69403 

.71995 

.70649  .70772 

3 

58 

.65562 

.75509 

.668701.74358 

.68157 

.73175 

.69424 

.711,74 

.70070  .70752 

2 

59 

.65584 

.75490 

.66891  .74334 

.68179 

.73155 

.69445 

.71954 

.70690  .70731 

1 

60 

.65606 

.75471 

.00913  .74314! 

.68200 

.73135 

.69466 

.71934 

.70711 

.70711 

0 

/ 

Cosin 

Sine 

Cosin  Sine  |  Cosin 

. 

Sine 

Cosin 

Sine 

Cosin  |  Sine 

/ 

49° 

48°    il   -47° 

46° 

45° 

234 


TABLE  XVI. —NATURAL  TANGENTS  AND  COTANGENTS. 


0° 

1° 

2° 

3° 

**" 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

!  Tang  |  Cotang 

/ 

0 

.00000 

In  Unite. 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811  |60 

1 

.00029 

3437.75 

.01775 

56.3506 

.03521 

28.3994 

.05270 

18.9755 

59 

2 

.00058 

1718.87 

.01804 

55.4415 

.03550 

28.1664 

.05299 

18.8711 

58 

3 

.00087 

1145.92 

.01833 

54.5(313 

.03579 

27.9372 

.05328 

18.7678 

57 

4 

.00116 

859.436 

.01862 

53.7086 

.03609 

27.7117 

.05357 

18.6656 

56 

5 

.00145 

687.549 

.01891 

52.8821 

.03638 

27.4899 

.05387 

18.5645 

55 

6 

.00175 

572.957 

.01920 

52.0807 

.03667 

27.2715 

.05416 

18.4645 

54 

7 

.00204 

491.106 

.01949 

51.3032 

.03696 

27.0566 

.05445 

18.3655 

53 

8 

.00233 

429.718 

.01978 

50.5485 

.03725 

26.8450 

.05474 

18.2677 

52 

9 

,00262 

381.971 

.02007 

49.8157 

.03754 

26.6367 

.05503 

18.1708 

51 

10 

.00291 

343.774 

.02036 

49.1039 

.03783 

26.4316 

.05533 

18.0750 

50 

11 

.00320 

312.521 

.02066 

48.4121 

.03812 

26.2296 

.05562 

17.9802 

49 

12 

.00349 

286.478 

.02095 

47.7395 

.03842 

26.0307 

.05591 

17.8863 

48 

13 

.00378 

264.441 

.02124 

47.0853 

.03871 

25.8348 

.05620 

17.7934 

47 

14 

.00407 

245.552 

.02153 

46.4489 

.03900 

25.6418 

.05649 

17.7015 

46 

15 

.00436 

229.182 

.02182 

45.8294 

.03929 

25.4517 

.05678 

17.6106 

45 

16 

.00465 

214.858 

.02211 

45.2261 

.03958 

25.2644 

.05708 

17.5205 

44 

17 

.00495 

202.219 

.02240 

44.6386 

.03987 

25.0798 

.05737 

17.4314 

43 

18 

.00524 

190.984 

.02269 

44.0661 

.04016 

24.8978 

.05766 

17.3432 

42 

19 

.00553 

180.932 

.02298 

43.5081 

.04046 

24.7185 

.05795 

17.2558 

41 

20 

.00582 

171.885 

.02328 

42.9641 

.04075 

24.5418 

.05824 

17.1693 

40 

21 

.00611 

163.700 

.02357 

42.4335 

.04104 

24.3675 

.05854 

17.0837 

39 

22 

.00640 

156.259 

.02386 

41.9158 

.04133 

24.1957 

.05883 

16.9990 

38 

23 

.00669 

149.465 

.02415 

41.4106 

.04162 

24.0263 

.05912 

16.9150 

37 

21 

.00698 

143.237 

.02444 

40.9174 

.04191 

23.8593 

.05941 

16.8319 

36 

25 

.00727 

137.507 

.02473 

40.4358 

.04220 

23.6945 

.05970 

16.7496 

35 

2(5 

.00756 

132.219 

,02502 

39.9655 

.04250 

23.5321 

.05999 

16.6681 

34 

27 

.00785 

127.321 

.02531 

39.5059 

.04279 

23.3718 

.06029 

16.5874 

33 

28 

.00815 

122.774 

.02560 

39.0508 

.04308 

23.2137 

.06058 

16.5075 

32 

29 

.00844 

118.540 

.02589 

38.6177 

.04337 

23.0577 

.06087 

16.4283 

31 

30 

.00873 

114.589 

.02619 

38.1885 

.04366 

22.9038 

.06116 

16.3499 

30 

31 

.00902 

110.892 

.02648 

37.7686 

.04395 

22.7519 

.06145 

16.2722 

29 

32 

.00931 

107.426 

.02677 

37.3579 

.04424 

22.6020 

.06175 

16.1952 

28 

33 

.00960 

104.171 

.02706 

36.9560 

.04454 

22.4541 

.06204 

16.1190 

27 

34 

.00989 

101.107 

.02735 

36.5627 

.04483 

22.3081 

.06233 

16.0435 

26 

35 

.01018 

98.2179 

.02704 

3G.1776 

.04512 

22.1640 

.06262 

15.9687 

25 

86 

.01047 

95.4895 

.02793 

35.8006 

.04541 

22.0217* 

.06291 

15.8945 

24 

37 

.01076 

92.9085 

.02822 

35.4313 

.04570 

21.8813 

.06321 

15.8211 

23 

38 

.01105 

90.4633 

.02851 

35.0695 

.04599 

21.7426 

.06350 

15.7483 

22 

:-;i) 

.01135 

88.1436 

.02881 

34.7151 

.04628 

21.6056 

.06379 

15.6762 

21 

40 

.01164 

85.9398 

.02910 

34.3678 

.04658 

21.4704 

.0&408 

15.6048 

20 

41 

.01193 

83.8435 

.02939 

34.0273 

.04687 

21.3369 

.06437 

15.5340 

19 

42 

.01222 

81.8470 

.02968 

33.6935 

.04716 

21.2049 

.06467 

15.4638 

18 

43 

.01251 

79.9434 

.02997 

33.3662 

.04745 

21.0747 

.06496 

15.3943 

17 

44 

.01280 

78.1263 

.03026 

33.0452 

.04774 

20  9460 

.06525 

15.3254 

16 

45 

.01309 

76.3900 

.03055 

32.7303 

.04803 

20.8188 

.06554 

15.2571 

15 

46 

.C1338 

74.7292 

.03084 

32.4213 

.04833 

20.6932 

.06584 

15.1893 

14 

47 

.01367 

73.1390 

.03114 

32.1181 

.04862 

20.5691 

.06613 

15.1222 

13 

48 

.01396 

71.6151 

.03143 

31.8205 

.04891 

20.4465 

.06642 

15.0557 

12 

4') 

.01425 

70.1533 

.03172 

31.5284 

.04920 

20.3253 

.06671 

14.9898 

11 

50 

.01455 

68.7501 

.03201 

31.2416 

.04949 

20.2056 

.06700 

14.9244 

10 

51 

.01484 

67.4019 

.03230 

30.9599 

.04978 

20.0872 

.06730 

14.8596 

9 

52 

.01513 

66.1055 

.03259 

30.  6833 

.05»7 

19.9702 

.06759 

14.7954 

8 

53 

.01542 

64.8580 

.03288 

30.4116 

.05037 

19.8546 

.06788 

14.7317 

7 

54 

.01571 

63.6567 

.03317 

30.1446 

.05066 

19.7403 

.06817 

14.6685 

6 

55 

.01600 

62.4992 

.03346 

29.8823 

.05095 

19.6273 

.06847 

14.6059 

5 

50 

.01629 

61.3829 

.0:3376 

29.6245 

.05124 

19.5156 

.06876 

14.5438 

4 

57 

.01658 

60.3058 

.03405 

29.3711 

.05153 

19.4051 

.06905 

14.4823 

3 

58 

.01687 

59.2659 

.03434 

29.1220 

.05182 

19.2959 

.06934 

14.4212 

2 

59 

.01716 

58.2612 

.03463 

28.8771 

.05212 

19.1879 

.06963 

14.3607 

1 

60 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

0 

f 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang  |    Tang 

t 

89° 

88° 

87° 

86° 

235 


TABLE  XVI.— NATURAL  TANGENTS  AND  COTANGENTS. 


i 

1° 

5° 

( 

5° 

i 

r° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

/ 

0 

.06993 

14.3007 

.08749 

11.4301 

I   .10510 

9.51436 

.12278 

8.14435 

(50 

1 

.07022 

14.2411 

.08778 

11.3919 

.10540 

9.487'81 

.12308 

8.12481 

59 

2 

.07051 

14.1821 

.08807 

11.3540 

i    .10569 

9.46141 

.12338 

8.10530 

68 

3 

.07080 

14.1235 

.08837 

11.3163 

.  10599 

9.43515 

.12307 

8.08600 

57 

4 

.07110 

14.0655 

.08866 

11.2789 

.10628 

9.40904 

.12397 

8.06074 

56 

5 

.07139 

14.0079 

.08895 

11.2417 

.10657 

9.38307 

.12426 

8.04756 

55 

0 

.07168 

13.9507 

.08925 

11.2048 

.10687 

9.35724 

.124E6 

8.02848 

54 

7 

.07197 

13.8940 

.08954 

11.1681 

.10716 

9.33155 

.12485 

8.00948 

53 

8 

.07227 

13.8378 

.08983 

11.1316 

.10746 

9.30599 

.12515 

7.99058 

52 

g 

.07256 

13.7821 

.09013 

11.0954 

.10775 

9.28058 

12544 

7.97176 

51 

10 

.07'285 

13.7267 

.09042 

11.0594 

.10805 

9.25530 

!  12574 

7.95302 

50 

11 

.07314 

13.6719 

.09071 

11.0237 

.10834 

9.23016 

.12603 

7.93438 

40 

12 

.07344 

13.6174 

.09101 

10.9882 

.10SC3 

9.2C516 

.1CGS3 

7.91C82 

4* 

13 

.07373 

13.5634 

.09130 

10.9529 

.10893 

9.18028 

.12GG2 

7.89734 

47 

14 

.07402 

13.5098 

.09159 

10.9178 

.10922 

9.15554 

.120C2 

7.87895 

40 

15 

.07431 

13.4566 

.09189 

10.8829 

1CG52 

9.13093 

.12722 

7.86064 

45 

1C 

.07461 

13.4039 

.09218 

10.8483 

!lC981 

9.1C646 

.12751 

7.84242 

44 

17 

.07490 

13.3515 

.09247 

10.8139 

.11C11 

9.08211 

.12781 

7.82428 

43 

18 

.07519 

13.2996 

.09277 

10.7797 

.11010 

9.05789 

.12810 

7.80022 

42 

1!) 

.07548 

13.2480 

.09306 

10.7457 

.11C70 

9.03379 

.12840 

7.78825 

41 

20 

.07578 

13.1969 

.09335 

10.7119 

.11099 

9.C0983 

.12869 

7.77035 

40 

21 

.07607 

13.1461 

.09365 

10.6783 

.11128 

8.S8598 

.12899 

7  .  75254 

39 

22 

.07636 

13.0958 

.09394 

10.6450 

.inns 

8.902*7 

.12929 

7.7'8480 

88 

23 

.07665 

13.0458 

.09423 

10.6118 

.11187 

8.  £3867 

.12958 

7.71715 

37 

24 

.07695 

12.9962 

.09453 

10.5789 

.11217 

8.91520 

.12988 

7.C9957 

30 

25 

.07724 

12.9469 

.09482 

10.5462 

.11246 

8.89165 

.13017 

7.68208 

85 

20 

.07753 

12.8981 

.C9511 

10.5136 

.11276 

8.868C2 

.13047 

7.66466 

84 

27 

.07782 

12.8496 

.C9541 

10.4813 

.11205 

8.84551 

.13076 

7.64732 

S3 

28 

.07812 

2.8014 

.09570 

10.4491 

.11S35 

8.82252 

.13106 

7.63005 

29 

.07841 

2.7536 

.09600 

10.4172 

.11804 

8.79964 

.13126 

7.61287 

31 

30 

.07870 

2.7062 

.09629 

10.3854 

.11394 

8.77689 

.13165 

7.59575 

30 

31 

.07899 

2.6591 

.09658 

10.3538 

.11423 

8.75425 

.13105 

7.57872 

20 

32 

.07929 

2.6124 

.09668 

10.3224 

.11452 

8.73172 

.13224 

7.50176 

28 

33 

.07958 

2.5660 

.09717 

10.2913 

.11482 

8.70931 

.12254 

7.54487 

27 

34 

.07987 

12.5199 

.09746 

10.2602 

.11511 

8.68701 

.13284 

7.52806 

26 

35 

.08017 

12.4742 

.09776 

10.2294 

.11541 

8.66482 

.13313 

7.51132 

25 

36 

.08046 

12.4288 

.09805 

10.1988 

.11570 

8.6427'5 

.13343 

7.49465 

24 

37 

.08075 

12.3838 

.09834 

10.1683 

.11600 

8.62078 

.13372 

7.47806 

23 

38 

.08104 

12.3390 

.09864 

10.1381 

.11629 

8.59893 

.13402 

7.40154 

22 

89 

.08134 

12.2946 

.09893 

10.1C80 

.11659 

8.57718 

.13422 

7.44509 

21 

40 

.08163 

12.2505 

.09923 

10.0780 

.11688 

8.55555 

.13461 

7.42871 

20 

41 

.08192 

12.2067 

.09952 

10.0483 

.11718 

f  53402 

.13491 

7.41240 

10 

42 

.08221 

12.1032 

.09981 

10.0187 

.11747 

8.51259 

.13521 

7.39616 

18 

43 

.08251 

12.1201 

.icon 

9.98931 

.11777 

8.49128 

.13550 

7.37999 

17 

44 

.08280 

12.0772 

.10040 

9.96007 

.11806 

8.47007 

.  13580 

7.30389 

10 

45 

.08309 

12.0346 

.10069 

9.93101 

.11836 

8.44896 

.13609 

7.34786 

15 

46 

.08339 

11.9923 

.10099 

9.90211 

.11805 

8.42795 

.13639 

7.83190 

14 

47 

.08368 

11.9504 

.10128 

9.87338 

.11895 

8.40705 

.13609 

7.31600 

13 

48 

.08397 

11.9087 

.10158 

9.84482 

.11924 

8.38625 

.13698 

7.30018 

12 

49 

.08427 

11.8673 

.10187 

9.81641 

.11954 

8.36555 

.13728 

7.28442 

11 

50 

.08456 

11.8262 

.10216 

9.7'8817 

.11983 

8.34496 

.13758 

7.26873 

10 

51 

J08485 

11.7853 

.10246 

8.76009 

.12013 

8.32446 

.13787 

7.25310 

9 

52 

.08514 

11.7448 

.10275 

9.73217 

.12042 

8.30406 

.13817 

7.23754 

8 

53 

.08544 

11.7045 

.10305 

9.70441 

.12072 

8.28376 

.13846 

7.22204 

f 

54 

.08573 

11.6645 

.10334 

9.67680 

.12101 

8.26355 

.13876 

7.20661 

0 

55 

.08602 

11.6248 

.10363 

9.64935 

.12131 

8.24345 

.13906 

7.19125 

5 

56 

.08632 

11.5853 

.10393 

9.62205 

.12160 

8.22344 

.13935 

7.17594 

4 

57 

.08661 

11.5461 

.10422 

9.59490 

.12190 

8.20352 

.13965 

7.16071 

3 

58 

.08690 

11.5072 

.10452 

9.56791 

.12219 

8.18370 

.13995 

7.14553 

2 

59 

.08720 

11.4685 

.10481 

9.54106 

.12249 

8.16398 

.14024 

7.13042 

1 

60 

.08749 

11.4301 

.10510 

9.51436 

.12278 

8.14435 

.14054 

7.11537 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

8 

5° 

3 

4° 

8 

3° 

8 

3° 

236 


TABLE  XVI.— NATURAL  TANGENTS  AND  COTANGENTS. 


8° 

9° 

10° 

11° 

Tang 

Cotang 

Tang     Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

~  .14054 

7.11537 

.15838 

6.31375 

.17633 

5.67128 

.19438 

5.14455 

60 

1 

.14084 

7.10038 

.15868 

6.30189 

.17663 

5.66165 

.19468 

5.13658 

59 

2 

.14113 

7.08546 

.15898 

6.29007 

.17693 

5.65205 

.19498 

5.12862 

58 

3 

,  14143 

7.07059 

.15928 

6.27829 

.17723 

5.64248 

.19529 

5.12069 

57 

4 

.14173 

7.0.5579 

.15958 

6.26655 

.17753 

5.63295 

.19559 

5.11279 

56 

5     .14202 

7.04105 

.15988 

6.25486 

.17783 

5.62344 

.19589 

5.10490 

55 

81   .14232 

7.02637 

.16017 

6.24321 

.17813 

5.61397 

.19619 

5.09704 

54 

7 

.14262 

6.91174 

.16047 

6.23160 

.17843 

5.60452 

.19649 

5.08921 

53 

8 

.14291 

6.99718 

.16077 

6.22003 

.17873 

5.59511 

.19680 

5.08139 

52 

9 

.14321 

6.98268 

.16107 

6.20851 

.17903 

5.58573 

.19710 

5.07360 

51 

10 

.14351 

6.96823 

.16137 

6.19703 

.17933 

5.57638 

.19740 

5.06584 

50 

11 

.14381 

6.95385 

.161G7 

6.18559 

.17963 

5.56706 

.19770 

5.05809 

49 

12 

.14410 

6.93952 

.10193 

6.17419 

.17993 

5.55777 

.19801 

5.05037 

48 

13 

.14440 

6.92525 

.16226 

6.16283 

.18023 

5.54851 

.19831 

5.04257 

47 

14 

.14470 

6.91104 

.1G256 

6.15151 

.18053 

5.53927 

.19861 

5.03499 

46 

15 

.14499 

6.89088 

.16286 

6.14023 

.18033 

5.53007 

.19891 

5.02734 

45 

16 

.14529 

6.83278 

.16316 

6.12399 

.18113 

5.52090 

.19921 

5.01971 

44 

17 

.14559 

6.83874 

.16346 

6.11779 

.18143 

5.51176 

.19952 

5.01210 

43 

18 

.14533 

6.85475 

.16376 

6.10364 

.10173 

5.50264 

.19982 

5.00451 

42 

19 

.14618 

6.84032 

.16405 

6.09552 

.18203 

5.49356 

.20012 

4.99695 

41 

20 

.14048 

6.82694 

.16435 

6.08444 

.18233 

5.48451 

.20042 

4.98940 

40 

21 

.14673 

6.81312 

.16465 

6.07340 

.18263 

5.47548 

.20073 

4.98188 

39 

22 

.147'07 

6.79036 

.16495 

6.03240 

.10293 

5.46648 

.20103 

4.974J38 

38 

23 

.14737 

6  .  70564 

.16525 

6.05143 

.10323 

5.457'51 

.20133 

4.96690 

37 

24 

.14767 

6.77199 

.10555 

6.04051 

.18353 

5.44857 

.20164 

4.95945 

36 

25 

.14796 

6.75838 

.16535 

6.02932 

.18384 

5.43966 

.20194 

4.95201 

35 

26 

.14826 

6.74483 

.16615 

6.01878 

.18414 

5.43077 

.20224 

4.94460 

34 

27 

.14856 

6.73133 

.16645 

6.00797 

.10444 

5.42192 

.20254 

4.93721 

33 

28 

.14885 

6.71789 

.16674 

5.99720 

.10474 

5.41309 

.20285 

4.92984 

32 

29 

.14915 

6.70450 

.16704 

5.93346 

.10504 

5.40429 

.20315 

4.92249 

31 

30 

.14945 

6.69116 

.16734 

5.97576 

.18534 

5.39552 

.20345 

4.91516 

30 

31 

.14975 

6.67787 

.16764 

5.96510 

.18564 

5.38677 

.20376 

4.90785 

29 

3;3 

.15005 

G.  63463 

.16794 

5.95448 

.18594 

5.37805 

.20406 

4.90056 

28 

83 

.15034 

6.65144 

.16324 

5.94390 

.18624 

5.36936 

.20436 

4.89330 

27 

34 

.15064 

6.63831 

.16854 

5.93335 

.18654 

5.3607-0 

.20466 

4.88605 

26 

35 

.15094 

6.62523 

.16834 

5.92283 

.10684 

5.35206 

.20497 

4.87882 

25 

36 

.15124 

6.61219 

.16914 

5.91236 

.10714 

5.34345 

.20527 

4.87162 

24 

37 

.15153 

6.59921 

.16944 

5.90191 

.10745 

5.33487 

.20557 

4.86444 

23 

38 

.15183 

6.58627 

.16974 

5.83151 

.18775 

5.32631 

.20588 

4.85727 

22 

39 

.15213 

6.5733.1 

.17004 

5.83114 

.10805 

5.31778 

.20618 

4.85013 

21 

40 

.15243 

6.56055 

.175083 

5.87080 

.18835 

5.30928 

.20648 

4.84300 

20 

41 

.15272 

6.54777 

.17063 

5.86051 

.18865 

5.30080 

.20679 

4.83590 

19 

42 

.15302 

6.53503 

.17003 

5.85024 

.10895 

5.29235 

.207C9 

4.82882 

18 

43 

.15332 

6.52234 

.17123 

5.84001 

.10925 

5.20393 

.20739 

4.82175 

17 

44 

.15362 

6.50970 

.17153 

5.82982 

.10955 

5.27553 

.20770 

4.81471 

16 

45 

.15391 

6.49710 

.17183 

5.81966 

.10986 

5.23715 

.20800 

4.00769 

15 

46 

.15421 

6.48456 

.17213 

5.80953 

.19016 

5.25880 

.20830 

4.00068 

14 

47 

.15451 

6.47206 

.17243 

5.79944 

.19046 

5.25048 

.20861 

4.79370 

13 

48 

.15481 

6.45931 

.17273 

5.73938 

.1907'6 

5.24213 

.20391 

4.7'8673 

12 

48 

.15511 

6.44720 

.17303 

5.77936 

.19106 

5.23391 

.20921 

4.77978 

11 

50 

.15540 

6.43484 

.17333 

5.76937 

.19136 

5.22566 

.20952 

4.77286 

10 

51 

.15570 

6.42253 

.17363 

5.75941 

.19166 

5.21744 

.20982 

4.76595 

9 

52 

.15600 

6.41026 

.17393 

5.74949 

.19197 

5.20925 

.21013 

4.75906 

8 

53 

.15630 

6.30804 

.17423 

5.73960 

.19227 

5.20107 

.21043 

4.75219 

7 

54 

.15660 

6.38587 

.17453 

5.72974 

.19257 

5.19293 

.21073 

4.74534 

6 

55 

.15689 

6.37374 

.17483 

5.71992 

.19287 

5.18480 

.21104 

4.73851 

5 

56 

.15719 

6.36165 

.17513 

5.71013 

.19317 

5.17671 

.21134 

4.73170 

4 

57 

.15749 

6.34961 

.17543 

5.70037 

.19347 

5.16863 

.21164 

4.72490 

3 

58 

.15779 

6.33761 

.17573 

5.69064 

.19378 

5.16058 

.21195 

4.71813 

2 

59 

.15809 

6.32566 

.17603 

5.68094 

.19408 

5.15256 

.21225 

4.71137 

1 

60 

.15838 

6.31375 

.17633 

5.67128 

.19438 

5.14455 

.21256 

4,70463 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

81° 

80°           1 

79° 

78°           1 

237 


TABLE  XVI. -NATURAL  TANGENTS  AND  COTANGENTS. 


12° 

13° 

14° 

15°             | 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

It 

0 

.21256 

4.70463 

.23087 

4.33148 

.249J33 

4.01078 

.26795 

3.73205 

60 

1 

.21286 

4.69791 

.23117 

4.32573 

.24964 

4.00582 

.26826 

3.72771 

59 

2 

.21316 

4.69121 

.23148 

4.32001 

.24995 

4.00086 

.26857 

3.72338 

58 

3 

.21347 

4.68452 

.23179 

4.31430 

.25026 

3.99592 

.26888 

3.71907 

57 

4 

.21377 

4.67786 

.23209 

4.30860 

.25056 

3.99099 

.26920 

3.71476 

56 

5 

.21408 

4.67121 

.23240 

4.30291 

.25087 

3.98607 

.26951 

3.71046 

55 

6 

.21438 

4.66458 

.23271 

4.29724 

.25118 

3.98117 

.26982 

3.70616 

54 

7 

.21469 

4.65797 

.23301 

4.29159 

.25149 

3.97627 

.27013 

3.70188 

53 

8 

.21499 

4.65138 

.23332 

4.28595 

.25180 

3.97139 

.27044 

3.69761 

52 

9 

.215£9 

4.64480 

.23363 

4.28032 

.25211 

3.96651 

.27076 

3.69335 

51 

10 

.21560 

4.63825 

.23393 

4.27471 

.25242 

3.96165 

.27107 

3.68909 

50 

11 

.21590 

4.63171 

.23424 

4.26911 

.25273 

3.95680 

.27138 

3.68485 

49 

12 

.21621 

4.62518 

.23455 

4.26352 

i   .25304 

3.95196 

.27169 

3.68061 

48 

13 

.21651 

4.61868 

.23485 

4.25795 

.25335 

3.94713 

.27201 

3.67638    47 

14 

.21682 

4.61219 

.23516 

4.25239 

.25366 

3.94232 

.27232 

3.67217    46 

15 

.21712 

4.60572 

.23547 

4.24685 

.25397 

3.93751 

.27263 

3.66796 

45 

16 

.21743 

4.59927 

.23578 

4.24132 

.25428 

3.93271 

.27294 

3.66376 

44 

17 

.21773 

4.59283 

.23608 

4.23580 

.25459 

3.92793 

.27326 

3.65957 

43 

18 

.21804 

4.58641 

.23639 

4.23030 

.25490 

3.92316 

.27357 

3.65538 

42 

19 

.21834 

4.58001 

.23670 

4.22481 

.25521 

3.91839 

.27388 

3.65121 

41 

20 

.21864 

4.57363 

.23700 

4.21933 

.25552 

3.91364 

.27419 

3.64705 

40 

21 

.21895 

4.56726 

.23731 

4.21387 

.25583 

3.90890 

.27451 

3.64289 

39 

22 

.21925 

4.56091 

.23702 

4.20842 

.25614 

3.90417 

.27482 

3.63874 

38 

23 

.21956 

4.55458 

.23793 

4.20298 

.25645 

3.89945 

.27513 

3.63461 

37 

24 

.21986 

4.54826 

.23823 

4.19756 

.25676 

3.89474 

.27545 

3.68048 

36 

25 

.22017 

4.54196 

.23854 

4.19215 

.25707 

3.89004 

.27576 

3.62636 

35 

26 

.22047 

4.53568 

.23885 

4.18675 

.25738 

3.88536 

.27607 

3.62224 

34 

27 

.22073 

4.52941 

.23916 

4.18137 

.25769 

3.88068 

.27638 

3.61814 

33 

28 

.22108 

4.52316 

.23946 

4.17600 

.25800 

3.87601 

.27670 

3.61405 

32 

29 

.22139 

4.51693 

.23977 

4.17064 

.25831 

3.87136 

.27701 

3.G0996 

31 

30 

.22169 

4.51071 

.24008 

4.16530 

.25862 

3.86671 

.27732 

3  G0588 

30 

31 

.22200 

4.50451 

.24039 

4.15997 

.25893 

3.86208 

.27764 

3.60181 

29 

•  -J 

.22231 

4.49832 

.24069 

4.15465 

.25924 

3.85745 

.27795 

3  .  59775 

23 

33 

.22261 

4.49215 

.24100 

4.14934 

.25955 

3.85284 

i   .27826 

3.59370 

27' 

34 

.22292 

4.48600 

.24131 

4.14405 

.25986 

3.84824 

.27858 

3.58966 

26 

35 

.22322 

4.47986 

.24162 

4.13877 

.26017 

3.84364 

.27889 

3.58562 

25 

36 

.22353 

4.47374 

.24193 

4.13350 

.26048 

3.83906 

.27921 

3.58160 

24 

37 

.22383 

4.46764 

.24223 

4.12825 

26070 

3.83449 

.27952 

3.57758 

23 

33 

.22414 

4.46155 

.24254 

4.12301 

.26110 

3.82992 

!   .27983 

3.57357 

22 

SO 

.22444 

4.45548 

.24285 

4.11778 

.26141 

3.82537 

.28015 

3.56957 

;:i 

40 

.22475 

4-44942 

.24316 

4.11256 

.26172 

3.82083 

.28046 

3.56557 

20 

41 

.22505 

4.44338 

.24347 

4.10736 

.26203 

3.81630 

.28077 

3.56159 

10 

42 

.22536 

4.43735 

.24377 

4.10216 

.26235 

3.81177 

.28109 

3.557'61 

18 

43 

.22567 

4.43134 

.24408 

4.09699 

.26266 

3.80726 

.28140 

3.55364 

17 

44 

.22597 

4.42534 

.24439 

4.09182 

.26297 

3.80273 

.28172 

3.54968 

16 

45 

.22G28 

4.41936 

.24470 

4.08666 

.26328 

3.79827 

.28203 

3.54573 

15 

46 

.22658 

4.41340 

.24501 

4.08152 

.26359 

3.79378 

.28234 

8.540 

14 

47 

.22089 

4.40745 

.24532 

4.07639 

.26390 

3.78931 

.28266 

3.53785 

13 

48 

.22719 

4.40152 

.24562 

4.07127 

.26421 

3.784R5 

.28297 

3.53393 

12 

49 

.22750 

4.33560 

.24593 

4.06G16 

.26452 

3.78040 

.28329 

3.53001 

11 

50 

.22781 

4.38969 

.24624 

4.06107 

.26483 

3.77595 

.28360 

3.52609 

10 

51 

.22811 

4.38381 

.24655 

4.05599 

.26515 

3.77152 

.28391 

3.52219 

9 

52 

.22842 

4.37793 

.24686 

4.05092 

.26546 

3.76709 

.28423 

3.51829 

8 

53 

.22872 

4.37207 

.24717 

4.04586 

.26577 

3.76268 

.28454 

3.51441 

7 

54 

.22903 

4.36623 

.24747 

4.04081 

.26608 

3.75828 

.28486 

3.51053 

6 

55 

.22934 

4.36040 

.24778 

4.03578 

.26639 

S.  75388 

.28517 

3.50666 

5 

56 

.22964 

4.35459 

.24809 

4.03076 

.26670 

3.74950 

.28549 

3.50279 

4 

57 

.22995 

4.34879 

.24840 

4.02574 

.26701 

3.74512 

.28580 

3.49894 

3 

58 

.23026 

4.34300 

.24871 

4.02074 

.26733 

3.74075 

.28612 

3.49509 

2 

59 

.23056 

4.33723 

.24902 

4.01576 

.26764 

3.73640 

.28643 

3.49125 

1 

60 

.23087 

4.33148 

.24933 

4.01078 

.26795 

3.73205 

.28075 

3.48741 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang     Tang 

Cotang     Tang 

/ 

77° 

76°           1!           75°           I 

74° 

238 


TABLE  XVI.— NATURAL  TANGENTS   AND  COTANGENTS. 


16° 

17° 

18° 

19° 

Tang 

Cotang 

Tang 

Cotang 

Tang     Cotang 

Tang 

Cotang 

' 

0 

.28675 

3.48741 

.30573 

3.27085 

.J12492 

3.07768 

.34433 

2.90421 

60 

1 

.28706 

3.48359 

.30605 

3.26745       .32524 

3.07464 

.34465 

2.90147 

59 

2 

.28738 

3.47977 

.30637 

3.2&406 

.32556 

3.07160 

.34498 

2.89873 

58 

a 

.28769 

3.47596 

.30669 

3.26067 

.32588 

3.06857 

.34530 

2.89600 

57 

4 

.28800 

3.47216 

.30700 

3.25729 

.32621 

3.06554 

.34563 

2.89327 

56 

5 

.28832 

3.46837 

.30732 

3.25392 

.32.353 

3.06252 

.34596 

2.89055 

55 

6 

.288t>4 

3.46458 

.30764 

3.25055    i    .32685 

3.05950 

.34628 

2.88783 

54 

7 

.28895 

3.46080 

.30796 

3.24719 

.32717 

3.05649 

.34661 

2.88511 

53 

S 

.28927 

3.45703 

.30828 

3.24383 

.32749 

3.05349 

.34693 

2.88240 

52 

9 

.28958 

3.45327 

.30860 

3.24049 

.327-82 

3.05049 

.34726 

2.87970 

51 

10 

.28990 

3.44951 

.30891 

3.23714 

.32814 

3.04749 

.34758 

2  87700 

50 

11 

.29021 

3.44576 

.30923 

3.23381 

.32846 

3.04450 

.34791 

2.87430 

49 

12 

.29053 

3.44202 

.30955 

3.2:3048 

.32878 

3.04152 

.34824 

2.87161 

48 

13 

.29084 

3.43829 

.30987 

3.22715 

.32911 

3.03854 

.34856 

2.86892 

47 

14 

.29116 

3.43456 

.31019 

3.22384 

.32943 

3.03556 

.34889 

2.86624 

46 

15 

.29147 

3.43084 

.31051 

3.22053 

.32975 

3.03260 

.34922 

2.86356 

45 

16 

.29179 

3.42713 

.31083 

3.21722 

.33007 

3.02963 

.34954 

2.86089 

44 

17 

.29210 

3.42343 

.31115 

3.21392 

.33040 

3.02667 

.34987 

2.85822 

43 

19 

.29242 

3.41973 

.31147 

3.21063 

.33072 

3.02372 

.85020 

2.85555 

42 

19 

.29274 

3.41604 

.31178 

3.20734 

.33104 

3.02077 

.35052 

2.85289 

41 

20 

.29305 

3.41236 

.31210 

3.20406 

.33136 

3.01783 

.35085 

2.85023 

40 

21 

.29337 

3.40869 

.31242 

3.20079 

.asie9 

3.01489 

.35118 

2.84758 

39 

22 

.29368 

3.40502 

.31274 

3.19752 

.£3201 

3.01196 

.35150 

2.84494 

38 

23 

.29400 

3.40136 

.31306 

3.19426 

.332S3 

3.00903 

.35183 

2.84229 

37 

24 

.29432 

3.39771 

.31338 

3.19100 

.332G6 

3.00611 

.35216 

2.83965 

36 

25 

.29463 

3.39406 

.31370 

3.18775 

.33298 

3.00319 

.35248 

2.83702 

85 

20 

.29495 

3.39042 

.31402 

3.18451 

.3&330 

3.00028 

.35281 

2.83439 

34 

27 

.29526 

3.38679 

.31434 

3.18127 

.33363 

2.99738 

.35314 

2.83176 

83 

28 

.29558 

3.38317 

.31466 

3.17804 

.33395 

2.99447 

.35346 

2.82914 

82 

29 

.29590 

3.37955 

.31498 

3.17481 

.33427 

2.99158 

.35379 

2.82653 

31 

80 

.29621 

3.37594 

.31530 

3.17159 

.33460 

2.98868 

.35412 

2.82391 

30 

51 

.29653 

3.37234 

.31562 

3.16838 

.33492 

2.98580 

.35445 

2.82130 

29 

32 

.29685 

3.36875 

.31594 

3.16517 

.33524 

2.98292 

.35477 

2.81870 

28 

33 

.29716 

3.36516 

.31626 

3.16197 

.33557 

2.98004 

.35510 

2.81610 

27 

34 

.29748 

3.36158 

.31658 

3.15877 

.33589 

2.97717 

.35543 

2.81350 

28 

:->5 

.29780 

3.35800 

.31690 

3.15558 

.33621 

2.97430 

.35576 

2.81091 

25 

36 

.29811 

3.35443 

.31722 

3.15240 

.33654 

2.97144 

.35608 

2.80833 

24 

37 

.29843 

3.3508? 

.31754 

3.14922 

.33686 

2.96858 

.35641 

2.80574 

23 

38 

.29875 

3.34732 

.31786 

3.14605 

.33718 

2.96573 

.35674 

2.80316 

22 

39 

.29906 

3.34377 

.31818 

3.14288 

.33751 

2.96288 

.35707 

2.80059 

21 

40 

.29938 

3.34023 

.31850 

3.13972 

.33783 

2.96004 

.35740 

2.79802 

20 

41 

.29970 

3.33670 

.31882 

3.13656 

.33816 

2.95721 

.35772 

2.79545 

19 

42 

.30001 

3.33317 

.31914 

3.13341 

.33848 

2.95437 

.35805 

2.79289 

18 

43 

.30033 

3.32965 

.31946 

3.13027 

.33881 

2.95155 

.85888 

2.79033 

17 

44 

.30065 

3.32614 

.31978 

3.12713 

.33913 

2.9487'2 

.85871 

2.78778 

10 

45 

.30097 

3.32264 

.32010 

3.12400 

.33945 

2.94591 

.35904 

2.78523 

15 

46 

.30123 

3.31914 

.32042 

3.12087 

.33978 

2.94309 

.35937 

2.78269 

14 

47 

.30160 

3.31565 

.32074 

3.11775 

.34010 

2.94028 

.35969 

2.78014 

13 

48 

.30192 

3.31216 

.32106 

3.11464 

.34043 

2.93748 

.36002 

2.77761 

12 

49 

.30224 

3.30868 

.32139 

3.11153 

.34075 

2.93468 

.36035 

2.77507 

11 

50 

.30255 

3.S0521 

.32171 

3.10843 

.34108 

2.93189 

.36068 

2.77254 

10 

51 

.30287 

3.30174 

.32203 

3.10532 

.34140 

2.92910 

.36101 

2.77002 

9 

52 

.30319 

3.29829 

.32235 

3.10223 

.34173 

2.92632 

.36134 

2.76750 

8 

53 

.30351 

3.29483 

.32267 

3.09914 

.34205 

2.92354 

.36167 

2.76498 

7 

54 

.30382 

3.29139 

.32299 

3.09606 

.34238 

2.92076 

.36199 

2.76247 

6 

55 

.30414 

3.28795 

.32331 

3.09298 

.34270 

2.91799 

.36232 

2.75996 

5 

56 

.30446 

3.28452 

.32363 

3.08991 

.34303 

2.91523 

.36265 

2.75746 

4 

57 

.30478 

3.28109 

.32396 

3.08685 

.34335 

2.91246 

.36298 

2.75496 

3 

58 

.30509 

3.27767 

.32428 

3.08379 

.34368 

2.90971 

.36331 

2.75246 

2 

59 

.30541 

3.27426 

.32460 

3.08073 

.34400 

2.90696 

.36364 

2.74997 

1 

GO 

.3057-3 

3.27085 

.32492 

3.077'08 

.34433 

2.90421 

.36397 

2.74748 

_0 

/ 

Cotanr^ 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

73° 

72° 

71° 

70° 

239 


TABLE  XVI.— NATURAL  TANGENTS  AND  COTANGENTS. 


20° 

21° 

22° 

23° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

' 

Oi   .30397 

2.74748 

.88886 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

00 

1 

.36430 

2.74499 

.38420 

2.60283 

.40436 

2.47302 

.42482 

2.35395 

51) 

c 

.36463 

2.74251 

.38453 

2.60057 

.40470 

2,47095 

.42516 

2.35205 

58 

3 

.36496 

2.74004 

.38487 

2.59831 

.40504 

2.46888 

.42551 

2.35015 

57 

^ 

.36529 

2.73756 

.38520 

2.59606 

.40538 

2.46682 

.42585 

2.34825 

50 

5 

.36562 

2.73509 

.38553 

2.59381 

.40572 

2.46476 

.42619 

2.34636 

55 

G 

.36595 

2.73263 

.38587 

2.59156 

.40606 

2.46270 

.42654 

2.34447 

54 

7 

.36628 

2.73017 

.38620 

2.58932 

.40640 

2.46065 

.42688 

2.34258 

53 

8 

.36661 

2.72771 

.38654 

2.58708 

.40674 

2.45860 

4^722 

2.34069 

52 

r 

.36694 

2.72526 

.38687 

2.58484 

.40707 

2.45655 

'.42757 

2.33881 

51 

10 

.36727 

2.72281 

.38721 

2.58261 

.40741 

2.45451 

.42791 

2.33693 

50 

11 

.36760 

2.72036 

.38754 

2.58038 

.40775 

2.45246 

.42826 

2.33505 

49 

13 

.36793 

2.71792 

.38787 

2.57815 

.40809 

2.45043 

.42800 

2.33317 

•18 

13 

.36823 

2.71548 

.33821 

2.57593 

.40843 

2.44839 

.42894 

2.33130 

47 

14 

.36859 

2.71305 

.38854 

2.57371 

.40877 

2.41636 

.42929 

2.32943 

40 

15 

.36892 

2.71062 

.38888 

2.57150 

.40911 

2.44433 

.42963 

2.32756 

45 

16 

.36925 

2.70819 

.38921 

2.56928 

.40945 

2.44230 

.42998 

2.32570 

44 

17 

.36958 

2.70577 

.38955 

2.56707 

.40979 

2.44027 

.43032 

2.32383 

43 

18 

.36991 

2.70335 

.33983 

2.56487 

.41013 

2.43025 

.43007 

2.32197 

42 

19 

.37024 

2.70094 

.39022 

2.56266 

.41047 

2.43623 

.43101 

2.32012 

41 

20 

.37057 

2.69853 

.39055 

2.56046 

.41081 

2.43422 

.43136 

2.31826 

40 

21 

.37090 

2.69612 

.39089 

2.55827 

.41115 

2.43220 

.43170 

2.31641 

39 

22 

.37123 

2.G9371 

.33122 

2.556G8 

.41149 

2.43019 

.43205 

2.31456 

88 

23 

.37157 

2.69131 

.39156 

2.55389 

.41183 

2.42319 

.43233 

2.31271 

87 

24 

.37190 

2.68892 

.39190 

2.55170 

.41217 

2.42618 

.43274 

2.31086 

9Q 

25 

.37223 

2.68653 

.39223 

2.54952 

.41251 

2.42418 

.43308 

2.30902 

85 

26 

.37256 

2.68414 

.39257 

2.54734 

.41285 

2.42218 

.43343 

2.30718 

31 

27 

.37289 

2.68175 

.39290 

2.54516 

.41319 

2.42019 

.43378 

2.30534 

83 

28 

.37322 

2  67937 

.39324 

2.54299 

.41353 

2.41019 

.43412 

2.30351 

32 

29 

.37355 

2.67700 

.39357 

2.54082 

.41307 

2.  41  020 

.43447 

2.30167 

31 

30 

.37388 

2.67462 

.39391 

2.53865 

.41421 

2.41421 

.43481 

2.29984 

30 

31 

.37422 

2.67225 

.39425 

2.53648 

.41455 

2.41223 

.43516 

2.29801 

29 

32 

.37455 

2.66989 

.39458 

2.53432 

.41490 

2.41025 

.43550 

2.29619 

28 

33 

.37488 

2.66752 

.39492 

2.53217 

.41521 

2.40827 

.43585 

2.29437 

27 

34 

.37521 

2.66516 

.39526 

2.53001 

.41558 

2.40629 

.43620 

2.29254 

20 

35 

.37554 

2.66281 

.39559 

2.52786 

.41592 

2.40432 

.43654 

2.29073 

25 

30 

.37588 

2.66046 

.39593 

2.52571 

.41626 

2.40235 

.43689 

2.28891 

24 

37 

.37621 

2.65811 

.39626 

2.52357 

.41660 

2.40038 

.43724 

2.28710 

23 

38 

.37654 

2.65576 

.39660 

2.52142 

.41694 

2.39841 

.43758 

2.28528 

22 

39 

.37687 

2.65342 

.39694 

2.519^9 

.41728 

2.39645 

.43793 

2.28348 

21 

40 

.37720 

2.65109 

.39727 

2.51715 

.41763 

2.39449 

.43828 

2:28167 

20 

41 

.37754 

2.64875 

.39761 

2.51502 

.41797 

2.39253 

.43862 

2.27987 

19 

42 

.37787 

2.64642 

.39795 

2.51289 

.41831 

2.3i*058 

.43897 

2.27806 

18 

43 

.37820 

2.64410 

.39829 

2.5107'6 

.41865 

2.38863 

.43932 

2.27'626 

17 

44 

.37853 

2.64177 

.39862 

2.50864 

41899 

2.38668 

.43066 

2.27'447 

10 

45 

.37887 

2.63945 

.39896 

2.50652 

.41933 

2.38473 

.44001 

2.27'267 

15 

46 

.37920 

2.63714 

.39930 

2.50440 

.41968 

2.38279 

.44036 

2.27'088 

14 

47 

.37953 

2.63483 

.39963 

2.50229 

.42002 

2.38084 

.44071 

2.20909 

13 

48 

.37986 

2.63252 

.39997 

2.50018 

.42036 

2.37891 

.44105 

2.26730 

12 

49 

.38020 

2.63021 

.40031 

2.49807 

.4207'0 

2.37697 

.44140 

2.26552 

11 

50 

.38053 

2.62791 

.40065 

2.49597 

.42105 

2.37504 

.44175 

2.26374 

10 

51 

.38086 

2.62561 

.40098 

2.49386 

.42139 

2.37311 

.44210 

2.26196 

9 

52 

.38120 

2.62332 

.40132 

2.49177 

.42173 

2.37118 

.44244 

2.26018 

8 

53 

.38153 

2.62103 

.40166 

2.48967 

.42207 

2.36925 

.44279 

2.25840 

7 

54 

.38186 

2.61874 

.40200 

2.487'58 

.42242 

2.36733 

.44314 

2.25663 

0 

55 

.38220 

2.61646 

.40234 

2.48549 

.42276 

2.36541 

.44349 

2.25486 

5 

56 

.38253 

2.61418 

.40267 

2  48340 

.42310 

2.36349 

.44384 

2.25309 

4 

57 

.38286 

2.61190 

.40301 

2.48132 

.42345 

2.36158 

.44418 

2.25132 

3 

58 

.38320 

2.60963 

.40335 

2.47924 

.42379 

2.35967 

.44453 

2.24956 

2 

59 

38353 

2.60736 

.40369 

2.47716 

.42413 

2.35776 

.44488 

2  24780 

1 

80 

38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

> 

69° 

68° 

67° 

66° 

240 


TABLE  XVI.— NATURAL  TANGENTS  AND  COTANGENTS. 


2 

4° 

2 

5° 

!             2 

6° 

2 

7° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.44523 

2.24604 

.46631 

2.14451 

.48773 

2.05030 

.50053 

1.96261 

60 

1 

.44558 

2.24428 

.46006 

2.14288 

.48809 

2.04879 

.50989 

1.96120 

59 

2 

.44593 

2.24252 

.46702 

2.14125 

.48845 

2.04728 

.51026 

1.95979 

58 

3 

.44627 

2.24077 

.46737 

2.13963 

.48881 

2.04577 

.51063 

1.95838 

57 

4 

.44062 

2.23902 

.46772 

2.13801 

.48917 

2.04426 

.51099 

1.95698 

56 

5 

.44697 

2.23727 

.46808 

2.13639 

.48953 

2.04276 

.51136 

1.95557 

55 

6 

.44732 

2.23553 

.46843 

2.13477 

.48989 

2.04125 

.51173 

1.95417 

54 

7 

.44767 

2.23378 

.46879 

2.13316 

.49026 

2.03975 

.51209 

1.95277 

53 

8 

.44802 

2.23204 

.46914 

2.13154 

.49062 

2.03825 

.51246 

1.95137 

5° 

9 

.44837 

2.230SO 

.46950 

2.12993 

.49098 

2.03675 

.51283 

1.94997 

51 

10 

.44872 

2.22857 

.46985 

2.12832 

.49134 

2.03526 

.51319 

1.94858 

50 

11 

.44907 

2.22683 

.47021 

2.12671 

.49170 

2.03376 

.51356 

1.94718 

49 

12 

.44942 

2.22510 

.47056 

2.12511 

.49206 

2.0G227 

.51393 

1.94579 

48 

13 

.44977 

2.22337 

.47'092 

2.12350 

.49242 

2.03078 

.51430 

1.94440 

47 

11 

.45012 

2.22164 

.47128 

2.12190 

.49278 

2.02929 

.51467 

1.94301 

40 

15 

.45047 

2.21992 

.47163 

2.12030 

.49315 

2.02780 

.51503 

1.94162 

45 

10 

.45082 

2.21819 

.47199 

2.11871 

.49351 

2.02631 

.51540 

1.94023 

44 

17 

.45117 

2.21647 

.47234 

2.11711 

.49387 

2.02483 

.51577 

1.93885 

43 

18 

.45152 

2.21475 

.47270 

2.11552 

.49423 

2.02335 

.51614 

1.93746 

42 

10 

.45187 

2.21304 

.47305 

2.11392 

.49459 

2.02187 

.51051 

1.93608 

41 

20 

.45222 

2.21132 

.47341 

2.11233 

.49495 

2.02039 

.51688 

1.93470 

40 

21 

.45257 

2.20961 

.47377 

2.11075 

.49532 

2.01891 

.51724 

1.93332 

39 

22 

.45292 

2.20790 

.47412 

2.10916 

.49508 

2.01743 

.51761 

1.93195 

38 

23 

.45327 

2.20619 

.47448 

2.10758 

.49004 

2.01596 

.51798 

1.93057 

37 

84 

.45362 

2.20449 

.47483 

2.10600 

.49040 

2.01449 

.51835 

1.92920 

30 

25 

.45397 

2.20278 

.47519 

2.10442 

.49677 

2.01302 

.61872 

1.92782 

35 

20 

.45432 

2.20108 

.47o55 

2.10284 

.49713 

2.01155 

.51909 

1.92645 

34 

27 

.45467 

2.19938 

.47590 

2.10126 

.497'49 

2.01008 

.51946 

1.92508 

33 

28 

.45502 

2.19769 

.47626 

2.09909 

.49786 

2.00862 

.51983 

1.92371 

32 

21) 

.45538 

2.10599 

.47602 

2.09811 

.49822 

2.00715 

.52020 

1.92235 

31 

30 

.45573 

2.19430 

.47698 

2.09654 

.49858 

2.00569 

.52057 

1.92098 

30 

31 

.45608 

2.19261 

.47733 

2.09498 

.49894 

2.00423 

.52094 

1.91962 

29 

32 

.45643 

2.19092 

.47769 

2.09341 

.49931 

2.00277 

.52131 

1.91826 

28 

33 

.4567'8 

2.18923 

.47805 

2.09184 

.49967 

2.00131 

.52168 

1.91690 

27 

34 

.45713 

2.18755 

.47840 

2.09028 

.50004 

1.99986 

.52205 

1.91554 

26 

35 

.45748 

2.18587 

.47876 

2.08872 

.50040 

1.99841 

.52242 

1.91418 

25 

30 

.45784 

2.18419 

.47912 

2.08716 

.50076 

1.99695 

.52279 

1.91282 

24 

37 

.45819 

2.18251 

.47948 

2.08560 

.50113 

1.99550 

.52316 

1.91147 

23 

38 

.43854 

2.18084 

.47984 

2.03405 

.50149 

1.99406 

.52353 

1.91012 

22 

39 

.45889 

2.17916 

.48019 

2.0;S250 

.50185 

1.99261 

.52390 

1.90876 

21 

40 

.45924 

2.17749 

.48055 

2.08094 

.50222 

1.99116 

.52427 

1.90741 

20 

41 

.45960 

2.17582 

.48091 

2.07939 

.50258 

1.98972 

.52464 

1.90607 

19 

42 

.45995 

2.17416 

.48127 

2.07785 

.50295 

1.98828 

.52501 

1.90472 

18 

43 

.46030 

2.17249 

.48163 

2.07630 

.50331 

.98684 

.52538 

1.90337 

17 

44 

.46065 

2.17083 

.48198 

2.07476 

.50368 

.98540 

52575 

1.90203 

16 

45 

.46101 

2.10917 

.48234 

2.07321 

.50404 

.98396 

!  52613 

1.90069 

15 

46 

.46136 

2.16751 

.48270 

2.07167 

.50441 

.98253 

.52650 

1.89935 

14 

47 

.46171 

2.16585 

.48306 

2.07014 

.50477 

.98110 

.52687 

1.8C801 

13 

48 

.46206 

2.16420 

.48342 

2.06860 

.50514 

.97966 

.52724 

1.89667 

12 

49 

.46242 

2.10255 

.48378 

2.06706 

.50550 

.97823 

.52761 

J.  89533 

11 

50 

.46277 

2.1G090 

.48414 

2.06553 

.50587 

.97681 

.52798 

1.89400 

10 

51 

.46312 

2.15925 

.48450 

2.06400 

.50623 

.97538 

.52836 

1.89266 

9 

52 

.46348 

2.15760 

.48486 

2.06247 

.50660 

.97395 

.52873 

1.89133 

8 

53 

.46383 

2.15596 

.48521 

2.06094 

.50696 

.97253 

.52910 

1.89000 

7 

64 

.46418 

2.15432 

.48557 

2.05942 

.50733 

.97111 

.52947 

1.88867 

6 

55 

.46454 

2.15268 

.48593 

2.05790 

.50769 

.96969 

.52985 

1.88734 

5 

56 

.46489 

2.15104 

.48629 

2.05637 

.50806 

.96827 

.53022 

1.88602 

4 

57 

.46525 

2.14940 

.48665 

2.05485 

.50843 

.96685 

.53059 

1.88469 

3 

58 

.46560 

2.14777 

.48701 

2.05333 

.50879 

.96544 

.53096 

1.88337 

2 

50 

.46595 

2.14614 

.48737 

2.05182 

.50916 

.96402 

.53134 

1.88205 

1 

60 

.46631 

2.14451 

.48773 

2.050:30 

.50953 

.96261 

.53171 

1.88073 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

r 

6 

5° 

6 

4° 

6 

3° 

6 

2° 

241 


TABLE  XVI. -NATURAL  TANGENTS  AND  COTANGENTS. 


2 

8° 

2 

9°           l 

1            3 

0° 

3 

1° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.53171 

1.88073 

.554.91 

1.80405 

.57735 

.73205 

.60086 

1.66428 

60 

1 

.53208 

1.87941 

.55469 

1.80281 

.57774 

.73089 

.60126 

1.66318 

59 

2 

.53246 

1.87809 

.55507 

1.80158 

.57813 

.72973 

.60165 

1.66209 

58 

3 

.53283 

1.87677 

.55545 

1.80034 

.57851 

.72857 

.60205 

1.60099 

57 

4 

.53320 

1.87546 

.55583 

1.79911 

.57890 

.72741 

.60245 

1.65990 

56 

5 

.53358 

1.87415 

.55621 

1.79788 

.57929 

.72625 

.60284 

1.65881 

55 

0 

.53395 

1.87283 

.55659 

1.79665 

.57968 

.72509 

.60324 

1.65772 

54 

7 

.53432 

1.87152 

.55697 

1.79542 

.58007 

.72393 

.60364 

1.65663 

53 

8 

.53470 

1.87021 

.55736 

1.79419 

.58046 

.72278 

.60403 

1.65554 

52 

9 

.53507 

1.86891 

.55774 

1.79296 

.58085 

.72163 

.60443 

1.65445 

51 

10 

.53545 

1.86760 

.55812 

1.79174 

.58124 

.72047 

.60483 

1.65337 

50 

11 

.53582 

1.86630 

.55850 

1.79051 

.58162 

.71932 

.60522 

1.65228 

49 

12 

.53620 

1.86499 

.55888 

1.78929 

.58201 

.71817 

.60562 

1.65120 

48 

18 

.53657 

1.86369 

.55926 

1.78807 

.58240 

.71702 

.C0602 

1.65011 

47 

14 

.53694 

1.86239 

.55964 

1.78685 

.58279 

.71588 

.60642 

1.64903 

46 

15 

.53732 

1.86109 

.5G003 

1.78563 

.58318 

.71473 

.60681 

1.64795 

45 

10 

.53769 

1.85979 

.56041 

1.78441 

.58357 

.71358 

.60721 

1.64687 

44 

17 

.53807 

1.85850 

.56079 

1.78319 

.58396 

.71244 

.60761 

1.64579 

43 

18 

.53844 

1.85720 

.56117 

1.78198 

.58435 

.71129 

.60801 

1.64471 

42 

19 

.53882 

1.85591 

.50156 

1.78077 

i   .58474 

.71015 

.60841 

1.64363 

41 

20 

.53920 

1.85463 

.56194 

1.77955 

.58513 

.70901 

.60881 

1.64256 

40 

21 

.53957 

1.85333 

.56232 

1.77834 

j   .58552 

.70787 

.60921 

1.64148 

39 

22 

.53995 

1.85204 

.50270 

1.77713 

i   .58591 

.70673 

.60960 

1.64041 

38 

23 

.54032 

1.85075 

.50309 

1.77592 

.58631 

.70560 

.61000 

1.63934 

37 

24 

.54070 

1.84946 

.56347 

1.77471 

.5867'0 

.70446 

.61040 

1.63826 

36 

25 

.54107 

1.84818 

.56385 

1.77351 

.58709 

.70332 

.61080 

1.63719 

35 

26 

.54145 

1.84689 

.56424 

1.77230 

.587'48 

.70219 

.61120 

1.63612 

34 

27 

.54183 

1.84561 

.50462 

1.77110 

.58787 

.70106 

.61160 

1.63505 

33 

28 

.54220 

1.84133 

.56501 

1.76990 

.58826 

.C9992 

.61200 

1.63398 

32 

29 

.54258 

1.84305 

.50539 

1.76869 

.588C5 

1.69879 

.61240 

1.63292 

31 

oO 

.54296 

1.84177 

.56577 

1.76749 

.58905 

1.69766 

.61280 

1.63185 

30 

31 

.54333 

1.84049 

.56616 

1.76629 

.58944 

1.69653 

.61320 

1.63079 

29 

32 

.54371 

1.83922 

.56654 

1.76510 

.58983 

1.69541 

.61360 

1.62972 

28 

33 

.54409 

1.83794 

.56693 

1.70390 

.59022 

1.69428 

.61400 

1.62866 

27 

34 

.54446 

1.83667 

.56731 

1.76271 

.59061 

1.69316 

.61440 

1.62760 

26 

35 

.54484 

1.83540 

.56769 

1.76151 

.59101 

1.69203 

.61480 

1.62654 

25 

30 

.54522 

1.83413 

.56808 

1.76032 

.59140 

1.69091 

.61520 

1.62548 

24 

37' 

.54560 

1.83286 

.56846 

1.75913 

.59179 

1.68979 

.61561 

1.62442 

23 

38 

.54597 

1.83159 

.56885 

1.75794 

.59218 

1.68866 

.61601 

1.62336 

22 

39 

.54635 

1.83033 

.56923 

1  .  75675 

.50258 

1.C8754 

.61641 

1.62230 

21 

40 

.54673 

1.82906 

.56962 

1.75556 

.59297 

1.68643 

.61681 

1.62125 

20 

41 

.54711 

1.82780 

.57000 

1.75437 

.59336 

1.68531 

.61721 

1.62019 

19 

42 

.547'48 

1.82654 

.57039 

1.75319 

.59376 

1.68419 

.61761 

1.61914 

18 

43 

.54786 

1.82528 

.57'078 

1.75200 

.59415 

1.68308 

.61801 

1.61808 

17 

44 

.54824 

1.82402 

.57116 

1.75082 

.59454 

1.68196 

.61842 

1.61703 

16 

45 

.54862 

1.82276 

.57155 

1.74964 

.59494 

.68085 

.61882 

1.61598 

15 

46 

.54900 

1.82150 

.57193 

1.74846 

.59533 

.67974 

.61922 

1.61493 

14 

47 

.54938 

1.82025 

.57232 

1.74728 

.59573 

.67863 

.61962 

1.61388 

13 

48 

.54975 

1.81899 

.57271 

1.74610 

.59612 

.67752 

.62003 

1.  61283 

12 

49 

.55013 

1.81774 

.57309 

1.74492 

.59651 

.67641 

.62043 

1.61179 

11 

50 

.55051 

1.81649 

.57348 

1.74375 

.59691 

.67530 

.62083 

1.61074 

10 

51 

.55089 

1.81524 

.57386 

1.74257 

.59730 

.67419 

.62124 

1.60970 

9 

52 

.55127 

1.81399 

.57425 

1.74140 

.59770 

.67309 

.62164 

1.60865 

8 

53 

.55165 

1.81274 

.57464 

1.74022 

.59809 

.67198 

.62204 

1.60761 

7 

54 

.55203 

1.81150 

.57503 

1.73905 

.59849 

.67088 

.62245 

1.60657 

6 

55 

.55241 

1.81025 

.57541 

1.73788 

.59888 

.66978 

.62285 

1.60553 

5 

56 

.55279 

1.80901 

.57580 

1.73671 

.59928 

.66867 

.62325 

1.60449 

4 

57 

.55317 

1.80777 

.57619 

1.73555 

.59967 

1.66757 

.62366 

1.60345 

3 

58 

.55355 

1.80653 

.57657 

1.73438 

.60007 

1.66647 

.62406 

1.60241 

2 

59 

.55393 

1.80529  i 

.57696 

1.73321 

.60046 

1.66538 

.62446 

1.60137 

1 

GO 

.55431 

1.80405  1 

.57735 

1.73205 

.60086 

1.66428 

.62487 

1.60033 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

6 

1° 

6 

0° 

5 

9° 

5 

3° 

242 


TABLE  XVI.— NATURAL  TANGENTS   AND  COTANGENTS. 


32° 

33° 

34°                        35° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.62487 

1.60033 

.64941 

1.53986 

.67451 

1.48256  J 

.70021 

1.42815 

60 

1 

.62527 

1.59930 

.64982 

1.53888 

.67493 

1.48163 

.70064 

1.42726 

59 

2 

.62568 

1.59826 

.65024 

1.53791 

.67536 

1  48070 

.70107 

1.42638 

58 

3 

.62608 

1.59723 

.65065 

1.53693 

.67578 

1.47977 

.70151 

1.42550 

57 

4 

.62649 

1.59620 

.65106 

1.53595 

.67620 

1.47885 

.70194 

1.42462 

56 

5 

.62689 

1.59517 

.65148 

1.53497 

.67663 

1.47792 

.70238 

1.42374 

55 

6 

.62730 

1.59414 

.65189 

1.53400 

.67705 

1.47699 

.70281 

1.42286 

54 

7 

.62770 

1.59311 

.65231 

1.53302 

.67748 

1.47607 

.70325 

1.42198 

53 

8 

.62811 

1.59208 

.65272 

1.53205 

.67790 

1.47514 

.70368 

1.42110 

52 

9 

.62852 

1.59105 

.65314 

1.53107 

.67832 

1.47422 

.70412 

1.42022 

51 

10 

.62892 

1.59002 

.65355 

1.53010 

.67875 

1.47330 

.70455 

1.41934 

50 

11 

.62933 

1.58900 

.65397 

1.52913 

.67917 

1.47238 

.70499 

1.41847 

49 

12 

.62973 

1.58797 

.65438 

1.52816 

.67960 

1.47146 

.70542 

1.41759 

48 

13 

.63014 

1.58095 

.65480 

1.52719 

.68002 

1.47053 

.70586 

1.41672 

47 

14 

.63055 

1.58593 

.65521 

1.52622 

.68045 

1.46962 

.70629 

1.41584 

46 

15 

.63095 

1.58490 

.65563 

1.52525 

.68088 

1.46870 

.70673 

1.41497 

45 

16 

.63130 

1.58388 

.65604 

1.52429 

.68130 

1.46778 

.70717 

1.41409 

44 

7 

.63177 

1.58286 

.65646 

1.52a32  i 

.68173 

1.46686 

.70760 

1.41322 

43 

18 

.63217 

1.58184 

.65688 

1.52235 

.68215 

1.46595 

.70804 

1.41235 

42 

19 

.63258 

1.58083 

.65729 

1.52139  1 

.68258 

1.46503 

.70848 

1.41148 

41 

20 

.63299 

1.57981 

.65771 

1.52043  j 

.68301 

1.46411 

.70891 

1.41061 

40 

21 

.63340 

1.57879 

.65813 

1.51946 

.68343 

1.46320 

.70935 

1.40974 

39 

22 

.63380 

1.57778 

.65854 

1.51850 

.68386 

1.46229 

.70979 

1.40887 

38 

23 

.63421 

1.57676 

.65896 

1.51754 

.68429 

1.46137 

.71023 

1.40800 

37 

24 

.63402 

1.57575 

.65938 

1.51658 

.68471 

1.46046 

.71066 

1.40714 

36 

25 

.63503 

1.57474 

.65980 

1.51562 

.68514 

1.45955 

.71110 

1.40627 

35 

26 

.63544 

1.57372 

.66021 

1.51,466 

.68557 

1.45864 

.71154 

1.40540 

*!4 

27 

.63584 

1.57271 

.00063 

1.51370 

.68600 

1.45773 

.71198 

1.40454 

33 

28 

.63625 

1.57170 

.66105 

1.51275 

.68642 

1.45682 

.71242 

1.40367 

32 

29 

.63666 

1.57069 

.C6147 

1.51179 

.68685 

1.45592 

.71285 

1.40281 

31 

30 

.63707 

1.56969 

.66189 

1.51084 

.68728 

1.45501 

.71329 

1.40195 

20 

31 

.63748 

1.56868 

.66230 

1.50988 

.68771 

1.45410 

.71373 

1.40109 

29 

32 

.63789 

1.50767 

.66272 

1.50893 

.C8814 

1.45320 

.71417 

1.40022 

28 

33 

.63830 

1.56667 

.66314 

1.50797 

.68857 

1.45229 

.714G1 

1.39936 

27 

34 

.63871 

1.56566 

.66356 

1.50702 

.68900 

1.45139 

.71505 

1.39850 

26 

35 

.63912 

1.56466 

.66398 

1.50607 

.68942 

1.45049 

.71549 

1.39764 

25 

36 

.63953 

1.56366 

.66440 

1.50512 

.08985 

1.44958 

.71593 

1.39679 

24 

37 

.63994 

1.56205 

.66482 

1.50417 

.69028 

1.44868 

.71637 

1.39593 

23 

38 

.64035 

1.56165 

.66524 

1.50322 

.69071 

1.44778 

.71681 

1.39507 

22 

39 

.64076 

1.56065 

.66506 

1.50228 

.69114 

1.44688 

.71725 

1.39421 

21 

40 

.64117 

1.55966 

.66608 

1.50133 

.69157 

1.44598 

.71769 

1.39336 

20 

41 

.64158 

1.55866 

.66650 

1.50038 

.69200 

1.44508 

.71813 

1.39250 

19 

42 

.64199 

1.55766 

66602 

1.49944 

.69243 

1.44418 

.7185  f 

1.39165 

18 

43 

.64240 

1.55666 

.66734 

1.49849 

.69288 

1.44329 

.71901 

1.39079 

17 

44 

.64281 

1.55567 

.66776 

1.497'55 

.69329 

1.44239 

.71946 

1.38994 

16 

45 

.64322 

1.55467 

.66818 

1.49661 

.69372 

1.44149 

.71990 

1.38909 

15 

46 

.64303 

1.55368 

.66860 

1.49566 

.69416 

1.44060 

.72034 

1.38824 

14 

41 

.64404 

1.55269 

.66902 

1.49472 

.69459 

1.43970 

.72078 

1.38738 

13 

48 

.64446 

1.55170 

.66944 

1.49378 

.69502 

1.43881 

.72122 

1.38653 

12 

49 

.64487 

1.55071 

.66986 

1.49284 

.69545 

1.43792 

.72167 

1.385G8 

11 

50 

.64528 

1.54972 

.67028 

1.49190 

.69588 

1.43703 

.72211 

1.3S484 

10 

51 

.64569 

1.54873 

.67071 

1.49097 

.69631 

1.43614 

.72255 

1.38399 

r 

52 

.64610 

1.54774 

.67113 

1.49003 

.09675 

1.43525 

.72299 

1.38314 

8 

53 

.64652 

1.54675 

.67155 

1.48909 

.69718 

1.43436 

.72344 

1.38229 

r 

54 

.64693 

1.54576 

.67197 

1.48816 

.69761 

1.43347 

,72388 

1.38145 

6 

5o 

.64734 

1.54478 

.67239 

1.48722 

.69804 

1.43258 

.72432 

1.38060 

P 

5 

.64775 

1.54379 

.67282 

1.48629 

.69847 

1.43169 

.72477 

1.37976 

4 

5 

.64817 

1.54281 

.67324 

1.48536 

.69891 

1.43080 

.72521 

1.37891 

f 

5 

.64858 

1.54183 

.67366 

1.48442 

.69934 

1.42992 

.72565 

1.37807 

2 

5 

.64899 

1.54085 

I   .67409 

1.48349 

.69977 

1.42903 

.72610 

1.37722 

1 

6 

.64941 

1.53986 

j    .67451 

1.48256 

.70021 

1.42815 

.72654 

1.37638 

0 

Cotang  |    Tang 

Cotang  |    Tang 

Cotang 

Tang 

Cotang 

Tang 

i 

57° 

!           56° 

55°           II           54° 

1 

243 


TABLE  XVI.— NATURAL  TANGENTS  AND  COTANGENTS. 


36° 

37°                        38°                        39° 

Tang 

Cotang 

Tang  |  Cotang 

Tang 

Cotang 

Tang   1  Cotang 

0 

.72654 

1.37638 

.73865 

1.32704 

.78129 

1.27994 

.80978 

1.23490 

60 

1 

.72699 

1.37554 

.75401 

1.32624 

.78175 

1.27917 

.81027 

1.23416 

59 

2 

.72743 

1.37470 

.75447 

1.32514 

.78222 

.27841 

.81075 

1.23343 

5? 

8 

.72788 

1.37386 

.75492 

1.32464 

.78269 

.27764 

.81123 

1.23270 

57 

4 

.72832 

1.37302 

.75538 

1.32384 

,.78316 

.27688 

.81171 

1.23196 

56 

5 

.72877 

1.37218 

.75584 

1.32304 

.78363 

.27611 

.81220 

1.23123 

55 

6 

.72921 

1.37134 

.75629 

1.32224 

.78410 

.27535 

.81268 

1.23050 

54 

.72966 

1.37050 

.75675 

1.32144  i 

.78457 

1.27458 

.81316 

1.22977 

53 

B 

.73010 

1.36967 

.75721 

1.32064 

.78504 

1.27382 

.81364 

1.22904 

52 

9 

.73055 

1.36883 

.75767 

1.31984  | 

.78551 

1.27806 

.81413 

1.22831 

51 

10 

.73100 

1.36800 

.75812 

1.31904 

.78598 

1.27230 

.81461 

1.22758 

50 

11 

.73144 

1.36716 

.75858 

1.31825 

.78645 

1.27153 

.81510 

1.22685 

49 

I* 

.73189 

1.36633 

.75904 

1.31745 

.78692 

1.27077 

.81558 

1.22612 

48 

13 

.73234 

1.36549 

.75950 

1.31666 

.78739 

1.27001 

.81606 

1.22539 

47 

14 

.73278 

1.36466 

.  75996 

1.31586 

.78786 

.26925 

.81655 

1.22467 

46 

15 

.73323 

1.36383 

.76042 

1.31507 

.78834 

.26849 

.81703 

1.22394 

45 

10 

.73368 

1.38300 

.76088 

1.31427 

.78881 

.26774 

.81752 

1.22321 

44 

17 

.73413 

1.36217 

.76134 

1.31348 

.78928 

.26698 

.81800 

1.22249 

43 

18 

.73457 

1.36134 

.76180 

1.31269 

.7897'5 

.26622 

.81849 

1.22176 

42 

19 

.73502 

1.38051 

.76226 

1.31190 

.79022 

.26546 

.81898 

1.22104 

41 

20 

.73547 

1.35968 

.76272 

1.31110 

.79070 

.26471 

.81946 

1.22031 

40 

21 

.73592 

1.35885 

.76318 

1.31031 

.79117 

1.2G395 

.81995 

1.21959 

39 

22 

.73637 

1.35802 

..76364 

1.30952 

.79164 

1.26319 

.82044 

1.21886 

38 

23 

.73681 

1.35719 

.76410 

1.30873 

.79212 

1.2G244 

.82092 

1.21814 

37 

24 

.73  72(i 

1.35637 

.76456 

1.30795 

.79259 

1.  201  69 

.82141 

1.21742 

36 

25 

.73771 

1.35554 

.76502 

1.30716 

.79306 

1.20093 

.82190 

1.2167'0 

35 

26 

.73816 

1.35472 

.76548 

1.30637 

.79354 

1.2G018 

.82238 

1.21598 

34 

27 

.73861 

1.35389 

.7'6594 

1.30558 

.79401 

1.25943 

.82287 

1.21526 

33 

28 

.73906 

1.35307 

.76640 

1.30480 

.79449 

1.25867 

.82336 

1.21454 

32 

2!) 

.73951 

1.35224 

.76686 

1.30401 

.79496 

1.25792 

.82385 

1.21382 

31 

30 

.73996 

1.35142 

.76733 

1.30323 

.79544 

1.25717 

.82434 

1.21310 

30 

31 

.74041 

1.35060 

.76779 

1.30244 

.79591 

1.25642 

.82483 

1.21238 

29 

32 

.74086 

1.34978 

.76825 

1.30166 

.79639 

1.25567 

.82531 

1.21166 

28 

33 

.74131 

1.34896 

.76871 

1.30087 

.79686 

1.25492 

.82580 

1.21094 

27 

34 

.74176 

1.34814 

.76918 

1.30009 

.79734 

1.25417 

.82629 

1.21023 

26 

35 

.74221 

1.34732 

.76964 

1.29931 

.79781 

1.25343 

.82678 

1.20951 

25 

86 

.74267 

1.34650 

.77010 

1.29853 

.79829 

1.25268 

.82727 

1.20879 

24 

37 

.74312 

1.34568 

.77057 

1.29775 

.79877 

1.25193 

.82776 

1.20808 

23 

38 

.74357 

1.34487 

.77103 

1.29696 

.79924 

1.25113 

.82825 

1.20736 

22 

39 

.74402 

1.34405 

.77149 

1.29618 

.79972 

1.25044 

.82874 

1.20665 

21 

40 

.74447 

1.34323 

.77196 

1.29541 

.80020 

1.24969 

.82923 

1.20593 

20 

41 

.74492 

1.34242 

.77242 

1.29463 

.80067 

1.24895 

.82972 

1.20522 

19 

42 

.74538 

1.34160 

.77289 

1.29385 

.80115 

1.24820 

.83022 

1.20451 

18 

43 

.74583 

1.34079 

.77335 

1.29307 

.80163 

1.24746 

.83071 

1.20379 

17 

44 

.74628 

1.33998 

.77382 

1.29229 

.80211 

1.24672 

.83120 

1.20308 

16 

45 

.74674 

1.33916 

.  77428 

1.29152 

.80258 

1.24507 

.83169 

1.20237 

15 

4(3 

.74719 

1.33835 

.77475 

1.29074 

.80306 

1.24523 

.83218 

1.20166 

14 

47 

.74764 

1.33754 

.77521 

1.28997 

.80354 

1.24449 

.83268 

1.20095 

13 

48 

.74810 

1.33673 

.77568 

1.28919 

.80402 

1.24375 

.83317 

1.20024  !12 

49 

.74855 

1.33592 

.77615 

1.28842 

.80450 

1.24301 

.a3366 

1.19953  111 

50 

.74900 

1.33511 

.77661 

1.28764 

.80498 

1.24227 

.83415 

1.19882 

10 

51 

.74946 

1.33430 

.77708 

1.28687 

.80546 

1.24153 

.83465 

1.19811 

9 

52 

.74991 

1.33349 

.77754 

1.28610 

.80594 

1.24079 

.83514 

1.19740 

8 

53 

.75037 

1.33268 

.77801 

1.28533 

.80642 

1.24005 

.83564 

1.19669 

7 

54 

.75082 

1.33187 

.77848 

1.28456 

.80600 

1.23931 

.83613 

1  .  19599 

6 

55 

.75128 

1.33107 

.77895 

1.28379 

.80738 

1.23858 

.83662 

1.19528 

5 

56 

.75173 

1.33026 

.77941 

1.28302 

.80786 

1.23784 

.83712 

1.19457 

4 

K 

.75219 

1.32946 

.77988 

1.28225 

.80834 

1.23710 

.83761 

1.19387 

3 

58 

.75264 

1.32865 

.78035 

1.28148 

.80882 

1.23637 

.83811 

1.19316 

2 

5! 

.75310 

1.32785 

.78082 

1.28071 

.80930 

1.23563 

.83860 

1  .  19246 

1 

at 

.75355 

1.32704 

.78129 

1.27994 

.80978 

1.23490 

.83910 

1.19175 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang     Tang 

f 

53° 

52° 

51° 

50° 

244 


TABLE  XVI.— NATURAL  TANGENTS  AND  COTANGENTS. 


4 

0° 

4 

1° 

4 

2° 

4 

3° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.83910 

.  19175 

".80929 

1  .  15037 

.90040 

.11061 

.93252 

1.07237 

60 

1 

.83960 

.19105 

.80980 

1.14909 

.90093 

.10996 

.93306 

1.07174 

59 

2 

.84009 

.19035 

.87031 

1.14902 

.90146 

.10931 

.93360 

1.07112 

58 

3 

.84059 

.18904 

.87082 

1.14834 

.90199 

.10867 

.93415 

1.07049 

57 

4 

.84108 

.18894 

.87133 

1.14707 

.90251 

.10802 

.93469 

1.06987 

50 

5 

.84158 

.18824 

.87184 

1  .  14099 

.90304 

.10737 

.93524 

1.06925 

55 

6 

.84208 

.18754 

.87'23G 

1.14032 

.90357 

.10072 

.93578 

1.00802 

54 

7 

.84258 

.18684 

.87287 

1  .  14505 

.90410 

.10607 

.93033 

1.06800 

53 

8 

.84307 

.18014 

.87:338 

1.14498 

.90403 

.10543 

.93088 

1.06738 

52 

9 

.84357 

.18544 

.87389 

1.14430 

.90516 

.10478 

.93742 

1.06676 

51 

10 

.84407 

.18474 

.87441 

1.14303 

.90569 

.10414 

.93797 

1.06613 

50 

11 

.84457 

.18404 

.87492 

1.14290 

.00021 

.10349 

.93852 

.06551 

49 

12 

.84507 

.18334 

.87543 

1  .  14229 

.90074 

.10285 

.93900 

.00489 

48 

18 

.84556 

.18204 

.87595 

1.14102 

.90727 

.10220 

.93901 

.00427 

47 

14 

.84006 

.18194 

.87046 

1.14095 

.90781 

.10150 

.94010 

.00305 

46 

15 

.84050 

.18125 

.87698 

1.14028 

.90834 

.10091 

.94071 

.00303 

45 

10 

.84700 

.18055 

.87749 

.13901 

.90887 

.10027 

.94125 

.00241 

44 

17 

.84756 

.17986 

.87801 

.13894 

.90940 

.09903 

.94180 

.00179 

43 

18 

.84800 

.17916 

.87852 

.13828 

.90993 

.09899 

.94235 

.00117 

42 

19 

.84850 

.17846 

.87904 

.13761 

.91046 

.09834 

.94290 

.00056 

41 

20 

.84900 

1.17777 

.87955 

.13094 

.91099 

.09770 

.94345 

.05994 

40 

21 

.84956 

1.17708 

.88007 

.13027 

.91153 

.09706 

.94400 

.05932 

39 

23 

.85000 

1  .  17638 

.88059 

.13501 

.91206 

.09042 

.94455 

.05870 

38 

23 

.85057 

1.17509 

.88110 

.13494 

.91259 

.09578 

.94510 

.05809 

37 

24 

.85107 

1  .  17500 

.88102 

.13428 

.91313 

.09514 

.94505 

.05747 

30 

25 

.85157 

1.17430 

.88214 

.13301 

.91366 

.09450 

.94620 

.05685 

35 

x:;i 

.85207 

1.17301 

.88205 

.13295 

.91419 

.09380 

.94676 

.05624 

34 

27 

.85257 

1.17292 

.88317 

.13223 

.91473 

.09322 

.94731 

.05562 

33 

28 

.85308 

1.17223 

.88309 

.13102 

.91526 

.09258 

.94786 

.05501 

32 

2.) 

.85358 

1.17154 

.88421 

.13096 

.91580 

.09195 

.94841 

.05439 

31 

30 

.85408 

1.17085 

.88473 

.13029 

.91633 

.09131 

.94896 

.05378 

30 

31 

.85458 

1.17016 

.88524 

.12963 

.91687 

.09007 

.94952 

.05317 

29 

32 

.85509 

1.10947 

.88576 

.12897 

.91740 

.09003 

.95007 

.05255 

28 

83 

.85559 

1.16878 

.88628 

.12831 

.91794 

.08940 

.95062 

.05194 

27 

84 

.85009 

1.10809 

.88680 

1.12705 

.91847 

.08876 

.95118 

.05133 

20 

35 

.85000 

1.10741 

.88732 

1.12099 

.91901 

1.08813 

.95173 

.05072 

25 

3(5 

.85710 

1.16672 

.88784 

1.12033 

.91955 

1.08749 

.95229 

.05010 

24 

37 

.85701 

.16603 

.88836 

1.12507 

.92008 

1.08686 

.95284 

.04949 

23 

38 

.85811 

.  16535 

.88888 

1.12501 

.92062 

1.08622 

.95340 

.04888 

22 

39 

.85802 

.10406 

.88940 

1.12435 

.92116 

1.08559 

.95395 

.04827 

21 

40 

.85912 

.16398 

.88992 

1.12309 

.92170 

1.08496 

.95451 

.04766 

20 

41 

.85963 

.10329 

.89045 

1.12303 

.92224 

1.08432 

.95506 

.04705 

19 

•12 

.86014 

.10201 

.89097 

1.12238 

.92277 

1.08309 

.95562 

.04644 

18 

43 

.80004 

.10192 

.89149 

1.12172 

.92331 

1.08306 

.95618 

.04583 

17 

44 

.80115 

.10124 

.89201 

1.12106 

.92385 

1.08243 

.95673 

.04522 

18 

45 

.80106 

.10056 

.89253 

1.12041 

.92439 

1.08179 

.95729 

.04461 

15 

40 

.86216 

.15987 

.89306 

1.11975 

.92493 

1.08116 

.95785 

.04401 

14 

47 

.80207 

.15919 

.89358 

1.11909 

.92547 

1.08053 

.95841 

.04340 

13 

48 

.80318 

.15851 

.89410 

1.11844 

.92601 

1  -07990 

.95897 

.04279 

12 

49 

.80308 

.15783 

.89403 

1  11778 

.92655 

1.07927 

.95952 

.04218 

11 

50 

.80419 

.15715 

.89515 

1.11713 

.92709 

1.07864 

.96008 

.04158 

10 

51 

.80470 

.15047 

.89507 

1.11648 

.92763 

1.07801 

.96064 

.04097 

9 

52 

.80521 

.15579 

.89020 

1.11582 

.92817 

.07738 

.96120 

.04036 

8 

53 

.80572 

.15511 

.89072 

.11517 

.92872 

.07676 

.96176 

.03976 

7 

54 

.80023 

.15443 

.89725 

.11452 

.92926 

.07613 

.96232 

.03915 

0 

55 

.80074 

1.15375 

.89777 

.11387 

.92980 

.07550 

.96288 

.03855 

5 

56 

.80725 

1.15308 

.89830 

.11321 

.93034 

.07487 

.96344 

1.03794 

4 

57 

.80776 

1.15240 

.89883 

.11256 

.93088 

.07425 

.96400 

1.03734 

3 

58 

.80827 

1.15172 

.89935 

1.11191 

.93143 

.07362 

.96457 

1.03674 

2 

59 

.80878 

1.15104 

.89988 

1.11126 

.93197 

.07299 

.96513 

1.03613 

1 

60 

.80929 

1  .  15037 

.90040 

1.11001 

.93252 

.07237 

.96569 

1.03553 

0 

/ 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

f 

4 

9° 

4 

8° 

4 

7° 

4 

6° 

245 


TABLE  XVI.— NATURAL  TANGENTS  AND  COTANGENTS. 


t 

4 

t4° 

4 

£0 

1 

4 

4° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.90569 

1.03553 

60 

20 

.97700 

1.02355 

40 

40 

.98843 

1.01170 

20 

1 

.90625 

1.03493 

59 

21 

.97756 

1.02295 

:;<> 

I  41 

.98901 

1.01112 

19 

2 

.96681 

1.0^33 

58 

22 

.97813 

1.02236 

:•« 

42 

.98958 

1.01053 

18 

3 

.96738 

1.03372 

57 

23 

.97870 

1.02176 

37 

43 

.99016 

1.00994 

17 

4 

.90794 

1.03312 

56 

24 

.97927 

1.02117 

3<> 

44 

.99073 

1.00935 

16 

5 

.96850 

1.03252 

55 

25 

.97984 

1.02057 

35 

45 

.99131 

1.00876 

15 

6 

.96907 

1.03192 

54 

26 

.98041 

1.01998 

34 

46 

.99189 

1.00818 

14 

7 

.96963 

1.03132 

53 

•27 

.98098 

1.01939 

33 

47 

.99247 

1.00759 

13 

8 

.97020 

1.03072 

52 

28 

.98155 

1.01879 

32 

48 

.99304 

1.00701 

12 

9 

.97076 

1.03012 

51 

29 

.98213 

1.01820 

31 

49 

.99362 

1.00642 

11 

10 

.97133 

1.02952 

50 

30 

.98270 

1.01761 

ao 

50 

.99420 

1.00583 

10 

11 

.97189 

1.02892 

49 

31 

.9&S27 

1.01702 

20 

51 

.99478 

1.00525 

9 

12 

.97246 

1.02832 

48 

32 

.98384 

1.01642 

28 

52 

.99536 

1.00467 

8 

13 

.97302 

1.02772 

47 

33 

.98441 

1.01583 

27 

53 

.99594 

1.00408 

7 

14 

.97359 

1.02713 

46 

34 

.98499 

1.01524 

2(5 

54 

.99652 

1.00350 

6 

15 

.97416 

1.02653 

45 

35 

.98556 

1.01465 

25 

55 

.99710 

1.00291 

5 

16 

.97472 

1.02593 

44 

36 

.98613 

1.01406 

24 

50 

.99768 

1.00233 

4 

1? 

.97529 

1.02533 

43 

37 

.98671 

1.01347 

23 

57 

.99826 

1.00175 

3 

18 

.97586 

1.02474 

42 

38 

.98728 

1.01288 

22 

58 

.99884 

1.00116 

2 

19 

.97643 

1.02414 

41 

39 

.98786 

1.01229 

21 

59 

.99942 

1.00058 

1 

20 

.97700 

1.02355 

40 

.40 

.98813 

1.01170 

20 

60 

1.00000 

1.00000 

0 

/ 

Cotang 

Tang 

/ 

/ 

Cotang 

Tang 

1 
/ 

/ 

Cotang 

Tang 

/ 

4 

5° 

4 

5° 

4 

5° 

246 


TABLE    XVII.— NATURAL  VERSED  SINES  AND    EXTERNAL   SECANTS. 


0 

0 

1 

0 

2 

0 

3 

o 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.00000 

.00000 

.00015 

.00015 

.00061 

.00061 

.00137 

.00137 

0 

1 

.00000 

.00000 

.00016 

.00016 

.00062 

.00062 

.00139 

00139 

1 

2 

.00000 

.00000 

.00016 

.00016 

.00063 

.00063 

.00140 

.00140 

2 

3 

.00000 

.00000 

.00017 

.00017 

.00064 

.00064 

.00142 

.00142 

3 

4 

.00000 

.00000 

.00017 

.00017 

.00065 

.00065 

.00143 

.00143 

4 

5 

.00000 

.00000 

.00018 

.00018 

.00066 

.00066 

.00145 

.00145 

5 

6 

.00000 

.00000 

.00018 

.00018 

.00067 

.00067 

.00146 

.00147 

6 

7 

.00000 

.00000 

.00019 

.00019 

.00068 

.00068 

.00148 

.00148 

7 

8 

.00000 

.00000 

.00020 

.00020 

.00069 

.00069 

.00150 

.00150 

8 

9 

.00000 

.00000 

.00020 

.00020 

.00070 

.00070 

.00151 

.00151 

9 

10 

.00000 

.00000 

.00021 

.00021 

.00071 

.00072 

.00153 

.00153 

10 

11 

.00001 

.00001 

.00021 

.00021 

.00073 

.00073 

.00154 

.00155 

11 

12 

.00001 

.00001 

.00022 

.00022 

.00074 

.00074 

.00156 

.00156 

12 

13 

.00001 

.00001 

.00023 

.00023 

.00075 

.00075 

.00158 

.00158 

13 

14 

.00001 

.00001 

.00023 

.00023 

.00076 

.00076 

.00159 

.00159 

14 

15 

.00001 

.00001 

.00024 

.00024 

.00077 

.00077 

.00161 

.00161 

15 

16 

.00001 

.00001 

.00024 

.00024 

.00078 

.00078 

.00162 

.00163 

ia 

17 

.00001 

.00001 

.00025 

.00025 

.00079 

.00079 

.00164 

.00164 

17 

18 

.00001 

.00001 

.00026 

.00026 

.00081 

.00081 

.00166 

.00166 

18 

19 

.00002 

.00002 

.00026 

.00026 

.00082 

.00082 

.00168 

.00168 

19 

20 

.00002 

.00002 

.00027 

.00027 

.00083 

.00083 

.00169 

.00169 

20 

21 

.00002 

.00002 

.00028 

.00028 

.00084 

.00084 

.00171 

.00171 

21 

22 

.0000.3 

.0000.3 

.00028 

.00028 

.00085 

.00085 

.00173 

.00173 

22 

23 

.00002 

.00002 

.00029 

.00029 

.00087 

.00087 

.00174 

.00175 

23 

24 

.00002 

.00002 

.00030 

.00030 

.00083 

.00088 

.00176 

.00176 

24 

25 

.00003 

.00003 

.00031 

.00031 

.00089 

.00089 

.00173 

-.00178 

25 

20 

.00003 

.00003 

.00031 

.00031 

.00090 

.00090 

.00179 

.00180 

26 

27 

.00003 

.00003 

.00032 

.00032 

.00091 

.00091 

.00181 

.00182 

27 

23 

.00003 

.00003 

.00033 

.00033 

.00093 

.00093 

.00183 

.00183 

28 

29 

.00004 

.00004 

.00034 

.00034 

.00094 

.00094 

.00185 

.00185 

29 

30 

.00004 

.00004 

.00034 

.00034 

.00095 

.00095 

.00187 

.00187 

30 

31 

.00004 

.00004 

.00035 

.00035 

.00096 

.00097 

.00188 

.00189 

31 

32 

.00004 

.00004 

.00036 

.00036 

.00098 

.00098 

.00190 

.00190 

32 

33 

.00005 

.00005 

.00037 

.00037 

.00099 

.00099 

.00192 

.00192 

33 

34 

.00005 

.00005 

.00037 

.00037 

.00100 

.00100 

.00194 

.00194 

34 

35 

.00005 

.00005 

.00038 

.00038 

.00102 

.00102 

.00196 

.00196 

35 

36 

.00005 

.00005 

.00039 

.00039 

.00103 

.00103 

.00197 

.00193 

33 

37 

.00006 

.00006 

.00040 

.00040 

.00104 

.00104 

.00199 

.00200 

37 

33 

.00006 

.00006 

.00041 

.00041 

.00106 

.00105 

.00201 

.00201 

38 

3D 

.00006 

.00006 

.00041 

.00041 

.00107 

.00107 

.00203 

.00203 

39 

40 

.00007 

.00007 

.00042 

.00042 

.00108 

.00108 

.00205 

.00205 

40 

41 

.00007 

.00007 

.00043 

.00043 

.00110 

.00110 

.00207 

.00207 

41 

42 

.00007 

.00007 

.00044 

.00044 

.00111 

.00111 

.00208 

.00209 

42 

43 

.00008 

.00008 

.00045 

.00045 

.00112 

.00113 

.00210 

.00211 

43 

44 

.00008 

.00008 

.00046 

.00046 

.00114 

.00114 

.00212 

.00213 

41 

45 

.00009 

.00009 

.00047 

.00047 

.00115 

.00115 

.00214 

.00215 

45 

43 

.00009 

.00009 

.00048 

.00048 

.00117 

.00117 

.00216 

.00216 

46 

47 

.00009 

.00009 

.00048 

.00048 

.00118 

.00118 

.00218 

.00213 

47 

48 

.00010 

.00010 

.00049 

.00049 

.00119 

.00120 

.00220 

.00220 

48 

49 

.00010 

.00010 

.00050 

.00050 

.00121 

.00121 

.00222 

.00222 

49 

50 

.00011 

.00011 

.00051 

.00051 

.00122 

.00122 

.00224 

.00224 

50 

51 

.00011 

.00011 

.00052 

.00052 

.00124 

.00124 

.00226 

.00226 

51 

52 

.00011 

.00011 

.00053 

.00053 

.00125 

.00125 

.00228 

.00223 

52 

53 

.00012 

.00012 

.00054 

.00054 

.00127 

.00127 

.00230 

.00230 

53 

54 

.00012 

.00012 

.00055 

.00055 

.00128 

.00128 

.00232 

.00232 

54 

55 

.00013 

.00013 

.00056 

.00056 

.00130 

.00130 

.00234 

.00234 

55 

56 

.00013 

.00013 

.00057 

.00057 

.00131 

.00131 

.00236 

.00236 

56 

57 

,00014 

.00014 

.00058 

.00058 

.00133 

.00133 

.00238 

.00238 

57 

58 

.00014 

.00014 

.00059 

.00059 

.00134 

.00134 

.00240 

.00240 

58 

59 

.00015 

.00015 

.00060 

.00060 

.00136 

.00136 

.00242 

.00242 

59 

60 

.00015 

.00015 

.00061 

.00061 

.00137 

.00137 

.00244 

.00244 

60 

247 


TABLE    XVII.— NATURAL  VERSED  SINES    AND  EXTERNAL   SECANTS 


4° 

5° 

6« 

7° 

Vers. 

Ex.  sec. 

Vers.  ,  Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.00244 

.00244 

.00381 

.00382 

.00548 

.00551 

.00745 

.00751 

0 

1 

.00246 

.00246 

.00383 

.00385 

.00551 

.00554 

.00749 

.00755 

1 

2 

.00248 

.00248 

.00386 

.00387 

.00554 

.00557  i 

.00752 

.(W58 

2 

3 

.00250 

.00250 

.00388 

.00390 

.00557 

.  00500  ! 

.00756 

.007'62 

3 

4 

.00252 

.00252 

.00391 

.00392 

.00560 

.00563  1 

.00760 

.00765 

4 

5 

.00254 

.00254 

.00393 

.00395 

.00563 

.00566  i 

.00763 

.00769 

5 

6 

.00256 

.00257 

.00396 

.00397 

.00566 

.00569 

.00767 

.00773 

6 

7 

.00258 

.00259 

.00398 

.00400 

.00569 

.00573 

.00770 

.00776 

7 

8 

.00260 

.00261 

.00401 

.00403 

.00572 

.00576 

.00774 

.00780 

8 

9 

.00262 

.00263 

.00404 

.00405 

.00576 

.00579 

.00178 

.00784 

9 

10 

.00264 

.00265 

.00406 

.00408 

.00579 

.00582 

.00781 

.00787 

10 

11 

.00266 

.00267 

.00409 

.00411 

.00582 

.00585 

.00785 

.00791 

11 

12 

.00269 

.00269 

.00412 

.00413 

.00585 

.00588 

.00789 

.00795 

12 

13 

.00271 

.00271 

.00414 

.00416 

.00588 

.00592 

.00792 

.00799 

13 

14 

.00273 

.00274 

.00417 

.00419 

.00591 

.00595 

.00796 

.00802 

14 

15 

.00275 

.00276 

.00420 

.00421 

.00594 

..00598 

.00800 

.00806 

15 

16 

.00277 

.00278 

.00422 

.00424 

.00598 

.00601 

.00803 

.00810 

16 

17 

.00279 

.00280 

.00425 

.00427 

.00601 

.00604 

.00807 

.00813 

17 

18 

.00281 

.00282 

.00428 

.00429 

.00604 

.00608 

.00811 

.00817 

18 

19 

.00284 

.00284 

.00430 

.00432 

.00607 

.00611 

.00814 

.00821 

19 

20 

.00286 

.00287 

.00433 

.00435 

.00610 

.00614 

.00818 

.00825 

20 

21 

.00288 

.00289 

.00435 

.C0438 

.00614 

.00617 

.00822 

.00828 

21 

22 

.00290 

.00291 

.00438 

.00440 

.00617 

.00621 

.00825 

.00832 

22 

23 

.00293 

.00293 

.00441 

.00443 

.00620 

.00624 

.00829 

.00836 

23 

24 

.00295 

.00296 

.00444 

.00440 

.00623 

.00627 

.00833 

.00840 

24 

25 

.00297- 

.00298 

.00-447 

.00449 

.00628 

.00630 

.00837 

.00844 

25 

26 

.00299 

.00300 

.00449 

.00451 

.00630 

.C0634 

.C0840 

.00848 

26 

27 

.00301 

.00302 

.00452 

.00454 

.00633 

.00637 

.00844 

.00851 

27 

28 

.00304 

.00305 

.00455 

.00457 

.00636 

.00640 

.00848 

.C0855 

28 

29 

.00306 

.00307 

.00458 

.00460 

.00640 

.00644 

.00852 

.00859 

29 

80 

.00308 

.00309 

.00460 

.004G3 

.00643 

.C0647 

.00856 

.00863 

30 

31 

.00311 

.00312 

.00463 

.00465 

.00646 

.00650 

.00859 

.00867 

31 

32 

.00313 

.00314 

.00466 

.00468 

.00649 

.00654 

.00863 

.00871 

32 

33 

.00315 

.00316 

.00469 

.00471 

.00653 

.00657  i 

.00867 

.00875 

33 

34 

.00317 

.00318 

.00472 

.00474 

.00656 

.00660 

.00871 

.00878 

34 

35 

.00320 

.00321 

.00474 

.00477 

.C0659 

.00664 

.00875 

.00882 

35 

36 

.00322 

.00323 

.00477 

.00480 

.00663 

.00667 

.00878 

.00886 

36 

37 

.00324 

.00326 

.00480 

.C0482 

.00666 

.00671 

.00882 

.00890 

37 

38 

.00327 

.00328 

.00483 

.00485 

.00669 

.00674 

.00886 

.00894 

38 

39 

.00329 

.00330 

.00486 

.00488 

.00673 

.00677 

.00890 

.00898 

39 

40 

.00332 

.00333 

.00489 

.00491 

.00676 

.00681 

.00894 

.00902 

40 

41 

.oo&34 

.00335 

.00492 

.00491 

.00680 

.00684 

.00898 

.00906 

41 

42 

.00336 

.00337 

.00494 

.00497 

.00683 

.00688  ! 

.C0902 

.00910 

42 

43 

.00339 

.00340 

.00497 

.00500 

.00686 

.00691 

.00906 

.00914 

43 

44 

.00341 

.00342 

.00500 

.00503 

.00690 

.00695  ! 

.00909 

.00918 

44 

45 

.00343 

.00345 

.00503 

.00506 

.00693 

.00698 

.00913 

.00922 

45 

46 

.00346 

.00347 

.00506 

.00509 

.00697 

.00701 

.00917 

.00926 

46 

47 

.00348 

.00350 

.00509 

.00512 

.00700 

.00705 

.00921 

.00930 

47 

48 

.00351 

.00352 

.00512 

.00515 

.00703 

.00708 

.00925 

.00934 

48 

49 

.00353 

.00354 

.00515 

.00518 

.00707 

.00712  I 

.00929 

.00938 

49 

50 

.00356 

.00357 

.00518 

.00521 

.00710 

.00715 

.00933 

.00942 

50 

51 

.00358 

.00359 

.00521 

.00524 

.00714 

.00719  ! 

.00937 

.00946 

51 

52 

.00361 

.003(52 

.00524 

.00527 

.00717 

.00722 

.00941 

.00950 

52 

53 

.00363 

.00364 

.00527 

.00530 

.00721 

.00726 

.00945 

.00954 

53 

54 

.00365 

.00367 

.00530 

.00533 

.<0724 

.00730 

.00949 

.00958 

54 

55 

.00368 

.00369 

.00533 

.00536 

.00728 

.00733 

.00953 

.00962 

55 

56 

.00370 

.00372 

.00536 

.00539 

.00731 

.007'37 

.00957 

.00966 

56 

57 

.00373 

.00374 

.00539 

.00542 

.00735 

.00740 

.00961 

.00970 

57 

58 

.00875 

.00377 

.00542 

.00545 

.00738 

.00744 

.00965 

.00975 

58 

59 

.00378 

.  .00379 

.00545 

.00548 

.00742 

.00747 

.00969 

.00979 

59 

60 

.00381 

.00382 

.00548 

.00551 

.007'45 

.00751 

.00973  |  .00983 

60 

248 


XVII.-NATURAL  VERSED  SINES  AND  EXTERNAL    SECANTS. 


8° 

9° 

10° 

11° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Sx.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.00973 

.00983  ! 

.01231 

.01247 

.01519 

.01543 

.01837 

.01872 

0 

1 

.00977 

.00987 

.01236 

.01251 

.01524 

.01548 

.01843 

.01877 

1 

2 

.00981 

.00991 

.01240 

.01256 

.01529 

.01553 

.01848 

.01883 

2 

3 

.00985 

.00995 

.01245 

.01261 

.01534 

.01558 

.01854 

.01889 

3 

4 

.00989 

.00999 

.01249 

.01265 

.01540 

.01564 

.01860 

.01895 

4 

5 

.00994 

.01004 

.01254 

.01270 

.01545 

.01569 

.01865 

.01901 

5 

6 

.00998 

.01008 

.01259 

.01275 

.01550 

.01574 

.01871 

.01906 

6 

7 

.01002 

.01012 

.01263 

.01279 

.01555 

.01579 

.01876 

.01912 

7 

8 

.01006 

.01016 

.01268 

.01284 

.01560 

.01585 

.01882 

.01918 

8 

9 

.01010 

.01020 

.01272 

.01289 

.01565 

.01590 

.01888 

.01924 

9 

10 

.01014 

.01024 

.01277 

.01294 

.01570 

.01595 

.01893 

.01930 

10 

11 

.01018 

.01029 

.01282 

.01298 

.01575 

.01601 

.01899 

.01936 

11 

12 

.010.22 

.01033 

.01286 

.01303 

.01580 

.01606 

.01904 

.01941 

12 

13 

.01027 

.01037 

.01291 

.01308 

.01586 

.01611 

.01910 

.01947 

13 

14 

.01031 

.01041 

.01296 

.01313 

.01591 

.01616 

.01916 

.01953 

14 

15 

.01035 

.01046 

.01300 

.01318 

.01596 

.01622 

.01921 

.01959 

15 

16 

.01039 

.01050 

.01305 

.01323 

.01601 

.01627 

.01927 

.01965 

16 

17 

.01043 

.01054 

.01310 

.01327 

.01606 

.01633 

.01933 

.01971 

17 

18 

.01047 

.01059 

.01314 

.01332 

.01612 

.01638 

.01939 

.01977 

18 

19 

.01052 

.01063  i 

.01319 

.01337 

.01617 

.01643 

.01944 

.01983 

19 

20 

.01056 

.01067 

.01324 

.01342 

.01622 

.01649 

.01950 

.01989 

20 

21 

.01000 

.01071 

.01329 

.01346 

.01627 

.01654 

.01956 

.01995 

21 

22 

.01064 

.01076 

.01333 

.01351 

i  .01632 

.01659 

.01961 

.02001 

22 

23 

.01069 

.01030 

.01338 

.01356 

.01638 

.01665 

.01967 

.02007 

23 

24 

.01073 

.01084 

.01343 

.01361 

.01643 

.01670 

.01973 

.02013 

24 

25 

.01077 

.01089 

.01348 

.01366 

.01648 

.01676 

.01979 

.02019 

25 

26 

.01081 

.01093 

.01352 

.01371 

.01653 

.01681 

.01984 

.02025 

26 

27 

.01086 

.01097 

.01357 

.01376 

.01659 

.01687 

.01990 

.02031 

27 

28 

.01090 

.01102 

.01362 

.01381 

.01664 

.01692 

.01996 

.02037 

28 

29 

.01094 

.01106 

.01367 

.01386 

.01669 

.01698 

.02002 

.02043 

29 

30 

.01098 

.01111 

.01371 

.01391 

.01675 

.01703 

.02008 

.02049 

30 

31 

.01103 

.01115 

.01376 

.01395 

.01680 

.01709 

.02013 

.02055 

31 

32 

.01107 

.01119 

.01331 

.01400 

.01685 

.01714 

.02019 

.02061 

32 

33 

.01111 

.01124 

.01383 

.01405 

.01690 

.01720 

.02025 

.02067 

as 

34 

.01116 

.01128 

.01391 

.01410 

.01696 

.01725 

.02031 

.02073 

34 

35 

.01120 

.01133 

.01396 

.01415 

.01701 

.01731 

.02037 

.02079 

35 

36 

.01124 

.01137 

.01400 

.01420 

.01706 

.01736 

,02042 

.02085 

36 

37 

.01129 

.01142 

.01405 

.01425 

.01712 

.01742 

.02048 

.02091 

37 

33 

.01133 

.01146 

.01410 

.01430 

.01717 

.01747 

.02054 

.02097 

38 

39 

.01137 

.01151 

.01415 

.01435 

.01723 

.01753 

.02000 

.02103 

39 

40 

.01142 

.01155 

.01420 

.01440 

.01728 

.01758 

.02066 

.02110 

40 

41 

.01146 

.01160 

.01425 

.01445 

.01733 

.01764 

.02072 

.02116 

41 

42 

.01151 

.01164 

.01430 

.01450 

.01739 

.01769 

.02078 

.02122 

42 

43 

.01155 

.01169 

.01435 

.01455 

.01744 

.01775 

.02084 

.02128 

43 

44 

.01159 

.01173 

.01439 

.01461 

.01750 

.01781 

.02090 

.02134 

44 

45 

.01164 

.01178 

.01444 

.01466 

.01755 

.01786 

.02095 

.02140 

45 

46 

.01168 

.01182 

.01449 

.01471 

.01760 

.01792 

.02101 

.02146 

46 

4? 

.01173 

.01187 

.01454 

•01476 

.01766 

.01798 

.02107 

.02153 

47 

48 

.01177 

.01191 

.01459 

.01481 

.01771 

.01803 

.02113 

.02159 

48 

49 

.01182 

.01196 

.01464 

.01486 

.01777 

.01809 

.02119 

.02165 

49 

50 

.01186 

.01200 

.01469 

.01491 

.01782 

.01815 

.02125 

.02171 

50 

51 

.01191 

.01205 

.01474 

.01496 

.01788 

.01820 

.02131 

.02178 

51 

52 

.01195 

.01209 

.01479 

.01501 

.01793 

.01826 

.02137 

.02184 

52 

53 

.01200 

.01214 

.01484 

.01506 

.01799 

.01832 

.02143 

.02190 

53 

54 

.01204 

.01219 

.01489 

.01512 

.01804 

.01837 

.02149 

.02196 

54 

55 

.01209 

.01223 

.01494 

.01517 

.01810 

.01843 

.02155 

.02203 

55 

56 

.01213 

.01228 

.01499 

.01522 

.01815 

.01849 

.02161 

.02209 

56 

57 

.01218 

.012:33 

.01504 

.01527 

.01821 

.01854 

.02167 

.02215 

57 

58 

.01222 

.01237 

.01509 

.01532 

.01826 

.01860 

.02173 

.02221 

58 

59 

.01227 

.01242 

.01514 

.01537 

.01832 

.01866 

.02179 

.02228 

59 

60 

.01231 

.01247 

.01519 

.01543 

.01837 

.01872 

.02185 

.02234 

60 

249 


TABLE     XVII.— NATURAL  VERSED  SINES  AND  EXTERNAL   SECANTS. 


/ 

12° 

13° 

14° 

15° 

/ 

Vers. 

Ex.  sec.  | 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.02185 

.02234 

.02563 

.02630 

.02970 

.03061 

.03407 

.03528 

0 

1 

.02191 

.02240 

.02570 

.02637 

.02977 

.03009 

.03415 

.03530 

1 

2 

.02197 

.02247 

.02576 

.02644 

.02985 

.03076 

.03422 

.03541 

2 

3 

.02203 

.02253 

.02583 

.02651 

.02992 

.03084 

.03430 

.03552 

3 

4 

.02210 

.02259 

.02589 

.02658 

.02999 

.03091 

.03438 

.03560 

4 

5 

.02216 

.02266 

.02596 

.02665 

.03006 

.03099  i 

.03445 

.03508 

5 

6 

.02222 

.02272 

.02602 

.02672 

.03013 

.03106  i 

.03453 

.03576 

6 

7 

.02228 

.02279 

.02609 

.02679 

.03020 

.03114 

.03400 

.03584 

7 

8 

.02234 

.02285 

.02616 

.C2G86 

.03027 

.03121 

.03408 

.03592 

8 

9 

.02240 

.02291 

.02622 

.02693 

.03034 

.03129 

.03476 

.03601 

9 

10 

.02246 

.02298 

.02629 

.02700 

.03041 

.03137 

.03483 

.03009 

10 

11 

.02252 

.02304 

.02635 

.02707 

.03048 

.03144 

.03491 

.03017 

11 

12 

.02258 

.02311 

.02042 

.02714 

.03055 

.03152  j 

.03498 

.03025 

12 

13 

.02205 

.02317 

.02649 

.02721 

.03063 

.03159 

.03506 

.03033 

13 

14 

.02271 

.02323 

.02655 

.02728 

.03070 

.03167 

.0-3514 

.03042 

14 

15 

.02277 

.02330 

.02662 

.02735 

.03077 

.03175 

.03521 

.03050 

15 

16 

.02283 

.02336 

.02669 

.02742 

.03084 

.03182 

.03529 

.03058 

16 

17 

.02289 

.02343 

.02675 

.02749 

.03091 

.03190 

.03537 

.03666 

17 

18 

.02295 

.02349 

.02682 

.02756 

.03098 

.03198 

.03544 

.03674 

18 

19 

.02302 

.02356 

.02689 

.02763 

.03106 

.03205 

.03552 

.03083 

19 

20 

.02308 

.02362 

.02696 

.02770 

.03113 

.03213 

.03560 

.03091 

20 

21 

.02314 

.02369 

.02702 

.02777 

.03120 

.03221 

.03567 

.03099 

21 

22 

.02320 

.02375 

.02709 

.02784 

.03127 

.03228 

.03575 

.03708 

22 

23 

.02327 

.02382 

.02716 

.02791 

.03134 

.03236 

.03583 

.03716 

23 

24 

.02333 

.02388 

.02722 

.02799 

.03142 

.03244 

.03590 

.03724 

24 

25 

.02339 

.02395 

.02729 

.02806 

.03149 

.03251 

.03598 

.03732 

25 

26 

.02345 

.03402 

.02736 

.02813 

.03156 

.03259 

.03006 

.03741 

26 

27 

.02352 

.02408 

.02743 

.02820 

.03163 

.03267 

.03614 

.03749 

27 

28 

.02358 

.02415 

.02749 

.02827 

.03171 

.03275 

.03621 

.03758 

28 

29 

.02364 

.02421 

.02756 

.02834 

.03178 

.03282 

.03629 

.03766 

29 

30 

.02370 

.02428 

.02763 

.02842 

.03185 

.03290 

.03037 

.03774 

30 

31 

.02377 

.02435 

.02770 

.02849 

.03193 

,03298 

.03645 

.03783 

31 

32 

.02383 

.02441 

.02777 

.02856 

.03200 

.03306 

.03053 

.03791 

32 

33 

.02389 

.02448 

.02783 

.02803 

.03207 

.03313 

.03000 

.03799 

33 

34 

.02396 

.02454 

.02790 

.02870 

.03214 

.03321 

.03008 

.03808 

34 

S5 

.02402 

.02461 

.02797 

.02878 

.03222 

.03329 

.03676 

.03816 

35 

36 

.02408 

.02468 

.02804 

.02885 

.03229 

.03337 

.03684 

.03825 

36 

37 

.02415 

.02474 

.02811 

.02892 

.03236 

.03345 

.03692 

.03833 

37 

38 

.02421 

.02481 

.02818 

.02899 

.03244 

.03353 

.03099 

.03842 

38 

39 

.02427 

.02488 

.02824 

.02907 

.03251 

.03360 

.03707 

.08850 

by 

40 

.02434 

.02494 

.02831 

.02914 

.03258 

.03368 

.03715 

.03858 

40 

41 

.02440 

.02501 

.02838 

.02921 

.03266 

.03376 

.03723 

.03867 

41 

42 

.02447 

.02508 

.02845 

.02928 

.03273 

.03384 

.03731 

.03875 

42 

43 

.02453 

.02515 

.02852 

.02936 

.03281 

.03392 

.03739 

.03884 

43 

44 

.02459 

.02521 

.02859 

.02943 

.03288 

.03400 

.03747 

.03892 

44 

45 

.02466 

.02528 

.02866 

.02950 

.03295 

.03408 

.03754 

.03901 

45 

46 

.02472 

.02535 

.02873 

.02958 

.03303 

.03416 

.03702 

.03909 

46 

47 

.02479 

.02542 

.02880 

.02965 

.03310 

.03424 

.03770 

.03918 

47 

48 

.02485 

.02548 

.02887 

.02972 

.03318 

.03432 

.03778 

.03927 

48 

49 

.02492 

.02555 

.02894 

.02980 

.03325 

.03439 

.03786 

.03935 

49 

50 

.02498 

.02562 

.02900 

.02987 

.03333 

.03447 

.03794 

.03944 

50 

51 

.02504 

.02569 

.02907 

.02994 

.03340 

.03455 

.03802 

.03952 

51 

52 

.02511 

.02576 

.02914 

.03002 

.03347 

.03463 

.03810 

.03961 

52 

53 

.02517 

.02582 

.02921 

.03009 

.03355 

.03471 

.03818 

.03969 

53 

54 

.02524 

.02589 

.02928 

.03017 

.03362 

.03479 

.03826 

.03978 

54 

55 

.02530 

.02596 

.02935 

.03024 

.03370 

.03487 

.03834 

.03987 

55 

56 

.02537 

.02603 

.02942 

.03032 

.03377 

.03495 

.03842 

.03995 

56 

57 

.02543 

.02610 

.02949 

.03039 

.03385 

.03503 

.03850 

.04004 

57 

58 

.02550 

.02617 

.02956 

.03046 

.03392 

.03512 

.03858 

.04013 

58 

59 

.02556 

.02624 

.02963 

.03054 

.03400 

.03520 

.03806 

.04021 

59 

60 

.02563 

.02030 

.02970 

.03061 

.03107 

.03528 

.03874 

.04030 

60 

TABLE     XVII.— NATURAL  VERSED  SINES    AND  EXTERNAL    SECANTS, 


16 

0 

M 

1 

18 

t° 

li 

>° 

Vers.  ; 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

| 

0 

.03874 

.04030  : 

.04370 

.04569 

.04894 

.05146 

.05448 

.05762 

0 

1 

.03882 

.04039 

.04378 

.04578 

.04903 

.05156 

.05458 

.05773 

1 

2 

.03890 

.04047 

.04387 

.04588 

.04912 

.05166 

.05467 

.05783 

2 

3 

.03898 

.04056 

.04395 

.04597 

.04921 

.05176 

.05477 

.05794 

3 

4 

.03906 

.04065 

.04404 

.04600 

.04930 

.05186 

.05486 

.05805 

4 

5 

.03914 

.04073 

.04412 

.04616 

.04939 

.05196 

.05496 

.05815 

5 

6 

.03922 

.04082 

.04421 

.04625 

.04948 

.05206 

.05505 

.05826 

6 

7 

.03930 

.04091 

.04429 

.04635 

.04957 

.05216 

.05515 

.05836 

7 

8 

.03938 

.04100 

.04438 

.04644 

.04907 

.05226 

.05524 

.05847 

8 

9 

.03946 

.04108 

.04446 

.04653 

.04976 

.05S36 

.05534 

.05858 

9 

10 

.03954 

.04117 

.04455 

.04663 

.04985 

.05246 

.05543 

.05869 

10 

11 

.03963 

.04126 

.04464 

.04672 

.04994 

.05256 

.05553 

.05879 

11 

12 

.03971 

.04135 

.04472 

.04682 

.05003 

.05266 

.05562 

.05890 

12 

13 

.03979 

.04144 

.04481 

.04691 

.05012 

.05276 

.05572 

.05901 

13 

14 

.03987 

.04152 

.04489 

.047'00 

.05021 

.05286 

.05582 

.05911 

14 

15 

.03995 

.04161 

.04498 

.04710 

.05030 

.05297 

.05591 

.05922 

15 

1G 

.04003 

.04170 

.04507 

.04719 

.05039 

.05307 

.05601 

.05933 

16 

17 

.04011 

.04179 

.04515 

.04729 

.05048 

.05317 

.05610 

.05944 

17 

18 

.04019 

.04188 

.04524 

.04738 

.05057 

.05327 

.05620 

.05955 

18 

19 

.04028 

.04197 

.04533 

.04748 

.05067 

.05,337 

.05630 

.05965 

19 

20 

.04036 

.04206 

.04541 

.04757 

.05076 

.05347 

.05639 

.05976 

20 

21 

.04044 

.04214 

.04550 

.04767 

.05085 

.05357 

.05649 

.05987 

21 

22 

.04052 

.04223 

.04559 

.04776 

.05094 

.05367 

.05658 

.05998 

22 

23 

.04060 

.04232 

.04567 

.04786 

.05103 

.05378  ! 

.05668 

.06009 

23 

21 

.04069 

.04241 

.04576 

.04795 

.05112 

.05388  ! 

.05678 

.06020 

24 

25 

.04077 

.04250 

.04585 

.04805 

.05122 

.05398  ! 

.05687 

.06030 

25 

26 

.04085 

.04259 

.04593 

.04815 

.05131 

.05408  i 

.05697 

.06041 

26 

27 

.04093 

.04268 

.04602 

.04824 

.05140 

.05418  i 

.05707 

.06052 

27 

28 

.04102 

.04277 

.04611 

.04834 

.05149 

.05429  ! 

.C5716 

.06063 

28 

.04110 

.04286 

.04620 

.04843 

.05158 

.05439 

.05726 

.06074 

29 

30 

.04118 

.04295 

.04628 

.04853 

.05168 

.05449 

.05736 

.06085 

30 

31 

.04126 

.04304 

.04637 

.04863 

.05177 

.05460  ! 

.05746 

.06096 

31 

32 

.04135 

.04313 

.04646 

.04872 

.05186 

.05470  ! 

.05755 

.06107 

32 

33 

.04143 

.04322 

.04655 

.04882 

.05195 

.05480 

.05765 

.06118 

33 

34 

.04151 

.04331 

.04663 

.04891 

.05205 

.05490  j 

.05775 

.06129 

34 

35 

.04159 

.04340 

.04672 

.04901 

.05214 

.05501 

.05785 

.06140 

35 

36 

.04168 

.04349  ! 

.04681 

.04911 

.05223 

.05511  | 

.05794 

.06151 

36 

37 

.04176 

.04358  1 

.04690 

.04920 

.05232 

.05521 

.05804 

.06162 

37 

38 

.04184 

.04367 

.04609 

.04930 

.05242 

.05532 

.05814 

.06173 

38 

39 

.04193 

.04376  : 

.04707 

.04940 

.05251 

.(5542 

.05824 

.06184 

39 

40 

.04201 

.04385 

.04716 

.0495J 

.05260 

.05552 

.05833 

.06195 

40 

41 

.04209 

.04394 

.04725 

.04959 

.05270 

.05563 

.05843 

.06206 

41 

42 

.04218 

.04403 

.04734 

.04969 

.05279 

.0557'3  ; 

.05853 

.06217 

42 

43 

.04226 

.04413 

.04743 

.0497-9 

.05288 

.05584 

.05863 

.06228 

43 

44 

.04234 

.04422 

.04752 

.04989 

.05298 

.05594 

.05873 

.06239 

44 

45 

.04243 

.04431 

.04760 

.04998 

.05307 

.05604 

.05882 

.06250 

45 

46 

.04251 

.04440 

.04769 

.05008 

.05316 

.05615 

.05892 

.06261 

46 

47 

.04260 

.04449 

.04778 

.05018 

.05326 

.05625 

.05902 

.06272 

47 

48 

.04268 

.04458 

.04787 

.05028 

.05335 

.05636  j 

.05912 

.06283 

48 

49 

.04276 

.04468 

.04796 

.05038 

.05344 

.05646 

.05922 

.06295 

49 

50 

.04285 

.04477 

.04805 

.05047 

.05354 

.05657  | 

.05932 

.06306 

50 

51 

.04293 

.04486 

.04814 

.05057 

.05363 

.05667 

.05942 

.06317 

51 

52 

.04302 

.04495 

.04823 

.05067 

.05373 

.05678 

.05951 

.06328 

52 

53 

.04310 

.04504 

.04832 

.05077 

.05382 

.05688 

.05961 

.06339 

53 

54 

.04319 

.04514 

.04841 

.05087 

.05391 

.05699 

.05971 

.06350 

54 

55 

.04327 

.04523 

.04850 

.05097 

.05401 

.05709 

.05981 

.06362 

55 

56 

.04336 

.04532 

.04858 

.05107 

.05410 

.05720 

.05991 

.06373 

56 

57 

.04344 

.04541 

.04867 

.05116 

.05420 

.05730 

.06001 

.06384 

57 

58 

.041353 

.04551 

.04876 

.05126 

.05429 

.05741 

.06011 

.06895 

58 

59 

.04361 

.04560 

.04885 

.05136 

.05439 

.05751 

.06021 

.06407 

59 

60 

.04370 

.04569 

.04894 

.05146 

.05448 

.05762 

.06031 

.06418 

60 

251 


TABLE    XVII.—  NATURAL  VERSED    SINES  AND  EXTERNAL    SECANTS, 


/ 

20° 

21° 

22° 

23° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.06031 

.06418 

.06042 

.07115 

.07282 

.07853 

.07950 

.08636 

0 

1 

.06041 

.06429 

.06652 

.07126 

.07293 

.07866 

.07961 

.08649 

1 

2 

.06051 

.06440 

.06663 

.07138 

.07303 

.07879 

.07972 

.08663 

2 

3 

.06061 

.06452 

.06673 

.07150 

.07314 

.07892 

.07984 

.08676 

3 

4 

.06071 

.06463 

.06684 

.07162 

.07325 

.07904 

.07995 

.08090 

4 

5 

.06081 

.06474 

.06694 

.07174 

.07336 

.07917 

.08006 

.08703 

5 

6 

.06091 

.06486 

.06705 

.07186 

.07347 

.07930 

.08018 

.08717 

6 

7 

.06101 

.06497 

.06715 

.07199 

.07358 

.07943 

.08029 

.08730 

7 

8 

.06111 

.06508 

.00726 

.07211 

.07369 

.07955 

.08041 

.08744 

8 

9 

.06121 

.06520 

.00736 

.07-<23 

.07380 

.07968 

.08052 

.08757 

9 

10 

.06131 

.06531 

.00747 

.07235 

.07391 

.07981 

.08004 

.08771 

10 

11 

.06141 

.06542 

.06757 

.07247 

.07402 

.07094 

.08075 

.08784 

11 

12 

.06151 

.06554 

.06768 

.07259 

.07413 

.08006 

.08080 

.08798 

12 

13 

.06161 

.06565 

.0677'8 

.07271 

.07424 

.08019 

.08098 

.08811 

13 

14 

.06171 

.06577 

.06789 

.07283 

.07435 

.08032 

.08109 

.08825 

14 

15 

.06181 

.06588 

.06799 

.07295 

.07446 

.08045 

.08121 

.08839 

15 

16 

.06191 

.00600 

.06810 

.07307 

.07457 

.08058 

.08132 

.08852 

16 

17 

.06201 

.06611 

.06820 

.07320 

.07468 

.08071 

.08144 

.08866 

17 

18 

.06211 

.06622 

.06831 

.07332 

.07479 

.08084 

.08155 

.08880 

18 

19 

.06221 

.06634 

.06841 

.07344 

.07490 

.08097 

.08167 

.08893 

19 

20 

.06231 

.06645 

.06852 

.07356 

.07501 

.08109 

.08178 

.08907 

20 

21 

.00241 

.06657 

.06863 

.07368 

.07512 

.08122 

.08190 

.08921 

21 

22 

.06252 

.06668 

.06873 

.07380 

.07523 

.08135 

.08201 

.08934 

22 

23 

.06262 

.06680 

.06884 

.07393 

.07534 

.08148 

.08213 

.08948 

23 

24 

.06272 

.06691 

.06894 

.07405 

.07545 

.08161 

.08225 

.08962 

24 

25 

.06282 

.05703 

.06905 

.07417 

.07556 

.08174 

.08236 

.08975 

25 

26 

.06292 

.06715 

.06916 

.07429 

.07568 

.08187 

.08248 

.08989 

26 

27 

.06302 

.06726 

.06926 

.07442 

.07579 

.08200 

.08259 

.09003 

27 

28 

.06312 

.06738 

.06937 

.07454 

.07590 

.08213 

.08271 

.09017 

23 

29 

.06323 

.06749 

.06948 

.07466 

.07601 

.08226 

.08282 

.09030 

20 

80 

.06333 

.00761 

.06958 

.07479 

.07612 

.08239 

.08294 

.09044 

30 

31 

.06343 

.00773 

.06969 

.07491 

.07623 

.08252 

.08306 

.09058 

SI 

32 

.06353 

.06784 

.06980 

.07503 

.07634 

.08265 

.08317 

.09072 

32 

as 

.06363 

.06796 

.06990 

.07516 

.07645 

.08278 

.08329 

.09086 

33 

34 

.06374 

.06807 

.07001 

.07528 

.07657 

.08291 

.08340 

.09099 

34 

35 

.06384 

.06819 

.07012 

.07540 

.07668 

.08305 

.08352 

.09113 

35 

36 

.06394 

.06831 

.07022 

.07553 

.07679 

.08318 

.08364 

.09127 

33 

37 

.06404 

.06843 

.07033 

.07565 

.07690 

.08331 

.08375 

.09141 

37 

38 

.06415 

.06854 

.07044 

.07578 

.07701 

.08344, 

.08387 

.09155 

38 

39 

.06425 

.06866 

.0?'055 

.07590 

.07713 

.08357 

.08399 

.09169 

39 

40 

.06435 

.06878 

.07065 

.07002 

.07724 

.08370 

.08410 

.09183 

40 

41 

.06445 

.06889 

.07076 

.07615 

.07735 

.08383 

.08422 

.09197 

41 

42 

.06456 

.06901 

.07087 

.07627 

.07746 

.08397 

.084:34 

.09211 

42 

43 

.06466 

.06913 

.07098 

.07640 

.07757 

.08410 

.08445 

.09224 

43 

44 

.06476 

.06925 

.07108 

.07652 

.07769 

.08423 

.08457 

.09238 

44 

45 

.06488 

.06936 

.07119 

.07665 

.07780 

.08430 

.08469 

.09252 

45 

46 

.06497 

.06948 

.07130 

.07677 

.07791 

.08449 

.08481 

.09266 

46 

47 

.06507 

.06960 

.07141 

.07690 

.07802 

.08403 

.08492 

.09280 

47 

48 

.06517 

.06972 

.07151 

.07702 

.07814 

.08476 

.08504 

.09294 

48 

49 

.06528 

.06984 

.07162 

.07715 

.07825 

.08489 

.08516 

.09308 

49 

50 

.06538 

.06995 

.07173 

.07727 

.07836 

.08503 

.08528 

.09323 

50 

51 

.06548 

.07007 

.07184 

.07740 

.07848 

.08516 

.08539 

.09337 

51 

52 

.06559 

.07019 

.07195 

.07752 

.07859 

.08529 

.08551 

.09351 

52 

53 

.06569 

.07031 

.07206 

.07765 

.07870 

.08542 

.08563 

.09365 

53 

54 

.06580 

.07043 

.07216 

.07778 

.07881 

.08556 

.08575 

.09379 

54 

55 

.06590 

.07055 

07227 

.07790 

.07893 

.08569 

.08586 

.09393 

.55 

56 

.06600 

.07067 

!  07238 

.07803 

.07904 

.08582 

.08598 

.09407 

56 

57 

.06611 

.07079 

.07249 

.07816 

.07915 

.08596 

.08610 

.09421 

57 

58 

.06621 

.07091 

.07260 

.07828 

.07927 

.08609 

.08622 

.09435 

58 

59 

.06632 

.07103 

.07271 

.07841 

.07938 

.08023 

.08634 

.09449 

59 

60 

.06642 

.07115 

.07282 

.07853 

.0795J 

.08636 

.08645 

.09464 

60 

262 


TABLE     XVIL—  NATURAL  VERSED    SINES    AND  EXTERNAL   SECANTS. 


21° 

25° 

26° 

27° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.08645 

.09464 

.09369 

.10338 

.10121 

.11260 

.10899 

.12233 

0 

1 

.08657 

.09478 

.09382 

.10353 

.10133 

.11276 

.10913 

.12249 

1 

2 

.08669 

.09492 

.09394 

.  10368 

.  10146 

.11292 

.10926 

.12266 

2 

3 

.08681 

.09506 

.09406 

.10383 

.10159 

.11308 

.10939 

.12283 

3 

4 

.08693 

.09520 

.09418 

.10398 

.10172 

.11323 

.10952 

.12291) 

4 

5 

.08705 

.09535 

.09431 

.10413 

.10184 

.11339 

.10965 

.12316 

5 

6 

.08717 

.09549 

.09443 

.10428 

.10197 

.11355 

.10979 

.12333 

6 

7 

.08728 

.09563 

.09455 

.10443 

.10210 

.11371 

.10992 

.12349 

7 

8 

.08740 

.09577 

.09468 

.10458  1 

.10223 

.11387 

.11005 

.12366 

8 

9 

.08752 

.09592 

.09480 

.10473 

.10236 

.11403 

.11019 

.12383 

9 

10 

.08764 

.09606 

.09493 

.10488 

.10248 

.11419 

.11032 

.12400 

10 

11 

.08776 

.09620 

.09505 

.10503 

.10261 

.11435 

.11045 

.12416 

11 

12 

.0878,8 

.09635 

.09517 

.10518 

.10874 

.11451 

.11058 

.12433 

12 

13 

08800 

.09649 

.09530 

.10533 

.10287 

.11467 

.11072 

.12450 

13 

14 

!  08812 

.09663 

.09542 

.10549 

.10300 

.11483 

.11085 

.12467 

14 

15 

.08824 

.09678 

.09554 

.10564 

.10313 

.11499 

.11098 

.12484 

15 

16 

.08836 

.09692 

.09567 

.10579 

.10326 

.11515 

.11112 

.12501 

16 

17 

.08848 

.09707 

.09579 

.10594 

.10338 

.11531 

.11125 

.12518 

17 

18 

.08860 

.09721 

.09592 

.10609 

.10351 

.11547 

.11138 

.12534 

18 

19 

.08872 

.09735 

.09604 

.10625 

.10304 

.11563 

.11152 

.12551 

19 

20 

.08884 

.09750 

.09617 

.10640 

.10377 

.11579 

.11165 

.12568 

20 

21 

.08896 

.09764 

.09629 

.10655 

.10390 

.11595 

.11178 

.12585 

2t 

22 

.08908 

.09779 

.09642 

.10670 

.10403 

.11611 

.11192 

.12602 

22 

23 

.08920 

.09793 

.09654 

.10686 

.10416 

.11627 

.11205 

.12619 

23 

24 

.08932 

.09808 

.09666 

.10701 

.10429 

.11643 

.11218 

.12636 

24 

25 

.08944 

.09822 

.09679 

.10716 

.10442 

.11659 

.11232 

.12653 

25 

26 

.08956 

.09837 

.09691 

.10731 

.10455 

.11675 

.11245 

.12670 

26 

27 

.08968 

.09851 

.09704 

.10747 

.10468 

.11691 

.11259 

.12687 

27 

28 

.08980 

.09866 

.09716 

.10762 

.10481 

.11708 

.11272 

.12704 

28 

29 

.08992 

.09880 

.09729 

.10777 

.10494 

.11724 

.11285 

.12721 

29 

30 

.09004 

.09895 

.09741 

.10793 

.10507 

.11740 

.11299 

.12738 

30 

31 

.09016 

.09909 

.09754 

.10808 

.10520 

.11756 

.11312 

.12755 

31 

32 

.09028 

.09924 

.09767 

.10824 

.10533 

.11772 

.11326 

.  12772 

32 

33 

.09040 

.09939 

.09779 

.10839 

.10546 

.11789 

.11339 

.12789 

33 

34 

.09052 

.09953 

.09792 

.10854 

.10559 

.11805 

.11353 

.12807 

34 

25 

.09004 

.09968 

.09804 

.10870 

.10572 

.11821 

.11366 

.12824 

35 

26 

.09076 

.09982 

.09817 

.10885 

.10585 

.11838 

.11380 

.12841 

36 

37 

.09089 

.09997 

.09829 

.10901 

.10598 

.11854 

.11393 

.12858 

37 

38 

.09101 

.10012 

.09842 

.10916 

.10611 

.11870 

.11407 

.12875 

38 

89 

.09113 

.10026 

.09854 

.10932 

.10621 

.11886 

.11420 

.12892 

39 

40 

.C9125 

.10041 

.09807 

.10947 

.10637 

.11903 

.11434 

.12910 

40 

41 

.09137 

.10055 

.09880 

.10963 

.10650 

.11919 

.11447 

.12927 

41 

43 

.09149 

.10071 

.09892 

.10978 

.10663 

.11036 

.11461 

.12944 

42 

43 

.09161 

.10085 

.09905 

.10994 

.10676 

.11952 

.11474 

.12961 

43 

44 

.09174 

.10100 

.09918 

.11009 

.10689 

.11968 

.11488 

.12979 

44 

45 

.09186 

.10115 

.09930 

.11025 

.10702 

.11985 

.11501 

.12996 

45 

46 

.09198 

.10130 

.C9943 

.11041 

.10715 

.12001 

.11515 

.13013 

46 

47 

.09210 

.10144 

.09955 

.11056 

.10723 

.12018 

.11528 

.13031 

47 

48 

.09222 

.10159 

.09968 

.11072 

.10741 

.12034 

.11542 

.13048 

48 

49 

.09234 

.10174 

.09981 

.11087 

.10755 

.12051 

.11555 

.13065 

49 

50 

.09247 

.10189 

.09993 

.11103 

.10708 

.12067 

.11569 

.13083 

50 

51 

.09259 

.10204 

.10006 

.11119 

.10781 

.12084 

.11583 

.13100 

51 

53 

.09271 

.10218 

.10019 

.11134 

.10794 

.1*3100 

.11596 

.13117 

52 

53 

.09283 

.10233 

.10032 

.11150 

.10807 

.12117 

.11610 

.13135 

53 

54 

.09296 

.10248 

.10044 

.11166 

.10820 

.12133 

.11623 

.13152 

54 

55 

.09308 

.10263 

.10057 

.11181 

.10833 

.12150 

.11637 

.13170 

55 

56 

.09320 

.10278 

.  10070 

.11197 

.10847 

.12166 

.11651 

.13187 

56 

57 

.09332 

.10293 

.10082 

.11213 

.10860 

.12183 

.11664 

.13205 

57 

58 

.09345 

.10308 

.10095 

.11229 

.10873 

.12199 

.11678 

.13222 

58 

59 

.09357 

.10323 

.10108 

.11244 

.10886 

.12216 

.11692 

.13240 

59 

60 

.093(59 

.10338 

.10121 

.11260 

.10899 

.12233 

.11705 

.13257 

60 

253 


XVII.-NATURAL   VERSED    SINES    AND  EXTERNAL  SECANTS. 


28° 

29° 

30° 

31° 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.11705 

.13257 

.12538 

.14335 

.13397 

.15470 

.14283 

.16663 

0 

1 

.11719 

.13275 

.12552 

.14354 

.13412 

.15489 

.14298 

.16084 

1 

2 

.11733 

.13292 

.12566 

.14372 

.13427 

.15509 

.14313 

.16704 

2 

ft 

.11746 

.13310 

.12580 

.14391 

.13441 

.15528 

.14328 

.16725 

3 

4 

.11760 

.1,3327 

.12595 

.14409 

'  .13456 

.15548 

.14343 

.16745 

4 

5 

.11774 

.13345 

.12609 

.14428 

.1347'0 

.  15567 

.14358 

.16706 

5 

6 

.11787 

.13362 

.12623 

.14446 

.13485 

.15587 

.14373 

.16786 

6 

7 

.11801 

.13380 

.12637 

.14465 

.13499 

.15006 

.14388 

.16806 

7 

8 

.11815 

.13398 

.12651 

.14483 

.13514 

.15626 

.14403 

.16827 

8 

9 

.11828 

.13415 

.12665 

.14502 

.13529 

.15645 

.14418 

.16848 

9 

10 

.11842 

.13433 

.12679 

.14521 

.13543 

.15665 

.14433 

.16868 

10 

11 

.11856 

.13451 

.12694 

.14539 

.13558 

.15684 

.14449 

.16889 

11 

12 

.11870 

.13468 

.12708 

.14558 

.13573 

.15704 

.14464 

.10909 

12 

13 

.11888 

.13486 

.12722 

.14576 

.13587 

.15724 

.14479 

.10930 

13 

14 

.11897 

.13504 

.12736 

.14595 

.13602 

.15743 

.14494 

.10950 

14 

15 

.11911 

.13521 

.12750 

.14614 

.13016 

.15763 

.14509 

.16971 

15 

16 

.11925 

.13539 

.12765 

.14632 

.13631 

.15782 

.14524 

.16992 

16 

17 

.11938 

.13557 

.12779 

.14651 

.13646 

.  15802 

.14539 

.17012 

17 

18 

.11952 

.13575 

.12793 

.14670 

.13660 

.15822 

.14554 

.17033 

18 

19 

.11966 

.13593 

.12807 

.14689 

.18675 

.15841 

.14569 

.17C54 

19 

20 

.11980 

.13610 

.12822 

.14707 

.13690 

.15801 

.14584 

.17075 

20 

21 

.11994 

.13628 

.12836 

.14726 

.13705 

.15881 

,  .14599 

.17095 

21 

22 

.12007 

.13646 

.12850 

.14745 

.13719 

.15901 

.14615 

.17116 

22 

23 

.12021 

.13664 

.12864 

.14764 

.13734 

.15920 

.14630 

.17137 

23 

24 

.12035 

.13682 

.12879 

.14782 

.13749 

.15940 

.14645 

.17158 

24 

25 

.12049 

.13700 

.12893 

.14801 

.13703 

.15960 

.14660 

.17178 

25 

26 

.12063 

.13718 

.12907 

.14820 

.13778 

.15980 

.14875 

.17199 

26 

27 

.12077 

.13735 

.12921 

.14839 

.13793 

.16000 

.14090 

.17220 

27 

28 

.12091 

.13753 

.12936 

.14858 

.13803 

.10019 

.14706 

.17241 

28 

09 

.12104 

.13771 

.12950 

.14877 

.13822 

.10039 

.14721 

.17262 

29 

30 

.12118 

.13789 

.12964 

.14896 

.13837 

.10059 

.14736 

.17283 

30 

31 

.12132 

.13807 

.12979 

.14914 

.13852 

.10079 

.14751 

.17304 

31 

32 

.12146 

.13825 

.12993 

.14933 

.13807 

.10099 

.14700 

.17325 

32 

33 

.12160 

.13843 

.13007 

.14952 

.13881 

.10119 

.14782 

.17346 

33 

31 

.12174 

.13861 

.13022 

.14971 

.13896 

.10139 

.14797 

.17367 

34 

35 

.12188 

.13879 

.13036 

.14990 

.13911 

.10159 

.14812 

.17388 

35 

88 

.12202 

.13897 

.13051 

.15009 

.13926 

.10179 

.14827 

.17409 

36 

87 

.12216 

.13916 

.13065 

.15028 

.13941 

.10199 

.14843 

.17430 

37 

33 

.12230 

.13934 

.13079 

.15047 

.13955 

.10219 

.14853 

.17451 

38 

£9 

.12244 

.13952 

.13094 

.15066 

.13970 

.10239 

.14873 

.17472 

39 

40 

.12257 

.13970 

.13108 

.15085 

.13985 

.10259 

.14888 

.17493 

40 

41 

.12271 

.13988 

.13123 

.15105 

.14000 

.10279 

.14904 

.17514 

41 

42 

.12285 

.14006 

.13137 

.15124 

.14015 

.10209 

.14919 

.17535 

42 

43 

.12299 

.14024 

.13151 

.15143 

.14030 

.10319 

.14934 

.17556 

43 

44 

.12313 

.14042 

.13166 

.15162 

.14044 

.10339 

.14949 

.17577 

44 

45 

.12327 

.14061 

.13180 

.15181 

.14059 

.16359 

.14905 

.17598 

45 

46 

.12341 

.14079 

.13195 

.15200 

.14074 

.16380 

.14960 

.17620 

46 

47 

.12355 

.14097 

.13209 

.15219 

.14089 

.10400 

.14995 

.17641 

47 

48 

.12369 

.14115 

.13223 

.15239 

.14104 

.10420 

.15011 

.17062 

43 

49 

.12383 

.14134 

.13238 

.15258 

.14119 

.10440 

.15025 

.17083 

43 

50 

.12397 

.14152 

.13252 

.15277 

.14134 

.16460 

.15041 

.17704 

50 

51 

.12411 

.14170 

.13267 

.15296 

.14149 

.16481 

.15057 

.17726 

51 

52 

.12425 

.14188 

.13281 

.15315 

.14164 

.16501 

.15072 

.17747 

52 

53 

.12439 

.14207 

.13296 

.15335 

.14179 

.16521 

.15087 

.17768 

53 

54 

.12454 

.14225 

.13310 

.15354 

.  .14194 

.16541 

.15103 

.17790 

54 

55 

.12468 

.14243 

.1-3325 

.15373 

.14208 

.16562 

.15118 

.17811 

55 

56 

.12482 

.14262 

.13339 

.15393 

.14223 

.16582 

.15134 

.17832 

56 

57 

.12496 

.14280 

.1.3354 

.15412 

.14238 

.16602 

.15149 

.17854 

57 

58 

.12510 

.14299 

.13368 

.15431 

.14253 

.16623 

.15164 

.17875 

58 

59 

.12524 

.14317 

.13383 

.15451 

.14268 

.  16643 

.15180 

.17896 

59 

60 

.12538 

.14335 

.13397 

.15470 

.14283 

.16663 

.15195 

.17918 

60 

254 


TABLE    XVII.— NATURAL  VERSED   SINES   AND   EXTERNAL  SECANTS. 


32° 

33° 

34° 

35° 

/ 

Vers. 

Ex.  sec 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec 

Vers. 

Ex.  sec 

0 

.15195 

.17918 

.16133 

.19236 

.17096 

.20622 

.18085 

.22077 

~o" 

1 

.15211 

.17939 

.16149 

.19259 

.17113 

.20645 

.18101 

.22102 

1 

2 

.  15226 

.17961 

.16165 

.19281 

.17129 

.20669 

.18118 

.22127 

2 

3 

.15241 

.17982 

.16181 

.19304 

.17145 

.20693 

.18135 

.22152 

3 

4 

.  15257 

.18004 

.16196 

.19327 

.17161 

.20717 

.18152 

.22177 

4 

5 

.15272 

.18025 

.16212 

.19349 

.17178 

.20740 

.18168 

.22202 

5 

6 

.  15288 

.18047 

.16228 

.19372 

.17194 

.20764 

.18185 

.22227 

6 

7 

.  15303 

.18068 

.16244 

.19394 

.17210 

.20788 

.18202 

.22252 

7 

8 

.15319 

.18090 

.16260 

.19417 

.17227 

.20812 

.18218 

.22277 

8 

9 

.15334 

.18111 

.16276 

.19440 

.17243 

.20836 

.18235 

.22302 

9 

10 

.15350 

.18133 

.16292 

.19463 

.17259 

.20859 

.18252 

.22327 

10 

11 

.15365 

.18155 

.16308 

.194a5 

.17276 

.20883 

.18269 

.22352 

11 

12 

.15381 

.18176 

.16324 

.19508 

.17292 

.20907 

.18286 

.22377 

12 

13 

.15396 

.18198 

.16340 

.19531 

.17308 

.20931 

.18302 

.22402 

13 

14 

.15413 

.18220 

.16355 

.19554 

.17325 

.20955 

.18319 

.22428 

14 

15 

.15427 

.18241 

.16371 

.19576 

.17341 

.20979 

.18336 

.22453 

15 

16 

.15443   .18263 

.16387 

.19599 

.17357 

.21003 

.18353 

.2247'8 

16 

17 

.15458   .18285 

.16403 

.19622 

.17374 

.21027 

.18369 

.22503 

17 

18 

.15174 

.18307 

.16419 

.19645 

.17390 

.21051 

.18386 

.22528 

18 

19 

.15489 

.18328 

.16435 

.19668 

.17407 

.21075 

.18403 

.22554 

19 

20 

.15505 

.18350 

.16451 

.19691 

.17423 

.21099 

.18420 

.22579 

20 

21 

.15520 

.18372 

.16467 

.19713 

.17439 

.21123 

.18437 

.22604 

21 

22 

.15536 

.18394 

.16483 

.19786 

.17456 

.21147 

.18454 

.22629 

22 

23 

.15552 

.  18416 

.16499 

.19759 

.17472 

.21171 

.18470 

.22655 

23 

24 

.15567 

.18437 

.16515 

.19782 

.17489 

.21195 

.18487 

.22680 

24 

25 

.15583 

.18459 

.16531 

.19805 

.17505 

.21220 

.18504 

.22706 

25 

26 

.15598 

.18481 

.16547 

.19828 

.17522 

.21244 

.18521 

.22731 

26 

27 

.15614 

.18503 

.16563 

.19851 

.17533 

.21268 

.18538 

.22756 

27 

28 

.15630 

.18525 

.16579 

.19874 

.17554 

.21292 

.18555   .22782 

28 

29 

.15645 

.18547 

.16595 

.19897 

.17571 

.21316 

.18572  !  .22807 

29 

30 

.15661 

.18569 

.16611 

.19920 

.17587 

.21341 

.18588 

.22833 

30 

31 

.15676 

.18591 

.16627 

.19944 

.17604 

.21365 

.18605 

.22858 

31 

32 

.15692 

.18613 

.16644 

.19967 

.17620 

.21389 

.18622 

.22884 

32 

33 

.15708 

.18635 

.16660 

.19990 

.17037 

.21414 

.18639 

.22909 

33 

34 

.157S3 

.18657 

.16676 

.20013 

.17653 

.21438 

.18656 

.22935 

34 

35 

.J573U 

.18679 

.16692   .20036 

.17670 

.21462 

.18673 

.22960 

35 

36 

.15755 

.18701 

.16708 

.20059 

.17686 

.21487 

.18690 

.22986 

36 

37 

.15770 

.18723 

.16724 

.20083 

.17703 

.21511 

.18707 

.23012 

37 

38 

.15786 

.18745 

.16740  j  .20106 

.17719 

.21535 

.18724 

.23037 

38 

39 

.15802 

.18767 

.16756 

.20129 

.17736 

.21560 

.18741 

.23003 

39 

40 

.15818 

.18790 

.16772 

.20152 

.17752 

.21584 

.18758 

.23089 

40 

41 

.15833 

.18812 

.16788 

.20176 

.17709 

.21609 

.18775 

.23114 

41 

42 

.15849 

.18834 

.16805 

.20193 

.17736 

.21033 

.18792 

.23140 

42 

43 

.15865 

.18856 

.16821 

.20222 

.17802 

.21658 

.18809 

.213166 

43 

44 

.15880 

.18878 

.16837 

.20246 

.17819 

.21682 

.18826 

.23192 

44 

45 

.15898 

.18901 

.16853 

.20269 

.  17cf<35 

.21707 

.18843 

.23217 

45 

46 

.15912 

.18923 

.16869 

.20292 

.17852 

.21731 

.18860 

.23243 

46 

47 

.15923 

.18945 

.16885 

.2C316 

.17808 

.21756 

.18877 

.23269 

47 

48 

.15943 

.18967 

.16902 

.20339 

.17885 

.21781 

.18894 

.23295 

48 

49 

.15959 

.18990 

.16918 

.20363 

.17902 

.21805 

.18911 

.23321 

49 

50 

.15975 

.19012 

.16934 

.20386 

.17918 

.21830 

.18928 

.23347 

50 

51 

.15991 

.19034 

.16950 

.20410 

.17935 

.21855 

.18945 

.23373 

51 

52 

.16006 

.19057 

.16906 

.20433 

.17952 

.21879 

.18962 

.23399 

52 

53 

.  16022 

.19079 

.16983 

.20457 

.17968 

.21904 

.18979 

.23424 

53 

54 

.16038 

.19102 

.16909 

.20480 

.17985 

.21929 

.18996 

.23450 

54 

55 

.16054 

.19124 

.17015 

.20501 

.18001 

.21953 

.19013 

.23476 

55 

56 

.16070 

.19146 

.17031 

.20527 

.18018 

.21978 

.19030 

.23502 

56 

57 

.16085 

.19169 

.17047 

.20551 

.18035 

.22003 

.19047 

.23529 

57 

58 

.16101 

.19191 

.17064 

.20575 

.18051 

.22028 

.19064 

.23555 

58 

59 

.16117 

.19214 

.17080 

.20598 

.18068 

.22053 

.19081 

.23581 

59 

60 

.16133 

.19236 

.17096 

.20622 

.18085 

.22077 

.19098 

.23607 

60 

255 


TABLE     XVII— NATURAL  VERSED   SINES   AND   EXTERNAL   SECANTS. 


1 

36° 

37° 

38° 

33° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.19098 

.23607 

.201S6 

.25214 

.21199 

.20902 

.22285 

.28676 

0 

1 

.19115 

.23633 

.20154 

.25241 

.21217 

.26931 

.22304 

.28706 

1 

2 

.19133 

.23659 

.20171 

.25269 

.21235 

.26960 

.22322 

.28737 

2 

3 

.19150 

.23685 

.20189 

.25296 

.21253 

.20988 

.22340 

.28767 

3 

4 

.19167 

.23711 

.20207 

.25324 

.21271 

.27017 

.22359 

.28797 

4 

5 

.19184 

.23738 

.20224 

.25351 

.21289 

.27040 

.22377 

.28828 

5 

6 

.19201 

.23764 

.20242 

.25379 

.21307 

.27075 

.22395 

.28858 

6 

7 

.19218 

.23790 

.20259 

.25406 

.21324 

.27104 

.22414 

.28889 

7 

*  8 

.19235 

.23816 

.20277 

.25434 

.21342 

.27133 

.22432 

.28919 

8 

9 

.19252 

.23843 

.20294 

.25402 

.21360 

.27102 

.22450 

.28950 

9 

10 

.19270 

.23869 

.20312 

.25489 

.21378 

.27191 

.22409 

.28980 

10 

11 

.19287 

.23895 

.20329 

.25517 

.21396 

27221 

.22487 

.29011 

11 

12 

.19304 

.23922 

.20347 

.25545 

.21414 

!  27250 

.22506 

.29042 

12 

13 

.19321 

.23948 

.20365 

.25572 

.21432 

.27279 

.22524 

.29072 

13 

14 

.19338 

.23975 

.20382 

.25600 

.21450 

.27308 

.22542 

.29103 

14 

15 

.19356 

.24301 

.20400 

.25628 

.21468 

.27337 

.22501 

.29133 

15 

1G 

.19373 

.24028 

.20417 

.25656 

.21486 

.27306 

.22579 

.29164 

16 

17 

.19390 

.24054 

.20435 

.25683 

.21504 

.27396 

.22598 

.29195 

17 

18 

.19407 

.24081 

.20453 

.25711 

21522 

.27425 

.22016 

.29226 

18 

19 

.19424 

.24107 

.20470 

.25739 

.'21540 

.27454 

.22634 

.29256 

19 

20 

.19442 

.24134 

.20488 

.25707 

.21558 

.27483 

.22653 

.29287 

20 

21 

.19459 

.24100 

.20506 

.25795 

.21576 

.27513 

.22671 

.29318 

21 

22 

.10476 

.24187 

.20523 

.25823 

.21595 

.27542 

.22090 

.29349 

22 

23 

.19493 

.24213 

.20541 

.25851 

.21013 

.27572 

.22708 

.29380 

23 

24 

.19511 

.24240 

.20559 

.25879 

.21031 

.27601 

.22727 

.29411 

24 

25 

.19528 

.24267 

.20576 

.25907 

.21649 

.27630 

.22745 

.29442 

25 

26 

.19545 

.24293 

.20594 

.25935 

.21667 

.27660 

.22764 

.2947'3 

20 

27 

.19562 

.24320 

.20612 

.25963 

.21685 

.27689 

.22782 

.29504 

27 

28 

.19580 

.24347 

.20029 

.25991 

.21703 

.27719 

.22801 

.29535 

28 

29 

.19597 

.24373 

.20647 

.20019 

.21721 

.27748 

.22819 

.29506 

20 

30 

.19614 

.24400 

.20665 

.26047 

.21739 

.27778 

.22838 

.29597 

30 

31 

.19632 

.24427 

.20082 

.26075 

.21757 

.27807 

.22856 

.29628 

31 

32 

.19649 

.24454 

.20700 

.26104 

.21775 

.27837 

.22875 

.29059 

32 

33 

.19666 

.24481 

.20718 

.20132 

.21794 

.27'8G7 

.22893 

.29690 

33 

34 

.1^684 

.24508 

.20736 

.20100 

.21812 

.27896 

.22912 

.29721 

34 

35 

.197'01 

.24534 

.20753 

.26188 

.21830 

.27926 

.22330 

.29752 

35 

30 

.19718 

.24561 

.20771 

.26216 

.21848 

.27956 

.22949 

.29784 

36 

37 

.19736 

.24588 

.20789 

.26245 

.21866 

.27985 

.22907 

.29815 

87 

38 

.19753 

.24615 

.20807 

.26273 

.21884 

.28015 

.22986 

.29846 

33 

39 

.19770 

.21642 

.20824 

.26301 

.21902 

.28045 

.23004 

.29877 

3!) 

40 

.19788 

.24609 

.20842 

.20330 

.21921 

.28075 

.23023 

.29909 

40 

41 

.19805 

.24696 

.20860 

.20358 

.21939 

.28105 

.23011 

.29940 

41 

42 

.19822 

.24723 

.20878 

.20387 

.21957 

.28134 

.230(50 

.29971 

42 

43 

.19840 

.24750 

.20895 

.20415 

.21975 

.28164 

.2307'9 

.30003 

43 

44 

.19857 

.24777 

.20913 

.20443 

.21993 

.28194 

.23097 

.30034 

44 

45 

.19875 

.24804 

.20931 

.20472 

.22012 

.28224 

.23116 

.30006 

45 

46 

.19892 

.24832 

.20949 

.26500 

.22030 

.28254 

.23134 

.30097 

46 

47 

.19909 

.24859 

.20967 

.26529 

.22048 

.28284 

.23153 

.30129 

47 

48 

.19927 

.24886 

.20985 

.26557 

.22066 

.28314 

.23172 

.30100 

48 

49 

.19944 

.24913 

.21002 

.26586 

.22084 

.28344 

.23190 

.30192 

49 

50 

.19962 

.24940 

.21020 

.26615 

.22103 

.28374 

.23209 

.30223 

50 

51 

.19979 

.24967 

.21038 

.20043 

.22121 

.28404 

.23228 

.30255 

51 

52 

.19997 

.24995 

.21056 

.20072 

.22139 

.28434 

.23246 

.30287 

52 

53 

.20014 

.25022 

.21074 

.20701 

.22157 

.28464 

.23205 

.30318 

53 

54 

.20032 

.25049 

.21092 

.20729 

.22176 

.28495 

.23283 

.30350 

54 

55 

.20049 

.25077 

.21109 

.20758 

.22194 

.28525 

.23302 

.30382 

55 

5G 

.20066 

.25104 

.21127 

.20787 

.22212 

.28555 

.23321 

.30413 

56 

57 

.20084 

.25131 

.21145 

.20815 

!  22231 

.28585 

.23339 

.30445 

57 

58 

.20101 

.25159 

.21163 

.26844 

.22249 

.28615 

.23358 

.30477 

58 

59 

.20119 

.25186 

.21181 

.20873 

.22267 

.28646  i 

.23377 

.30509 

5'J 

60 

.20136 

.25214  ! 

.21199 

.20902 

.22285 

.28076  ! 

.233% 

.30541 

60 

25G 


TABLE     XVII.— NATURAL  VERSED   SINES  AND   EXTERNAL   SECANTS. 


40° 

41° 

42° 

43° 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers.  Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.23396 

.30541 

.24529 

.32501 

.25686 

.34563 

.26865 

.36733 

0 

1 

.23414 

.30573 

.24548 

.32535 

.25705 

.34599 

.26884 

.36770 

1 

2 

.23433 

.30605 

.24567 

.32508 

.257-24 

.34634 

.20904 

.36807 

2 

3 

.23452 

.30636 

.24586 

.32002 

.25744 

.34669 

.26924 

.36844 

3 

4 

.23470 

.30668 

.24605 

.32636 

.25703 

.34704 

.26944 

.36881 

4 

5 

.23489 

.30700 

.24625 

.32609 

.25783 

.34740 

.20964 

.36919 

5 

6 

.23508 

.30732 

.24644 

.32703 

.25802 

.34775 

.26984 

.36956 

6 

7 

.23527 

.30764 

.24663 

.32737 

.25822 

.34811 

.27'004 

.36993 

7 

8 

.23545 

.30796 

.24682 

.32770 

.25841 

.34846 

.27024 

.37030 

8 

9 

.23564 

.30829 

.24701 

.32804 

.25801 

.34882 

.27043 

.37'068 

9 

10 

.23583 

.308G1 

.24720 

.32838 

.25880 

.34917 

.27003 

.37105 

10 

11 

.23602 

.30893 

.24739 

.32872 

.25900 

.84053 

.27083 

.37143 

11 

12 

.23620 

.30925 

.24759 

.32905 

.25920 

.34988 

.271C3 

.37180 

12 

13 

.23639 

.30957 

.2477'8 

.32939 

.25939 

.35024 

.27123 

.37218 

13 

14 

.23658 

.30989 

.24797 

.32973 

.25959 

.35060 

.27143 

.37255 

14 

15 

.23677 

.31022 

.24816 

-.33007 

.25978 

.£5095 

.27103 

.37293 

15 

16 

.23696 

.31054 

.248S5 

.33041 

.25998 

.35131 

.27183 

.37'330 

16 

17 

.23714 

.31086 

.24854 

.33075 

.26017 

.35167 

.27203 

.37368 

17 

18 

.23733 

.31119 

.24874 

.33109 

.26037 

.35203 

.27223 

.37406 

18 

19 

.23752 

.31151 

.24893 

.33143 

.26056 

.8.;2;:8 

.27243 

.37443 

19 

20 

.23771 

.31183 

.24912 

.33177 

.26076 

S5274 

.27263 

.37481 

20 

21 

.23790 

.81216 

.24931 

.33211 

.26096 

.35310 

.27283 

.37519 

21 

22 

.23808 

.31248 

.24950 

.33245 

.20115 

.35:346 

.27303 

.37556 

2:2 

23 

.23827 

.31281 

.24970 

.33279 

.20135 

.35382 

.27323 

.37'594 

2i 

24 

.23846 

.31313 

.24989 

.33314 

.26154 

.35418 

.27343 

.37'632 

24 

25 

.23865 

.31346 

.25008 

.33343 

.26174 

.35454 

.273C3 

.37070 

25 

26 

.23884 

.31373 

.25027 

.3a382 

.26104 

.35490 

.27383 

.377C8 

26 

27 

.23903 

.31411 

.25047 

.33416 

.26213 

.35526 

.27403 

.37746 

27 

28 

.23922 

.31443 

.25066 

.33451 

.26233 

.35502 

.27423 

.37784 

28 

29 

.23941 

.31476 

.25085 

.33485 

.26253 

.35598 

.27443 

.37822 

29 

30 

.23959 

.31509 

.25104 

.33519 

.26272 

.35634 

.27403 

.37860 

£0 

31 

.23978 

.81541 

.25124 

.33554 

.26202 

.35070 

.27483 

.37898 

31 

32 

.23997 

.31574 

.25143 

.33588 

.20312 

.357'07 

.27503 

.37936 

32 

33 

.24016 

.31607 

.251C3 

.33622 

.20381 

.35743 

.27523 

.37'974 

33 

34 

.24035 

.31040 

.25182 

.33C57 

.20351 

.35779 

.27543 

.38012 

34 

35 

.24054 

.31072 

.25201 

.33091 

.26371 

.35815 

.27CG3 

.38051 

35 

36 

.24073 

.31705 

.25220 

.33726 

.26300 

.35852 

.27583 

.38089 

36 

37 

.24092 

.31733 

.25240 

.33700 

.20410 

.35888 

.27603 

.38127 

37 

38 

.24111 

.81771 

252r9 

.33795 

.20430 

.35924 

.27623 

.38165 

33 

39 

.24130 

.31804 

*  2527  3 

.33830 

.26449 

.35901 

.27643 

.38204 

39 

40 

.24149 

.31837 

!  25297 

.338G4 

.26469 

.35997 

.27063 

.38242 

40 

41 

.24168 

.31870 

.25317 

.33899 

.26489 

.36034 

.27683 

.38280 

41 

42 

.24187 

.31903 

.25333 

.33934 

.265C9 

.30070 

.277'03 

.38319 

42 

43 

.24206 

.31936 

.25355 

.33CG8 

.20528 

.36107 

.27723 

.38357 

43 

44 

.24225 

.31969 

.25375 

.3-1003 

.26543 

.36143 

.27743 

.38396 

44 

45 

.24244 

.32002 

.25394 

.34GC3 

.26508 

.36180 

.27764 

.38434 

45 

46 

.24262 

.32035 

.25414 

.3407'3 

I  .26588 

.36217 

.27784 

.38473 

46 

47 

.24281 

.32008 

.25433 

.34108 

.26007 

.36253 

.27'804 

.38512 

47 

48 

.24300 

.32101 

.25452 

.34142 

.20627 

.36290 

.27'824 

.38550 

48 

49 

.24320 

.32134 

25472 

.34177 

.26647 

.36327 

.27844 

.38589 

49 

50 

.24339 

.32168 

!  25491 

.34212 

.26667 

.36363 

.27864 

,.38628 

50 

51 

.24358 

.32201 

.25511 

.34247 

.26686 

.36400 

.27884 

.38666 

51 

52 

.24377 

.32234 

.25530 

.34282 

.26706 

.36437 

.27905 

.387'05 

52 

53 

.24396 

.32267 

.25549 

.34317 

.26726 

.36474 

.27925 

.38744 

53 

54 

.24415 

.32301 

.25569 

.34352 

.26746 

.36511 

.27945 

.38783 

54 

55 

.24434 

.32334 

.25588 

.34387 

.26766 

.36548 

.27965 

.38822 

55 

56 

.24453 

.32368 

.25608 

.34423 

.20785 

.36585 

.27985 

.38860 

56 

57 

.24472 

.32401 

.25627 

.34458 

.26805 

.36022 

.28005 

.38899 

57 

58 

.24491 

.32434 

.25647 

.34493 

.26825 

.36659 

.28026 

.33938 

58 

59 

.24510 

.32468 

.25666 

.34528 

.38845 

.30096 

.28046 

.38977 

59 

60 

.24529 

.32501 

.25686 

.34563 

.26865 

.36733 

.28066 

.39016 

60 

257 


TABLE    XVII. -NATURAL  VERSED   SINES  AND  EXTERNAL  SECANTS. 


44° 

45° 

46° 

47° 

1 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers.  i  Ex.  sec. 

0 

.28066 

.39016 

.29289 

.41421 

.30534 

.43956 

.31800 

.46628 

0 

1 

.28086 

.39055 

.29310 

.41463 

.30555 

.43999 

.31821 

.46674 

1 

2 

.28106 

.39095 

.29330 

.41504 

.30576 

.44042 

.31843 

.46719 

2 

3 

.28127 

.39134 

.29351 

.41545 

.30597 

.44086 

.31864 

.46765 

3 

4 

.28147 

.39173 

.29372 

.41586 

.30618 

.44129 

.31885 

.46811 

4 

5 

.28167 

.39212 

.29392 

.41627 

.30639 

.44173 

.31907 

.46857 

5 

6 

.28187 

.39251 

.29413 

.41669 

.30660 

.44217 

.31928 

.46903 

6 

7 

.28208 

.39291 

.29433 

.41710 

.30681 

.44260 

.31949 

.46949 

7 

8 

.28228 

.39330 

.29454 

.41752 

.30702 

.44304 

.31971 

.46995 

8 

9 

.28248 

.39369 

.29475 

.41793 

.30723 

.44347 

.31992 

.47041 

9 

10 

.28268 

.39409 

.29495 

.41835 

.30744 

.44391 

.32013 

.47087 

10 

11 

.28289 

.39448 

.29516 

.41876 

.30765 

.44435 

.32035 

.47134 

11 

12 

.28309 

.39487 

.29537 

.41918 

.30786 

.44479 

.32056 

.47180 

12 

13 

.28329 

.39527 

.29557 

.41959 

.30807 

.44523 

.32077 

.47226 

13 

14 

.28350 

.39566 

.29578 

.42001 

.30828 

.44567 

.32099 

.47272 

14 

15 

.28370 

.39606 

.29599 

.42042 

.30849 

.44610 

.32120 

.47319 

15 

16 

.28390 

.39646 

.29619 

.42084 

.30870 

.44654 

.32141 

.47365 

16 

17 

.28410 

.39685 

.29640 

.42126 

.30891 

.44698 

.32163 

.47411 

17 

18 

.28431 

.39725 

.29661 

.42168 

.30912 

.44742 

.32184 

.47458 

18 

19 

.28451 

.39764 

.29681 

.42210 

.30933 

.44787 

.32205 

.47504 

19 

20 

.28471 

.39804 

.29702 

.42251 

.30954 

.44831 

.32227 

.47551 

20 

21 

.28492 

.39844 

.29723 

.42293 

.30975 

.44875 

.32248 

.47598 

21 

22 

.28512 

.39884 

.29743 

.42335 

.30936 

.44919 

.32270 

.47644 

22 

23 

.28532 

.39924 

.29764 

.42377 

.31017 

.44963 

.32291 

.47691 

23 

24 

.28553 

.39963 

.29785 

.42419 

.31038 

.45007 

.32312 

.47738 

24 

25 

.28573 

.40003 

.29805 

.42401 

.31059 

.45052 

.32334 

.47784 

25 

26 

.28593 

.40043 

.29826 

.42503 

.31080 

.45096 

.32355 

.47831 

26 

27 

.28614 

.40083 

.20847 

.42545 

.31101 

.45141 

.32377 

.47878 

27 

28 

.28634 

.40123 

.298G8 

.42587 

.31122 

.45185 

.32398 

.47925 

28 

29 

.28655 

.40163 

.29888 

.42630 

.31143 

.45229 

.32420 

.47972 

29 

80 

.28675 

.40203 

.29909 

.42672 

.31105 

.45274 

.32441 

.48019 

30 

31 

.28695 

.40243 

.29930 

.42714 

.31186 

.45319 

.32462 

.48066 

31 

32 

.28716 

.40283 

.29951 

.42756 

.31207 

.45363 

.32484 

.48113 

32 

33 

.28736 

.40324 

.29971 

.42799 

.31228 

.45408 

.32505 

.48160 

33 

34 

.28757 

.40364 

.29902 

.42841 

.31249 

.45452 

.32527 

.48207 

34 

35 

.28777 

.40404 

.30013 

.42883 

.31270 

.45497 

.32548 

.48254 

35 

36 

.28797 

.40444 

.30034 

.42926 

.31291 

.45542 

.32570 

.48301 

36 

37 

.28818 

.40485 

.30054 

.42968 

.31312 

.45587 

.32591 

.48349 

37 

38 

.28838 

,40525 

.30075 

.43011 

.31324 

.45031 

.32613 

.48396 

38 

39 

.28859 

.40565 

.30006 

.43053 

.318H5 

.45076 

.32034 

.48443 

39 

40 

.28879 

.40606 

.30117 

.43096 

.31376 

.45721 

.32656 

.48491 

40 

41 

.28900 

.40646 

.30138 

.43139 

.31397 

.45766 

.32677 

.48538 

41 

42 

.28920 

.40687 

.30158 

.43181 

.31418 

.45811 

.32699 

.48586 

42 

43 

.28941 

.40727 

.30179 

.43224 

.31439 

.45856 

.32720 

.48633 

43 

44 

.28961 

.407'68 

.30200 

.43267 

.31461 

.45901 

.32742 

.48081 

44 

45 

.28981 

.40808 

.30221 

.43310 

.31482 

.43946 

.32763 

.48728 

45 

46 

.29002 

.40849 

.30242 

.43352 

.31503 

.45992 

.32785 

.48776 

46 

47 

.29022 

.40890 

.30263 

.43395 

.31524 

.40037 

.32806 

.48824 

47 

48 

.29043 

.40930 

.30283 

.43138 

.31545 

.46082 

.32828 

.48371 

48 

49 

.29063 

.40971 

.30304 

.43481 

.31567 

.46127 

.32849 

.48919 

49 

50 

.29084 

.41012 

.30325 

.43524 

.31588 

.46173 

.32871 

.48967 

50 

51 

.29104 

.41053 

.30346 

.43567 

.31609 

.46218 

.32893 

.49015 

51 

52 

.29125 

.41093 

.30367 

.43610 

.31630 

.46263 

.32914 

.49063 

52 

53 

.29145 

.41134 

.30388 

.43653 

.31651 

.46309 

.32936 

.49111 

53 

54 

.29166 

.41175 

.30409 

.43696 

.31673 

.46354 

.32957 

.49159 

54 

55 

.29187 

.41216 

.30430 

.43739 

.31694 

.40400 

.32979 

.49207 

55 

56 

.29207 

.41257 

.30451 

.43783 

.31715 

.40445 

.33001 

.49255 

56 

57 

.29228 

.41298 

.30471 

.43826 

.31736 

.46491 

.33022 

.49303 

57 

58 

.29248 

.41339 

.30492 

.43869 

.31758 

.40537 

.33044 

.49351 

58 

59 

.29269 

.41380 

.30513 

.43912 

.31779 

.46582 

.33065 

.49399 

59 

GO 

.29289 

.41421 

.30534 

.43956 

.31800 

.46628 

.33087 

.49448 

60 

258 


TABLE    XVII.— NATURAL  VERSED    SINES    AND  EXTERNAL   SECANTS. 


' 

48° 

49° 

50* 

51° 

/ 

Vers. 

I 
Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.33087 

.49448 

.34394 

.52425 

.35721 

.55572 

.37068 

.58902 

0 

1 

.33109 

.49496 

.34416 

.52476 

.35744 

.55626 

.37091 

.58959 

1 

2 

.33130 

.49544 

.34438 

.52527 

.35766 

.55680 

.37113 

.59016 

2 

3 

.33152 

.49593 

.34460 

.52579 

.35788 

.55734 

.37136 

.59073 

3 

4 

.33173 

.49641 

.34482 

.52630 

.35810 

.55789 

.37158 

.59130 

4 

5 

.33195 

.49690 

.34504 

.52681 

.35833 

.55843 

.37181 

.59188 

5 

6 

.33217 

.49738 

.34526 

.52732 

.35855 

.55897 

.37204 

.59245 

6 

7 

.33238 

.49787 

.34548 

.52784 

.35877 

.55951 

.37226 

.59302 

7 

8 

.33260 

.49835 

.34570 

.52835 

.35900 

.56005 

.37249 

.59360 

8 

9 

.33282 

.49884 

.34592 

.52886 

.35922 

.56060 

.37272 

.59418 

9 

10 

.33303 

.49933 

.34614 

.52938 

.35944 

.56114 

.37294 

.59475 

10 

11 

.33325 

.49981 

.34636 

.52989 

.35967 

.56169 

.37317 

.59533 

11 

12 

.33347 

.50030 

.34658 

.53041 

.35989 

.56223 

.37340 

.59590 

12 

13 

.33368 

.50079 

.34680 

.53092 

.36011 

.56278 

.37362 

.59648 

13 

14 

.33390 

.50128 

.34702 

.53144 

.36034 

.56332 

.37385 

.59706 

14 

15 

.33412 

.50177 

.34724 

.53196 

.36056 

.56387 

.37408 

.59764 

15 

16 

.33434 

.50226 

.34746 

.53247 

.36078 

.56442 

.37430 

.59822 

16 

17 

.33455 

.50275 

.34768 

.53299 

.36101 

.56497 

.37453 

.59880 

17 

18 

.33477 

.50324 

.34790 

.53351 

.36123 

.56551 

.37476 

.59938 

18 

19 

.33499 

.50373 

.34812 

.53403 

.36146 

.56606 

.37498 

.59996 

19 

20 

.33520 

.50422 

.34834 

.53455 

.36168 

.56661 

.37521 

.60054 

20 

21 

.33542 

.50471 

.34856 

.53507 

.36190 

.56716 

.37544 

.60112 

21 

22 

.33564 

.50521 

.34878 

.53559 

.36213 

.56771 

.37'567 

.60171 

22 

23 

.33586 

.50570 

.34900 

.53611 

.36235 

.56826 

.37589 

.60229 

23 

24 

.33607 

.50619 

.34923 

.53663 

.36258 

.56881 

.37612 

.60287 

24 

25 

.33629 

.50669 

.34945 

.53715 

.36280 

.56937 

.37635 

.60346 

25 

26 

.33651 

.50718 

.34967 

.53768 

.36302 

.56992 

.37658 

.60404 

26 

27 

.33673 

.50767 

.34989 

.53820 

.36325 

.57047 

.37680 

.60463 

27 

28 

.33694 

.50817 

.35011 

.53872 

.36347 

.57103 

.37703 

.60521 

28 

29 

.33716 

.50866 

.35033 

.53924 

.36370 

.57158 

.37726 

.60580 

29 

30 

.33738 

.50916 

.35055 

.53977 

.36392 

.57213 

.37749 

.60639 

30 

31 

.33760 

.50966 

.35077 

.54029 

.36415 

.57269 

.37771 

.60698 

31 

32 

.33782 

.51015 

.35099 

.54082 

.36437 

.57324 

.37794 

.60756 

32 

33 

.33803 

.51065 

.35122 

.54134 

.36460 

.57380 

.37817 

.60815 

33 

31 

.33825 

.51115 

.35144 

.54187 

.36482 

.57436 

.37840 

.60874 

34 

35 

.33847 

.51165 

.35166 

.54240 

.36504 

.57491 

.37'862 

.60933 

35 

36 

.33809 

.51215 

.35188 

.54292 

.36527 

.57547 

.37885 

.60992 

36 

37 

.33891 

.51265 

.35210 

.54345 

.36549 

.57603 

.37908 

.61051 

37 

38 

.33912 

.51314 

.35232 

.54398 

.36572 

.57659 

.37931 

.61111 

38 

39 

.33934 

.51364 

.35254 

.54451 

.36594 

.57715 

.37954 

.61170 

39 

40 

.33956 

.51415 

.35277 

.54504 

.36617 

.57771 

.37976 

.61229 

40 

41 

.33978 

.51465 

.35299 

.54557 

.36639 

.57827 

.37999 

.61288 

41 

42 

.34000 

.51515 

.35321 

.54610 

.36662 

.57883 

.38022 

.61348 

42 

43 

.34022 

.51565 

.35343 

.54663 

.36684 

.57939 

.38045 

.61407 

43 

44 

.34044 

.51615 

.35365 

.54716 

.36707 

.57995 

.38068 

.61467 

44 

45 

.34065 

.51665 

.35388 

.54769 

.36729 

.58051 

.38091 

.61526 

45 

46 

.34087 

.51716 

.35410 

.54822 

.36752 

.58108 

.38113 

.61586 

46 

47 

.34109 

.51766 

.35432 

.54876 

.36775 

.58164 

.38136 

.61646 

47 

48 

.34131 

.51817 

.35454 

.54929 

.36797 

.58221 

.38159 

.61705 

48 

49 

.34153 

.51867 

.35476 

.54982 

.36820 

.58277 

.38182 

.61765 

49 

50 

.34175 

.51918 

.35499 

.55036 

.36842 

.58333 

.38205 

.61825 

50 

51 

.34197 

.51968 

.35521 

.55089 

.36865 

.58390 

.38228 

.61885 

51 

52 

.34219 

.52019 

.35543 

.55143 

.36887 

.58447 

.38251 

.61945 

52 

53 

.34241 

.52069 

.35565 

.55196 

.36910 

.58503 

.38274 

.62005 

53 

54 

.34262 

.52120  1 

.a5588 

.55250 

.36932 

.58560 

.38296 

.62065 

54 

55 

.34284 

.52171 

.35610 

.55303 

.36955 

.58617 

.38319 

.62125 

55 

56 

.34306 

.52222 

.35632 

.55357 

.36978 

.58674 

.38342 

.62185 

56 

57 

.34328 

.52273 

.35654 

.55411 

.37000 

.58731 

.38365 

.62246 

57 

58 

.34350 

.52323 

.35677 

.55465 

.37023 

.58788 

.38388 

.62306 

58 

59 

.34372 

.52374 

.35699 

.55518 

.37045 

.58845 

.38411 

.62366 

59 

60 

.34394 

.52425 

.35721 

.55572 

.37068 

.58902 

.38434 

.62427 

60 

259 


TABLE    XVTT.-NATURAL   VERSED   SINES   AND   EXTERNAL  SECANTS 


/ 

52° 

53° 

54° 

55° 

j 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers.  j  Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.38434 

.62427 

.39819 

.66164 

.41221 

.70130 

.42642 

.74345 

0 

1 

.38457 

.62487 

.39842 

.66228 

.41245 

.70198 

.42666 

.74417 

1 

2 

.38480 

.62548 

.39865 

.66292 

.41269 

.70267 

.42690 

.74490 

2 

3 

.38503 

.62609 

.39888 

.66357 

.41292 

.70335 

.42714 

.74562 

3 

4 

.38526 

.62669 

.39911 

.66421 

.41316 

.70403 

.42738 

.74635 

4 

5 

.38549 

.62730 

.39935 

.66486 

.41&39 

.70472 

.42762 

.74708 

5 

6 

.38571 

.62791 

.39958 

.66550 

.41363 

.70540 

.42785 

.74781 

6 

7 

.38594 

.62&52 

.39981 

.66615 

.41386 

.70609 

.42809 

.74854 

7 

8 

.38617 

.62913 

.40005 

.66679 

.41410 

.70677 

.42833 

.74927 

8 

9 

.38640 

.62974 

.40028 

.66744 

.41433 

.70746 

.42857 

.75000 

9 

10 

.38663 

.63035 

.40051 

.66809 

.41457 

.70815 

.42881 

.75073 

10 

11 

.38686 

.63096 

.40074 

.66873 

.41481 

.70884 

.42905 

.75146 

11 

12 

.38709 

.63157 

.40098 

.66938 

.41504 

.70953 

.42929 

.75219 

13 

.38732 

.63218 

.40121 

.67003 

.41528 

.71022 

.42953 

.75293 

13 

14 

.38755 

.63279 

.40144 

.67068 

.41551 

.71091 

.42976 

.75366 

14 

15 

.38778 

.63341 

.40168 

.67133 

.41575 

.71160 

.43000 

.75440 

15 

16 

.38801 

.63402 

.40191 

.67199 

.41599 

.71229 

.43024 

.75513 

16 

17 

.38824 

.63464 

.40214 

.67264 

.41622 

.71298 

.43048 

.75587 

17 

18 

.38847 

.63525 

.40237 

.67329 

.41646 

.71368 

.43072 

.75661 

18 

19 

.38870 

.6358? 

.40261 

.67394 

.41670 

.71437 

.43096 

,75734 

19 

20 

.38893 

.63648 

.40284 

.67460 

.41693 

.71506 

.43120 

.75808 

20 

21 

.38916 

.63710 

.40307 

.67525 

.41717 

.71576 

.43144 

.75882 

21 

22 

.38939 

.63772 

.40331 

.67591 

.41740 

.71646 

.43168 

.75956 

22 

23 

.38962 

.63834 

.40354 

.67656 

.41764 

.71715 

.43192 

.76031 

23 

24 

.38985 

.63895 

.40378 

.67722 

.41788 

.71785 

.43216 

.76105 

24 

25 

.39009 

.63957 

.40401 

.67788 

.41811 

.71855 

.43240 

.76179 

25 

26 

.39032 

.64019 

.40424 

.67853 

.41835 

.71925 

.43264 

.76253 

26 

27 

.39055 

.64081 

.40448 

.67919 

.41859 

.71995 

.43287 

.76328 

27 

28 

.39078 

.64144 

.40471 

.67985 

.41882 

.72065 

.43311 

.76402 

28 

29 

.39101 

.64206 

.40494 

.68051 

.41906 

.72135 

.43335 

.76477 

29 

30 

.39124 

.64268 

.40518 

.68117 

.41930 

.72205 

.43359 

.76552 

30 

31 

.39147 

.64330 

.40541 

.68183 

.41953 

.72275 

.43383 

.76626 

31 

32 

.39170 

.64393 

.40565 

.68250 

.41977 

.72346 

.43407 

.76701 

32 

33 

.39193 

.64455 

.40588 

.68316 

.42001 

.72416 

.43431 

.76776 

33 

34 

.39216 

.64518 

.40611 

.68382 

.42024 

.72487 

.43455 

.76851 

34 

35 

.39239 

.G4580 

.40635 

.68449 

.42048 

.72557 

.43479 

.  7^926 

35 

36 

.39262 

.64643 

.40658 

.68515 

.42072 

.72628 

.43503 

.77001 

36 

37 

.39286 

.64705 

.40682 

.G8582 

.42096 

.72698 

.43527 

.77077 

37 

38 

.39309 

.64768 

.40705 

.68648 

.42119 

.72769 

.43551 

.77152 

38  . 

39 

.39332 

.64831 

.40728 

.08715 

.42143 

.72840 

.43575 

.77227 

39 

40 

.39355 

.64894 

.40752 

.68782 

.42167 

.72911 

.43599 

.77303 

40 

41 

.39378 

.64957 

.40775 

.68848 

.42191 

.72982 

.43623 

.77378 

41 

42 

.39401 

.65020 

.40799 

.68915 

.42214 

.73053 

.43647 

.77454 

42 

43 

.39424 

.65083 

.40822 

.68982 

.42238 

.73124 

.43671 

\77530 

43 

44 

.39447 

.65146 

.40846 

.69049 

.42262 

.73195 

.43695 

.77606 

44 

45 

.39471 

.65209 

.40869 

.69116 

.42285 

.73267 

.43720 

.77681 

45 

46 

.39494 

.65272 

.40893 

.69183 

.42309 

.73338 

.43744 

.77757 

46 

47 

.39517 

.65336 

.40916 

.G9S50 

.42333 

.73409 

.43768 

.77833 

47 

48 

.39540 

.65399 

.40939 

.69318 

.42357 

.73481 

.43792 

.77910 

48 

49 

.39563 

.65462 

.40963 

.69385 

.42381 

.73552 

.43816 

.77986 

49 

50 

.39586 

.65526 

.40986 

.69452 

.42404 

.73624 

.43840 

.78062 

50 

51 

.39610 

.65589 

.41010 

.69520 

.42428 

.73696 

.43864 

.78138 

51 

52 

.39633 

.65653 

.41033 

.69587 

.42452 

.73768 

.43888 

.78215 

62 

53 

.39656 

.65717 

.41057 

.69655 

.42476 

.73840 

.43912 

.78291 

53 

54 

.39679 

.65780 

.41080 

.69723 

.42499 

.73911 

.43936 

.78368 

54 

55 

.39702 

.65844 

.41104 

.69790 

.42523 

.73983 

.43960 

.78445 

55 

56 

.39726 

.65908 

.41127 

.69858 

.42547 

74056 

.43984 

.78521 

56 

57 

.39749 

.65972 

.41151 

.69926 

.42571 

.74128 

.44008 

.78598 

57 

58 

.39772 

.66036 

.41174 

.69994 

.42595 

.74200 

.44032 

.78675 

68 

59 

.39795 

.66100 

.41198 

.70062 

.42619 

.74272 

.44057 

.78752 

59 

60 

.39819 

.66164 

.41221 

.70130 

.42642 

.74345 

.44081 

.78829 

60 

260 


TABLE    XVII.— NATURAL  VERSED   SINES  AND   EXTERNAL  SECANTO 


56° 

57° 

58° 

59° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers.  ;Ex.sec. 

0 

.44081 

.78829 

.45536 

.83608 

.47008 

.88708 

.48496 

.94160 

0 

1 

.44105 

.78906 

.45560 

.83690 

.47033 

.88796 

.48521 

.94254 

1 

2 

.44129 

.78984 

.45585 

.83773 

.47057 

.88884 

.48546 

.94349 

2 

3 

.44153 

.79061 

.45609 

.83855 

.47082 

.88972 

.48571 

.94443 

3 

4 

.44177 

.79138 

.45634 

.83938 

.47107 

.89060 

.48596 

.94537 

4 

5 

.44201 

.79216 

.45658 

.84020 

.47131 

.89148 

.48621 

.94632 

5 

6 

.44225 

.79293 

.45683 

.84103 

.47156 

.89237 

.48646 

.94726 

6 

7 

.44250 

.79371 

.45707 

.84186 

.47181 

.89325 

.48671 

.94821 

7 

8 

.44274 

.79449 

.45731 

.84269 

.47206 

.89414 

.48696 

.94916 

8 

9 

.44298 

.79527 

.45756 

.84352 

.47230 

.89503 

.48721 

.95011 

9 

10 

.44322 

.79604 

.45780 

.84435 

.47255 

.89591 

.48746 

.95106 

10 

11 

.44346 

.79682 

.45805 

.84518 

.47280 

.89680 

.48771 

.95201 

11 

12 

.44370 

.79761 

.45829 

.84601 

.47304 

.89769 

.48796 

.95296 

12 

13 

.44395 

.79839 

.45854 

.84685 

.47329 

.89858 

.48821 

.95392 

13 

14 

.44419 

.79917 

.45878 

.84768 

.47354 

.89948 

.48846 

.95487 

14 

15 

.44443 

.79995 

.45903 

.84852 

.47379 

.90037 

.48871 

.95583 

15 

16 

.44467 

.80074 

.45927 

.84935 

.47403 

.90126 

.48896 

.95678 

16 

17 

.44491 

.80152 

.45951 

.85019 

.47428 

.90216 

.48921 

.95774 

17 

18 

.44516 

.80231 

.45976 

.85103 

.47453 

.90305 

.48946 

.95870 

18 

19 

.44540 

.80309 

.46000 

.85187 

.47478 

.90395 

.48971 

.95966 

19 

20 

.44564 

.80388 

.46025 

.85271 

.47502 

.90485 

.48996 

.96062 

20 

21 

.44588 

.80467 

.46049 

.85355 

.47527 

.90575 

.49021 

.96158 

21 

22 

.44612 

.80546 

.46074 

.85439 

.47552 

.90665 

.49046 

.96255 

22 

23 

.44637 

.80625 

.46098 

.85523 

.47577 

.90755 

.49071 

.96351 

23 

24 

.44661 

.80704 

.46123 

.85608 

.47601 

.90845 

.49096 

.96448 

24 

25 

.44685 

.80783 

.46147 

.85692 

.47626 

.90935 

.49121 

.96544 

25 

26 

.44709 

.80862 

.46172 

.85777 

.47651 

.91026 

.49146 

.96641 

26 

27 

.44734 

.80942 

.46196 

.85861 

.47676 

.91116 

.49171 

.967'38 

27 

28 

.44758 

.81021 

.46221 

.85946 

.47701 

.91207 

.49196 

.96835 

28 

29 

.44782 

.81101 

.46246 

.86031 

.47725 

.91297 

.49221 

.96932 

29 

30 

.44806 

.81180 

.46270 

.86116 

.47750 

.91388 

.49246 

.97029 

30 

31 

.44831 

.81260 

.46295 

.86201 

.47775 

.91479 

.49271 

.97127 

31 

32 

.44855 

.81340 

.46319 

.86286 

.47800 

.91570 

.49296 

.97224 

32 

33 

.44879 

.81419 

.46344 

.86371 

.47825 

.91661 

.49321 

.97322 

33 

34 

.44903 

.81499 

.46368 

.86457 

.47849 

.91752 

.49346 

.97420 

34 

35 

.44928 

.81579 

.46393 

.86542 

.47874 

.91844 

.49372 

.97517 

35 

36 

.44952 

.81659 

.46417 

.86627 

.47899 

.91935 

.49397 

.97615 

36 

37 

.44976 

.81740 

.46442 

.86713 

.47924 

.92027 

.49422 

.97713 

37 

38 

.45001 

.81820 

.46466 

.86799 

.47949 

.92118 

.49447 

.97811 

38 

39 

.45025 

.81900 

.46491 

.86885 

.47974 

.92210 

.49472 

.97910 

39 

40 

.45049 

.81981 

.46516 

.86990 

.47998 

.92302 

.49497 

.98008 

40 

41 

.45073 

.82061 

.46540 

.87056 

.48023 

.92394 

,49522 

.98107 

41 

42 

.45098 

.82142 

.46565 

.87142 

.48048 

.92486 

.49547 

.98205 

42 

43 

.45122 

.82222 

.46589 

.87229 

.48073 

.9.2578 

.49572 

.98304 

43 

44 

.45146 

.82303 

.46614 

.87315 

.48098 

.92670 

.49597 

.98403 

44 

45 

.45171 

.82384 

.46639 

.87401 

.48123 

.92762 

.49623 

.98502 

45 

46 

.45195 

.82465 

.46663 

.87488 

.48148 

.92855 

.49648 

.98601 

46 

47 

.45219 

.82546 

.46688 

.87574 

.48172 

.92947 

.49673 

.98700 

47 

48 

.45244 

.82627 

.46712 

.87661 

.48197 

.93040 

.49698 

.98799 

48 

49 

.45268 

.82709 

.46737 

.87748 

.48222 

.93133 

.49723 

.98899 

49 

50 

.45292 

.82790 

.46762 

.87834 

.48247 

.93226 

.49748 

.98998 

50 

51 

.45317 

.82871 

.46786 

.87921 

.48272 

.93319 

.49773 

.99098 

51 

52 

.45341 

.82953 

.46811 

.88008 

.48297 

.93412 

.49799 

.99198 

52 

53 

.45365 

.83034 

.46836 

.88095 

.48322 

.93505 

.49824 

.99298 

53 

54 

.45390 

.83116 

.46860 

.88183 

.48347 

.93598 

.49849 

.99398 

54 

55 

.45414 

.83198 

.46885 

.88270 

.48372 

.93602, 

.49874 

.99498 

55 

56 

.45439 

.a3280 

.46909 

.88357 

.48396 

.93785 

.49899 

.99598 

56 

57 

.45463 

.8-3362 

.46934 

.88445 

.48421 

.93879 

.49924 

.99698 

57 

58 

.45487 

.83444 

.46959 

.88532 

.48446 

.93973 

.49950 

.99799 

58 

59 

.45512 

.83526 

.46983 

.88620 

.48471 

.94066 

.49975 

.99899 

59 

60 

.45536 

.83608 

.47008 

.88708  1 

.48496 

.94160 

.50000 

.00000 

60 

361 


TABLE    XVII. -NATURAL  VERSED  SINES  AND  EXTERNAL   SECANTS. 


€ 

0° 

6 

1° 

6 

2° 

€ 

3° 

Vers. 

Ex  .se 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.50000 

1.00000 

.51519 

1.06267 

.53053 

1.13005 

.54601 

1.20269 

0 

1 

.50025 

1.00101 

.51544 

1.06375 

.53079 

1.13122 

.54627 

1.20395 

1 

2 

.50050 

1.00202 

.51570 

1.06483 

.53104 

1.13239 

.54653 

1.20521 

2 

3 

.50076 

1.00303 

.51595 

1.06592 

.53130 

1.13356 

.54679 

1.20647 

3 

4 

.50101 

1.00404 

.51621 

1.06701 

.53156 

1.13473 

.54705 

1.20773 

4 

5 

.50126 

1.00505 

.51646 

1.06809 

.53181 

1.13590 

.54731 

1.20900 

5 

6 

.50151 

1.00607 

.51672 

1.06918 

.53207 

1.13707 

.54757 

1.21026 

6 

7 

.50176 

1.00708 

.51697 

1.07027 

.53233 

1.13825 

.54782 

1.21153 

7 

8 

.50202 

1.00810 

.51723 

1.07137 

.53258 

1.13942 

.54808 

1.21280 

8 

9 

.50227 

1.00912 

.51748 

1.07246 

.53284 

1.14060 

.54834 

1.21407 

9 

10 

.50252 

1.01014 

.51774 

1.07356 

.53310 

1.14178 

.54860 

1.21535 

10 

11 

.50277 

1.01116 

.51799 

1.07465 

.53336 

1.14296 

.54886 

1.21662 

11 

12 

.50303 

1.01218 

.51825 

1.07575 

.53361 

1.14414 

.54912 

1.21790 

12 

13 

.50328 

1.01320 

.51850 

1.07685 

.53387 

1.14533 

.54938 

1.21918 

13 

14 

.50353 

1.01422 

.51876 

1.07795 

.53413 

1.14651 

.54964 

1.22045 

14 

15 

.50378 

1.0)525 

.51901 

1.07905 

.5:3439 

1.14770 

.54990 

.22174 

15 

16 

.50404 

1.01628 

.51927 

1.08015 

.53464 

1.14889 

.55016 

.22302 

16 

17 

.50429 

1.01730 

.51952 

1.08126 

.53490 

1.15008 

.55042 

.22430 

17 

18 

.50454 

1.01833 

.51978 

1.08236 

.53516 

1.15127 

.55068 

.22559 

18 

19 

.50479 

1.01936 

.52003 

1.08347 

.53542 

1.15246 

.55094 

.22688 

19 

20 

.50505 

1.02039 

.52029 

1.08458 

.53567 

1.15366 

.55120 

.22817 

20 

21 

.50530 

1.02143 

.52054 

1.08569 

.53593 

1.15485 

.55146 

1.22946 

21 

22 

.50555 

1.02246 

.52080 

1.08680 

.53619 

1.15605 

.55172 

1.23075 

22 

23 

.50581 

1.02349 

.52105 

1.08791 

.53645 

1.15725 

.55198 

1.23205 

23 

24 

.50606 

1.02453 

.52131 

1.08903 

.53670 

1.15845 

.55224 

1.23334 

24 

25 

.50631 

1.02557 

.52156 

1.09014 

.53096 

1.15965 

.55250 

1.23464 

25 

26 

.50656 

1.02661 

.52182 

1.09126 

.53722 

1.16085 

.55276 

1.23594 

26 

27 

.50682 

1.02765 

.52207 

1.09238 

.53748 

1.16206 

.55302 

1.23724 

27 

28 

.50707 

1.02869 

.52233 

1.09350 

.53774 

1.16326 

.55328 

1.23855 

28 

29 

.50732 

1.02973 

.52259 

1.09462 

.53799 

1.16447 

.55354 

1.23985 

29 

30 

.50758 

1.03077 

.52284 

1.09574 

.53825 

1.16568 

.55380 

1.24116 

30 

31 

.50783 

1.03182 

.52310 

1.09686 

.53851 

1.16689 

.55406 

1.24247 

31 

32 

.50808 

1.03286 

.52335 

1.09799 

.53877 

1.16810 

.55432 

1.24378 

32 

33 

.50834 

1.03391 

.52361 

1.09911 

.53903 

1.16932 

.55458 

1.24509 

33 

34 

.50859 

1.03496 

.52386 

1.10024 

.53928 

1.17053 

.55484 

1.24640 

34 

35 

.50884 

1.03601 

.52412 

1.10137 

.53954 

1.17175 

.55510 

1.24772 

35 

36 

.50910 

1.03706 

.52438 

1.10250 

.53980 

1.17297 

.55536 

1.24903 

36 

37 

.50935 

1.03811 

.52463 

1.10363 

.54006 

1.17419 

.55563 

1.25035 

37 

38 

.50960 

1.03916 

.52489 

1.10477 

.54032 

1.17541 

.55589 

1  25167 

38 

39 

.50986 

1.04022 

.52514 

1.10590 

.54058 

1.17663 

.55615 

1.25300 

39 

40 

.51011 

1.04128 

.52540 

1.10704 

.54083 

1.17786 

.55641 

1.25432 

40 

41 

.51036 

1.04233 

.52566 

1.10817 

.54109 

1.17909 

.55667 

1.25565 

41 

42 

.51062 

1.04339 

.52591 

1.10931 

.54135 

1.18031 

.55693 

1.25697 

42 

43 

.51087 

1.04445 

.52617 

1.11045 

.54161 

1  .  18154 

.55719 

1.25830 

43 

44 

.51113 

1.04551 

.52642 

1.11159 

.54187 

1.18277 

.55745 

1.25963 

44 

45 

.51138 

1.04658 

.52668 

1.11274 

.54213 

1.18401 

.55771 

1.26097 

45 

46 

.51163 

1.04764 

.52694 

1.11388 

.54238 

1.18524 

.55797 

1.26230 

46 

47 

.51189 

1.04870 

.52719 

1.11503 

.54264 

1.18648 

.55823 

1.26364 

47 

48 

.51214 

1.04977 

.52745 

1.11617 

.54290 

1.18772 

.55849 

1.26498 

48 

49 

.51239 

1.05084 

.52771 

1.11732 

.54316 

1.18895 

.55876 

1.26632 

49 

50 

.51265 

1.05191 

.52796 

1.11847 

.54342 

1.19019 

.55902 

1.26766 

50 

51 

.51290 

1.05298 

.52822 

1.11963 

.54368 

1.19144 

.55928 

1.26900 

51 

52 

.51316 

1.05405 

.52848 

1.12078 

.54394 

1.19268 

.55954 

1.27035 

52 

53 

.51341 

1.05512 

.52873 

1.12193 

.54420 

1.19393 

.55980 

1.27169 

53 

54 

.51366 

1.05619 

.52899 

1.12309 

.54446 

1.19517 

.56006 

1.27304 

54 

55 

.51392 

1.05727 

.52924 

1.12425 

.54471 

1.19642 

.56032 

1.27439 

55 

56 

.51417 

1.05835 

.52950 

1.12540 

.54497 

1.19767 

.56058 

1.27574 

56 

57 

.51443 

1.05942 

.52976 

1.12657 

.54523 

1.19892 

.56084 

1.27710 

57 

58 

.51468 

1.06050 

.53001 

1.12773 

.54549 

1.20018 

.56111 

1.27845 

58 

59 

.51494 

1.06158 

.53027 

1.12889 

.54575 

1.20143 

.56137 

1.27981 

59 

60 

.51519 

1.06267 

.53053 

1.13005 

.54001 

1.20269 

.56163 

1.28117 

60 

262 


TABLE    XVII.— NATURAL  VERSED  SINES  AND   EXTERNAL  SECANTS. 


6 

40 

6 

5° 

6 

6« 

6 

7° 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.56163 

1.28117 

.57738 

1.36620  ! 

.59326 

1.45859 

.60927 

.55930 

0 

1 

.56189 

1.28253 

.57765 

1.36768  ; 

.59353 

1.46020 

.60954 

.56106 

1 

2 

.56215 

1.28390 

.57791 

1.36916 

.59379 

1.46181 

.60980 

.56282 

2 

a 

.56241 

1.28526 

.57817 

1.37064 

.59406 

1.46342 

.61007 

.56458 

3 

4 

.56267 

1.28663 

.57844 

1.37212 

.59433 

1.46504 

.61034 

.56634 

4 

5 

.56294 

1.28800 

.57870 

1.37361 

.59459 

1.46665 

.61061 

.56811 

5 

6 

.56320 

1.28937  I 

.57896 

1.37509  i 

.59486 

1.46827 

.61088 

.56988 

6 

7 

.56346 

1.29074  i 

.57923 

1.37658 

.59512 

1.46989 

.61114 

.57165 

7 

8 

.56372 

1.29211 

.57949 

1.37808 

.59539 

1.47152 

.61141 

.57342 

8 

9 

.56398 

1.29349  j 

.57976 

1.37957 

.59566 

1.47314 

.61168 

.57520 

9 

10 

.56425 

1.29487 

.58002 

1.3810? 

.59592 

1.  47477 

.61195 

.57698 

10 

11 

.56451 

1.29625 

.58028 

1.38256 

.59619 

1.47640 

.61222 

.57876 

11 

12 

.56477 

1-29763 

.58055 

1.38406 

.59645 

1.47804 

.61248 

.58054 

12 

13 

.56503 

1.29901 

.58081 

1.38556 

'.59672 

1.47967 

.61275 

.58233 

13 

14 

.56529 

1.30040 

.58108 

1.38707 

.59699 

1.48131 

.61302 

.58412 

14 

15 

.56555 

1.30179 

.58134 

.38857 

.59725 

1.48295 

.61329 

.58591 

15 

16 

.56582 

1.30318 

.58160 

.39008 

.59752 

1.48459 

.61356 

.58771 

16 

17 

.56608 

1.30457 

.58187 

.39159 

.59779 

1.48624 

.61383 

.58950 

17 

18 

.56634 

1.30596 

.58213 

.39311 

.59805 

1.48789  : 

.61409 

.59130 

18 

19 

.56660 

1.307.35  ! 

.58240 

.39462 

.59832 

1.48954 

.61436 

.59311 

19 

20 

.56687 

1.30875 

.58266 

.39614 

.59859 

1.49119 

.61463 

.59491 

20 

21 

.56713 

1.31015 

.58293 

.39766 

.59885 

1.49284 

.61490 

.59672 

21 

22 

.56739 

1.31155 

.58319 

.39918 

.59912 

1.49450 

.61517 

.59853 

22 

23 

.56765 

1.31295 

.58345 

.40070 

.59938 

1.49616 

.61544 

.60035 

23 

24 

.56791 

1.31436 

.58372 

1.40222 

.59965 

1.49782 

.61570 

.60217 

24 

25 

.56818 

1.31576 

.58398 

1.40375 

.59992 

1.49948 

.61597 

.60399 

25 

2(5 

.56844 

1.31717 

.58425 

1.40528 

.60018 

1.50115 

.61624 

.60581 

26 

27 

.56870 

1.31858 

.58451 

1.40681 

.60045 

1.50282 

.61651 

.60763 

27 

28 

.56896 

1.31999 

.58478 

1.40835 

.60072 

1.50449 

.61678 

.60946 

28 

29 

.56923 

1.32140 

.58504 

1.40988 

.60098 

1.50617 

.61705 

.61129 

29 

30 

.56949 

1.32282 

.58531 

1.41142 

.60125 

1.50784 

.61732 

.61313 

30 

31 

.56975 

1.32424 

.5R557 

1.41296 

.60152 

1.50952 

.61759 

.61496 

31 

32 

.57001 

1.32566 

.58584 

1.41450 

.60178 

1.51120 

.61785 

.61680 

32 

33 

.57028 

1.32708 

.58610 

1.41605 

.60205 

1.51289 

.61812 

.61864 

33 

34 

.57054 

1.32850 

.58637 

1.41760 

.60232 

1.51457 

.61839 

.62049 

34 

35 

.57080 

1.32993 

.58663 

1.41914 

.60259 

1.51626 

.61866 

.62234 

35 

30 

.57106 

1.  .33135 

.58690 

1.42070 

.60285 

1.51795 

.61893 

.62419 

36 

37 

.571  as 

1.33278 

.58716 

1.42225 

.60312 

.51965 

.61920 

.62604 

37 

38 

.57159 

1.33422 

.58743 

1.42380 

.60339 

.52134 

.61947 

.62790 

38 

39 

.57185 

1.,  33565 

.58769 

1.42536 

.60365 

.52304 

.61974 

.62976 

39 

40 

.57212 

1.33708 

.58796 

1.42692 

.60392 

.52474 

.62001 

.63162 

40 

41 

.57238 

1.33852 

.58822 

1.42848 

.60419 

.52645 

.62027 

.63348 

41 

42 

.57264 

1.33996 

.58849 

1.43005 

.60445 

.52815  i 

.62054 

.63535 

42 

43 

.57291 

1.34140 

.58875 

1.43162 

.60472 

.52986 

.62081 

.63722 

43 

44 

.57317 

1.34284 

.58902 

1.43318 

.60499 

.53157 

.62108 

.63909 

44 

45 

.57343 

1.34429 

.58928 

1.43476 

.60526 

.53329 

.62135 

.64097 

45 

40 

.57369 

1.34573 

.58955 

.43633 

.60552 

.53500 

.62162 

.64285 

46 

47 

.57396 

1.34718 

.58981 

.43790 

.60579 

.53672 

.62189 

.64473 

47 

48 

.57422 

1.34863 

.59008 

.43948 

.60606 

.53845 

.62216 

.64662 

48 

49 

.57448 

1.35009 

.59034 

.44106 

.60633 

.54017 

.62243 

.64851 

49 

50 

.  57475 

1.35154 

.59061 

.44264 

.60659 

.54190 

.62270 

.65040 

50 

51 

.57501 

1.35300 

.59087 

.44423 

.60686 

.54363 

.62297 

.65229 

51 

58 

.57527 

1.,  35446  i 

.59114 

.44582 

.60713 

.54536 

.62324 

.65419 

52 

53 

.57554 

1.35592 

.59140 

.44741 

.60740 

.54709 

.62351 

.65609 

53 

54 

.57580 

1.35738 

.59167 

.44900 

.60766 

.54883 

.62378 

.65799 

54 

55 

.57606 

1.35885 

.59194 

.45059 

.60793 

.5505? 

.62405 

.65989 

55 

56 

.57633 

1.36031 

.59220 

.45219 

.60820 

.55231 

.62431 

1.66180 

50 

57 

.57659 

1.36178 

.59247 

.45378 

.60847 

.55405 

.62458 

1.66371 

57 

68 

.57685 

1.36325 

.59273 

.45539 

.60873 

.55580 

.62485 

1.66563 

58 

59 

.57712 

1.36473 

.59300 

.45699 

.60900 

.55755 

.62512 

1.66755 

59 

60 

.57738 

1.36620 

.59326 

.45859 

.60927 

.55930 

.62539 

1.66947 

00 

263 


TABLE    XVII.— NATURAL  VERSED  SINES  AND   EXTERNAL  SECANTS. 


/ 

68' 

69° 

70° 

71° 

> 

Vers, 

Ex.  sec 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec 

1 

.62539 

1.66947 

.64103 

1.79043 

1  .65798 

1.92380 

.67443  2.07155 

0 

• 

.62566 

1.67139 

.64190 

1.79254 

.65825 

1.92614 

.67471  2.07'415 

1 

ji 

.62593 

1.67332 

.64218 

1.79466 

.65853 

1.92849 

.67498  2.07675 

2 

J 

.62620 

1.67525 

.64245 

1.79679 

.65880 

1.93083 

.67526  2.07936 

3 

i 

.62647 

1.67718 

.64272 

1.79891 

.65907 

1.93318 

.67553 

2.08197 

i 

t 

.62674 

1.67911 

.64299 

1.80104 

.65935 

1.93554 

.67581 

2.08459 

t 

t 

.62701 

1.68105 

.64326 

1.80318 

.65962 

1.93790 

.67608 

2.087'21 

e 

( 

.62728 

1.68299 

.64353 

1.80531 

.65989 

1.94026 

.67636 

2.089&3 

5 

8 

.62755 

1.68494 

.64381 

1.80746 

.66017 

1.94263 

.67663 

2.09246 

8 

9 

.62782  1.68689 

.64408 

1.80960 

.66044 

1.94500 

.67691 

2.09510 

9 

10 

.62809 

1.68884 

.64435 

1.81175 

.66071 

1.94737 

.67718 

2.09774 

10 

11 

.62836 

1.69079 

.64462 

1.81390 

.66099 

1.94975 

.67746 

2.10038 

11 

12 

.62863 

1.69275 

.64489 

1.81605. 

.66126 

1.95213 

.67773 

2.10303 

12 

13 

.62890 

1.69471 

.64517 

1.81821 

.66154 

1.95452 

.67801 

2.10568 

13 

14 

.62917 

1.69667 

.64544 

1.82037 

.66181 

1.95691 

.67829 

2.10834 

14 

15 

.62944 

1:69864 

.64571 

1.82254 

.66208 

1.95931 

.67856 

2.11101 

15 

16 

.62971 

1.70061 

.64598 

1.82471 

.66236 

1.96171 

.67884 

2.11367 

16 

17 

.62998 

1.70258 

.64625 

1.82688 

.GG2G3 

1.96411 

.67911 

2.11635 

17 

18 

.63025 

1.70455 

.64653 

1.82906 

.66290 

1.96652 

.67939 

2.11903 

18 

19 

.63052 

1.70653 

.64680 

1.83124 

.66318 

1.96893 

.G7966 

2.12171 

19 

20 

.63079 

1.70851 

.64707 

1.83342 

.66345 

1.97135 

.67994 

2.12440 

20 

21 

.63106 

1.71050 

.64734 

1.83561 

.66373 

1.97377 

.68021 

2.12709 

21 

22 

.63133 

1.71249 

.64761 

1.83780 

.(56400 

1.97619 

.68049 

2.12979 

22 

23 

.63161 

1.71448 

.64789 

1.83999 

.66427 

1.97862 

.68077 

2.13249 

23 

24 

.63188 

1.71647 

.64816 

1.84219 

.66455 

1.98106 

.68104 

2.13520 

24 

25 

.63215 

1.71847 

.64843 

1.84439 

.66482 

1.98349 

.68132 

2.13791 

25 

26 

.63242 

1.72047 

.64870 

1.84659 

.66510 

1.  98594 

.68159 

2.14063 

26 

27 

.63269 

1.72247 

.64898 

1.84880 

.66537 

1.98838 

.68187 

2.14335 

27 

28 

.63296 

1.72448 

.64925 

1.85102 

.66564 

1.99083 

.68214 

2.14608 

28 

29 

.63323 

1.72619 

.64952 

1.85323 

.66592 

1.99329 

.68242 

2.14881 

29 

30 

.63350 

1.72850 

.64979 

1.85545 

.66619 

1.99574 

.68270 

2.15155 

30 

31 

.63377 

1.73052 

.65007 

1.85767 

.66647 

1.99821 

.68297 

2.15429 

31 

32 

.63404 

1.73254 

.65034 

1.85990 

.66674 

2.00067 

.68325 

2.15704 

32 

33 

.63431 

1.73456 

.65061 

1.86213 

.66702 

2.00315 

.68352 

2.15979 

33 

34 

.63458 

1.73659 

.65088 

1.86437 

.66729 

2.00562 

.68380 

2.16255 

34 

35 

.63485 

1.73862 

.65116 

1.86661 

.66756 

2.00810 

.68408 

2.16531 

35 

36 

.63512 

1.74065 

.65143 

1.86885 

.66784 

2.01059 

.68435 

2.16808 

36 

37 

.63539 

1.74269 

.65170 

1.87109 

.66811 

2.01308 

.68463 

2.17085 

37 

38 

.63566 

1.74473 

.65197 

1.87334 

.66839 

2.01557 

.68490 

2.17363 

38 

39 

.63594 

1.74677 

.65225 

1.87560 

.66866 

2.01807 

.68518 

2.17641 

39 

40 

.63621 

1.74881 

.65252 

1.87785 

.66894 

2.02057 

.68546 

2.17920 

40 

41 

.63648 

1.75036 

.65279 

1.88011 

.66921 

2.02308 

.68573 

2.18199 

41 

42 

.63675 

1.75292 

.65306 

1.88238 

.66949 

2.02559 

.68601 

2.18479 

42 

43 

.63702 

1.75497 

.65334 

1.88465 

.6697'6 

2.02810 

.68628 

2.18759 

43 

44 

.63729 

1.75703 

.65361 

1.88692 

.67003 

2.03062 

.68656 

2.19040 

44 

45 

.63756 

1.75909 

.65388 

1.88920 

.67031 

2.03315 

.68684 

2.19322 

45 

46 

.63783 

1.76116 

.65416 

1.89148 

.67058 

2.03568 

.68711 

2.19604 

46 

47 

.63810 

1.76323 

.65443 

1.89376 

.67086 

2.03821 

.68739 

2.19886 

47 

48 

.63838 

1.76530 

.65470 

1.89605 

.67113 

2.04075 

.68767 

2.20169 

48 

49 

.63865 

1.76737 

.65497 

1.89834 

.67141 

2.04329 

.68794 

2.20453 

49 

50 

.63892 

1.76945 

.65525 

1.90063 

.67168 

2.04584 

.68822 

2.20737 

50 

51 

.63919 

1.77154 

.65552 

1.90293 

.67196 

2.04839 

.68849 

2.21021 

51 

52 

.63946 

1.77362  ! 

.65579 

1.90524 

.67223 

2.05094 

.68877 

2.21306 

52 

53 

.63973 

1.77571  ! 

.65607 

1.90754 

.67251 

2.05350 

.68905 

2.21592 

53 

54 

.64000 

1  77780  I 

.65634 

1.90986 

.67278 

2.05607 

.68932 

2.21878 

54 

55 

.64027 

1.77990  ! 

.65661 

1.91217 

.67306 

2.05864 

.68960 

2.22165  55 

56 

.64055 

1.78200 

.65689 

1.91449 

.67333 

2.06121 

.68988 

2.22452 

56 

57 

.64082 

1.78410 

.65716 

1.91681 

.67361 

2.06379 

.69015 

2.22740 

57 

58 

.64109 

1.78621 

.65743 

1.91914 

.67388 

2.06637 

.69043 

2.23028 

58 

59 

.64136 

1.78832 

.65771 

1.92147 

.67416 

2.06896 

.69071 

2.23317 

59 

60 

.64163 

1.79043 

.65798 

1.92380  1 

.67443  2.07155 

.69098 

2.23607 

60 

264 


TABLE    XVII.— NATURAL  VERSED  SINES  AND    EXTERNAL  SECANTS. 


' 

72° 

73° 

74° 

75° 

• 

Vers. 

Ex.  sec. 

Vsrs. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.69098 

2.23607 

.70763 

2.42030 

.72436 

2.62796 

.74118 

2.86370 

0 

1 

.69126 

2.23897 

.70791 

2.42356 

.72404 

2.63164 

.74146 

2.86790 

1 

2 

.69154 

2.24187 

.70818 

2.42683 

.72492 

2  63533 

.74174 

2.87211 

2 

3 

.69181 

2.24478 

.70846 

2.43010 

.72520 

2.63903 

.74202 

2.87633 

3 

4 

.69209 

2.24770 

.70874 

2.43337 

.72548 

2.64274 

.74231 

2.88056 

4 

5 

.69237 

2.25062 

.70902 

2.43666 

.72576 

2.64645 

.74259 

2.88479 

5 

6 

69264 

2.25355 

.70930 

2.43995 

.72604 

2.65018 

.74287 

2.88904 

6 

7 

.69292 

2.25648 

.70958 

2.44324 

.72632 

2.65391 

.74315 

2.89330 

7 

8 

.69320 

2.25942 

.7'0985 

2.44655 

.72660 

2.65765 

.74343 

2.89756 

8 

9 

.69347 

2  26237 

.71013 

2.44986 

.72688 

2.66140 

.74371 

2.90184 

9 

10 

.69375 

2.26531 

.71041 

2.45317 

.72716 

2.66515 

.74399 

2.90613 

10 

11 

.69403 

2.26827 

.71069 

2.45650 

.72744 

2.66892 

.74427 

2.91042 

U 

13 

.69430 

2.27123 

.71097 

2.45983 

.72773 

2.67269 

.74455 

2.91473 

IS 

13 

.69458 

2.27420 

.71125 

2.46316 

.72800 

2.67647 

.74484 

2.91904 

13 

14 

.69486 

2.27717 

.71153 

2.46651 

.72828 

2.68025 

.74512 

2.92337 

14 

15 

.69514 

2.28015 

.71180 

2.46986 

.72856 

2.68405 

.74540 

2.92770 

15 

10 

.69541 

2.28313 

.71208 

2.47321 

.72884 

2.68785 

.74568 

2.93204 

10 

17 

.69569 

2.28612 

.71236 

2.47658 

.72912 

2.69167 

.74596 

2.93640 

17 

18 

.69597 

2.28912 

.71264 

2.47995 

.72940 

2.69549 

.74024 

2.94076 

18 

19 

.69624 

2.29212 

.71292 

2.48333 

.72968 

2.69931 

.74052 

2.94514 

19 

20 

.69652 

2.29512 

.71320 

2.48671 

.72996 

2.70315 

.74680 

2.94952 

20 

21 

.69680 

2.298J4 

.71348 

2.49010 

.73024 

2.70700 

.74709 

2.95392 

21 

22 

.69708 

2.30115 

.71375 

2.49350 

.73052 

2.71085 

.  74737 

2.95832 

22 

23 

.69735 

2.30418 

.71403 

2.49691 

.73080 

2.71471 

.74765 

2.96274 

23 

24 

.69703 

2.30721 

.71431 

2.50032 

.73108 

2.71858 

.74793 

2.96716 

24 

25 

.69791 

2.31024 

.71459 

2.50374 

.73136 

2.72246 

.74821 

2.97160 

25 

26 

.69818 

2.31328 

.71487 

2.50716 

.73164 

2.72635 

.74849 

2.97604 

20 

27 

.69846 

2.31633 

.71515 

2.51000 

.73192 

2.73024 

.74878 

2.98050 

27 

28 

.69874 

2.31939 

.71543 

2.51404 

.73220 

2.73414 

.74906 

2.98497 

28 

29 

.69902 

2  32244 

.71571 

2.51748 

.73248 

2.73800 

.74934 

2.98944 

29 

30 

.69929 

2.32551 

.71598 

2.52094 

.7'3276 

2.74198 

.74962 

2.99393 

30 

31 

.69957 

2.32858 

.71026 

2.52440 

.73304 

2.74591 

.74990 

2.99843 

31 

32 

.69985 

2.33166 

.71054 

2.52787 

.73332 

2.7'4984 

.75018 

3.00293 

32 

33 

.70013 

2.33474 

.71082 

2.53134 

.73360 

2.75379 

.75047 

3.00745 

33 

34 

.70040 

2.33783 

.71710 

2.53482 

.73388 

2.75775 

.75075 

3.01198 

34 

35 

.70008 

2.34092 

.71738 

2.53831 

.73416 

2.76171 

.75103 

3.01652 

35 

30 

.70096 

2.34403 

.71766 

2.54181 

.73444 

2.76568 

.75131 

3.02107 

30 

37 

.70124 

2.34713 

.71794 

2.54531 

.73472 

2.76906 

.75159 

3.02503 

37 

38 

.70151 

2.35025 

.71822 

2.54883 

.73500 

2.77305 

.75187 

3.03020 

38 

39 

.70179 

2.35336 

.71850 

2.55235 

.73529 

2.77705 

.75216 

3.03479 

39 

40 

.70207 

2.35649 

.71877 

2.55587 

.73557 

2.78166 

.75244 

3.03938 

40 

41 

.70235 

2.35962 

.71905 

2.55940 

.73585 

2.78568 

.75272 

3.04398 

41 

42 

.70263 

2.36276 

.71933 

2.56294 

.73613 

2.78970 

.75300 

3.04860 

42 

43 

.70290 

2.36590 

.71961 

2.56649 

.73641 

2.79374 

.75328 

3.05322 

43 

44 

.70318 

2.36905 

.71989 

2.57005 

.73009 

2.79778 

.75356 

3.05786 

44 

45 

.70346 

2.37221 

.72017 

2.57361 

.73097 

2.80183 

.75385 

3.06251 

45 

40 

.70374 

2.37537 

.72045 

2.57718 

.73725 

2.80589 

.75413 

3.06717 

40 

47 

.70401 

2.37854 

.72073 

2.58076 

.73753 

2.80996 

.75441 

3.07184 

47 

48 

.70429 

2.38171 

.72101 

2.58434 

.73781 

2.81404 

.75469 

3.07652 

48 

49 

.70457 

2.38489 

.72129 

2.58794 

.73809 

2.81813 

.75497 

3.08121 

49 

50 

.70485 

2.38808 

.72157 

2.59154 

.73837 

2.82223 

.75526 

3.08591 

50 

51 

.70513 

2.39128 

.72185 

2.59514 

.73865 

2.82633 

.75554 

3.09063 

51 

52 

.70540 

2.39448 

.72213 

2.59876 

.73893 

2.83045 

.75582 

3.09535 

52 

53 

.70568 

2.39768 

.72241 

2.60238 

.73921 

2.83457 

.75610 

3.10009 

53 

54 

.70596 

2.40089 

.72269 

2.60601 

.73950 

2.83871 

.75639 

3.10484 

54 

55 

.70624 

2.40411 

.72296 

2.60965 

.73978 

2.84285 

.75667 

3.10960 

55 

50 

.70652 

2.40734 

.72324 

2.61330 

.74006 

2.84700 

.75695 

3.11437 

50 

57 

.70679 

2.41057 

.72352 

2.61695 

.74034 

2.85116 

.75723 

3.11915 

57 

58 

.70707 

2.41381 

.72380 

2.62061 

.74062 

2.85533 

.75751 

3.12394 

58 

59 

.70735 

2.41705 

.72408 

2.62428 

.74090 

2.85951 

.75780 

3.12875 

59 

60 

.70763 

2.42030 

.72436 

2.6279G 

.74118 

2.86370 

.75808 

3.13357 

60 

265 


XVII.— NATURAL  VERSED  SINES  AND  EXTERNAL   SECANTS, 


/ 

7 

6° 

7 

7° 

7 

8° 

7 

9° 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.75808 

3.13357 

.77505 

3.44541 

.79209 

3.80973 

.80919 

4.24084 

0 

1 

.75836 

3.13839 

.77533 

3.45102 

.79237 

3.81633 

.80948 

4.24870 

1 

2 

.75804 

3.14323 

.77562 

3.45664 

.79266 

3.82294 

.80976 

4.25658 

2 

3 

.75892 

3.14809 

.77590 

3.46228 

.79294 

3.82956 

.81005 

4.26448 

3 

4 

.75921 

3.15295 

.77618 

3.46793 

.79323 

3.83621 

.81033 

4.27241 

4 

5 

.75949 

3.15782 

.77647 

3.47360 

.79351 

3.84288 

.81062 

4.28036 

5 

6 

.75977 

3.16271 

.77675 

3.47928 

.79380 

3.84956 

.81090 

4.28833 

6 

7 

.76005 

3.16761 

.77703 

3.48498 

.79408 

3.85627 

.81119 

4.29634 

7 

8 

.76034 

3.17252 

.77732 

3.49069 

.79437 

3.86299 

.81148 

4.30436 

8 

9 

.76062 

3.17744 

.77760 

3.49642 

.79-165 

3.86973 

.81176 

4.31241 

9 

10 

.76090 

3.18238 

.77788 

3.50216 

.7'9493 

3.87649 

.81205 

4.32049 

10 

11 

.76118 

3.187&3 

.77817 

3.50791 

.79522 

3.88327 

.81233 

4.32859 

11 

12 

.76147 

3.19228 

.77845 

3.51368 

.79550 

3.89007 

.81262 

4.33671 

12 

13 

.76175 

3.19725 

.77874 

3.51947 

.79579 

3.89689 

.81290 

4.34486 

13 

14 

.76203 

3.20224 

.77902 

3.52527 

.79607 

3.90373 

.81319 

4.35304 

14 

15 

.76231 

3.20723 

.77930 

3.53109 

.79636 

3.91058 

.81348 

4.36124 

15 

16 

.76260 

3.21224 

.77959 

3.53692 

.79664 

3.91746 

.81376 

4.36947 

16 

17 

.76288 

3.21726 

.77987 

3.54277 

.79693 

3.92436 

.81405 

4.37772 

17 

18 

.76316 

3.22229 

.78015 

3.54863 

.79721 

3.93128 

.81433 

4.38600 

18 

19 

.76344 

8.22734 

.78044 

3.55451 

.79750 

3.93821 

.81462 

4.39430 

19 

20 

.76373 

3.23239 

.78072 

3.56041 

.79778 

3.94517 

.81491 

4.40263 

20 

21 

.76401 

3.23746 

.78101 

3.56632 

.79807 

3.95215 

.81519 

4.41099 

21 

22 

.76429 

3.24255 

.78129 

3.57224 

.79835 

3.95914 

.81548 

4.41937 

22 

23 

.76458 

3.24764 

.78157 

3.57819 

.79864 

3.96616 

.81576 

4.42778 

"•'» 

24 

.76486 

3.25275 

.78186 

3.58414 

.79892 

3.97320 

.81605 

4.43622 

24 

25 

.76514 

3.25787 

.78214 

3.59012 

.79921 

3.98025 

.81633 

4.44468 

25 

26 

.76542 

3.26300 

.78242 

3.59611 

.79949 

3.98733 

.81662 

4.45317 

26 

27 

.76571 

3.26814 

.78271 

3.60211 

.79978 

3.99443 

.81691 

4.46169 

27 

28 

.76599 

3.27330 

.78299 

3.60813 

.80006 

4.00155 

.81719 

4.47023 

28 

29 

.76627 

3.27847 

.78328 

3.61417 

.80035 

4.00869 

.81748 

4.47881 

29 

30 

.76655 

3.28366 

.78356 

3.62023 

.80063 

4.01585 

.81776 

4.48740 

30 

31 

.76684 

3.28885 

.78384 

3.62630 

.80092 

4.02303 

.81805 

4.49603 

31 

32 

.76712 

3.29406 

.78413 

3.63238 

.80120 

4.03024 

.81834 

4.50468 

82 

33 

.76740 

3.29929 

.78441 

3.63849 

.80149 

4.03746 

.81862 

4.51337 

33 

34 

.76769 

3.30452 

.78470 

3.64461 

.80177 

4.04471 

.81891 

4.52208 

34 

35 

.76797 

3.30977 

.7'8498 

3.65074 

.80206 

4.05197 

.81919 

4.53081 

35 

36 

.76825 

3.31503 

.78526 

3.65690 

.802C4 

4.05926 

.81948 

4.53958 

36 

37 

.76854 

3.32031 

.7'8555 

3.66307 

.80203 

4.06657 

.81977 

4.54837 

37 

38 

.76882 

3.32560 

.78583 

3.66925 

.80291 

4.07'390 

.82005 

4.55720 

88 

39 

.76910 

3.33090 

.78612 

3.67545 

.80320 

4.08125 

.82034 

4.56605 

39 

40 

.76938 

3.33622 

.78640 

3.68167 

.80348 

4.08863 

.82063 

4.57493 

40 

41 

.76967 

3.34154 

.78669 

3.68791 

.80377 

4.09602 

.82091 

4.58383 

41 

42 

.76995 

3.34689 

.78697 

3.69417 

.80405 

4.10344 

.82120 

4.59277 

42 

43 

.77023 

3.35224 

.787'25 

8.70044 

.80434 

4.11088 

.82148 

4.60174 

43 

44 

.77052 

3.35761 

.78754 

3.70673 

.80462 

4.11835 

.82177 

4.81073 

44 

45 

.77080 

3.36299 

.78782 

3.71303 

.80491 

4.12583 

.82206 

4.61976 

45 

46 

.77108 

3.36839 

.78811 

3.71935 

.80520 

4.13334 

.82234 

4.62881 

40 

47 

.77137 

3.37380 

.78839 

3.72569 

.80548 

4.14087 

.82263 

4.63790 

47 

48 

.77165 

3.37923 

.78868 

3.73205 

.80577 

4.14842 

.82292 

4.64701 

48 

49 

.77193 

3.38466 

.78896 

3.73843 

.80605 

4.15599 

.82320 

4.65616 

49 

50 

.77222 

3.39012 

.78924 

3.74482 

.80634 

4.16359 

.82349 

4.66533 

50 

51 

.77250 

3.39558 

.78953 

3.75123 

.80602 

4.17121 

.82377 

4.67454 

51 

52 

.77278 

3.40106 

.78981 

3.75766 

.80691 

4.17886 

.82406 

4.68377 

52 

53 

.77307 

3.40656 

.79010 

3.76411 

.80719 

4.18652 

.82435 

4.6S304 

58 

54 

.77335 

3.41206 

.79038 

3.77057 

.80748 

4.19421 

.82463 

4.70234 

54 

55 

.77363 

3.41759 

.79067 

3.77705 

.80776 

4.20193 

.82492 

4.71166 

55 

56 

."7392 

3.42312 

.79095 

3.78355 

.80805 

4.20966 

.82521 

4.72102 

56 

57 

."7420 

3.42867 

.79123 

3.79007 

.80833 

4.21742 

82549 

4.73041 

57 

58 

."7448 

3.43424 

.79152 

3.79661 

.80862 

4.22521 

.82578 

4.73983 

58 

59 

."7477 

3.43982 

.79180 

3.80316 

.80891 

4.23301 

.82607 

4.74929 

59 

60 

."7505 

3.44541 

.  79209 

3.80973 

.80919 

4.24084 

.82635 

4.75877 

60 

266 


TABLE    XVII.— NATURAL,  VERSED   SINES  AND  EXTERNAL  SECANTS. 


' 

80° 

81°         82° 

83° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.82635 

4.75877 

.84357 

5.39245 

.86083 

6.18530 

.87813 

7.20551 

0 

1 

.82664 

4.76829 

.84385 

5.40422 

.86112 

6.20020 

.87842 

7.22500 

1 

2 

.82692 

4.77784 

.84414 

5.41602 

.86140 

6.21517 

.87871 

7.24457 

2 

8 

.82721 

4.78742 

.84443 

5.42787 

.86169 

6.23019 

.87900 

7.26425 

3 

4 

.82750 

4.797'03 

.84471 

5.43977 

.86198 

6.24529 

.87929 

7.28402 

4 

5 

.82778 

4.80667 

.84500 

5.45171 

.86227 

6.26044 

.87957 

7.30388 

5 

G 

.82807 

4.81635 

.84529 

5.46369 

.86256 

6.27566 

.87986 

7.32384 

6 

7 

.82836 

4.82606 

.84558 

5.47572 

.86284 

6.29095 

.88015 

7.34390 

7 

8 

.82864 

4.  "83581 

.84586 

5.48779 

.86313 

6.30630 

.88044 

7.36405 

8 

9|  .82893 

4.84558 

.84615 

5.49991 

.86342 

6.32171 

.88073 

7.38431 

9 

10 

.82922 

4.85539 

.84644 

5.51208 

.86371 

6.33719 

.88102 

7.40466 

10 

11 

.82950 

4.86524 

.84673 

5.52429 

.86400 

6.35274 

.88131 

7.42511 

11 

12 

.82979 

4.87511 

.84701 

5.53655 

.86428 

6.36835 

.88160 

7.44566 

12 

13 

.83008 

4.88502 

.84730 

5.54886 

.86457 

6.38403 

.88188 

7.46632 

13 

14 

.83036 

4.89497 

.84759 

5.56121 

.86486 

6.39978 

.88217 

7.48707 

14 

15 

.83065 

4.90495 

.84788 

5.57361 

.86515 

6.41560 

.88246 

7.50793 

15 

16 

.83094 

4.91496 

.84816 

5.58606 

.86544 

6.43148 

.88275 

7.52889 

16 

17 

.83122 

4.92501 

.84845 

5.59855 

.86573 

6.44743 

.88304 

7.54996 

17 

18 

.83151 

4.93509 

.84874 

5.61110 

.86601 

6.46346 

.88333 

7.57113 

18 

19 

.83180 

4.94521 

.84903 

5.62369 

.88630 

6.47955 

.88362 

7.59241 

19 

20 

.83208 

4.95536 

.84931 

5.63633 

.86659 

6.49571 

.88391 

7.61379 

20 

21 

.83237 

4.96555 

.84960 

5.64902 

.86688 

6.51194 

.88420 

7.63528 

21 

22 

.83266 

4.97577 

.84989 

5.66176 

.86717 

6.52825 

.88448 

7.65688 

22 

23 

.83294 

4.98603 

.85018 

5.67454 

.86746 

6.54462 

.88477 

7.67859 

23 

24 

.83323 

4.99633 

.85046 

5.68738 

.86774 

6.56107 

.88506 

7.70041 

24 

25 

.83352 

5.00666 

.85075 

5.70027 

.86803 

6.57759 

.88535 

7.72234 

25 

26 

.83380 

5.01703 

.85104 

5.71321 

.86832 

6.59418 

.88564 

7.74438 

26 

27 

.83409 

5.02743 

.85133 

5.72620 

.86861 

6.61085 

.88593 

7.76653 

27 

28 

.83438 

5.03787 

.85162 

5.73924 

.86890 

6.62759 

.88622 

7.78880 

28 

29 

.83467 

5.04834 

.85190 

5.75233 

.86919 

6.64441 

.88651 

7.81118 

29 

30 

.83495 

5.05886 

.85219 

5.76547 

.86947 

6.66130 

.88680 

7.83367 

30 

31 

.83524 

5.06941 

.85248 

5.77866 

.86976 

6.67826 

.88709 

7.85628 

31 

32]  .83553 

5.08000 

.85277 

5.79191 

.87005 

6.69530 

.88737 

7.87901 

32 

33 

.83581 

5.09062 

.85305 

5.80521 

.87034 

6.71242 

.88766 

7.90186 

33 

34 

.83610 

5.10129 

.85334 

5.81856 

.87063 

6.72962 

.88795 

7.92482 

34 

35 

.83639 

5.11199 

.85363 

5.83196 

.87092 

6.74689 

.88824 

7.94791 

35 

36 

.83667 

5.12273 

.85392 

5.84542 

.87120 

6.76424 

.88853 

7.97111 

36 

37 

.83696 

5.13350 

.85420 

5.85893 

.87149 

6.78167 

.88882 

7.99444 

37 

38 

.83725 

5.14432 

.85449 

5.87250 

.87178 

6.79918 

.88911 

8.01788 

38 

39 

.83754 

5.15517 

.85478 

5.88612 

.87207 

6.81677 

.88940 

8.04146 

39 

40 

.83782 

5.16607 

.85507 

5.89979 

.87236 

6.83443 

.88969 

8.06515 

40 

41  i  .83811 

5.17700 

.85536 

5.91352 

.87265 

6.85218 

.88998 

8.08897 

41 

42  .83840 

5.18797 

.85564 

5.92731 

.87294 

6.87001 

.89027 

8.11292 

42 

43 

.83868 

5.19898 

.85593 

5.94115 

.87322 

6.88792 

.89055 

8.13699 

43 

44 

.83897 

5.21004 

.85622 

5.95505 

.87351 

6.90592 

.89084 

8.16120 

44 

45 

.83926 

5.22113 

.85651 

5.96900 

.87380 

6.92400 

.89113 

8.18553 

45 

46  :  .83954 

5.23226 

.85680 

5.98301 

.87409 

6.94216 

.89142 

8.20999 

46 

47j  .83983 

5.24:343 

.85708 

5.99708 

.87438 

6.96040 

.89171 

8.23459 

47 

48:  .84012 

5.25464 

.85737 

6.01120 

.87467 

6.97873 

.89200 

8.25931 

48 

49'  .84041 

5.26590 

.85766 

6.02538 

.87496 

6.99714 

.89229 

8.28417 

49 

50 

.84069 

5.27719 

.85795 

6.03962 

.87524 

7.01565 

.89258 

8.30917 

50 

51 

.84098 

5.28853 

.85823 

6.05392 

.87553 

7.03423 

.89287 

8.&3430 

51 

52 

.84127 

5.29991 

.85852 

6.06828 

.87582 

7.05291 

.89316 

8.35957 

52 

53 

.84155 

5.31133 

.&5881 

6.08269 

.87611 

7.07167 

.89345 

8.38497 

53 

54 

.84184 

5.32279 

.85910 

6.09717 

.87640 

7.09052 

.89374 

8.41052 

54 

55 

.84213 

5.33429 

.85939 

6.11171 

.87669 

7.10946 

.89403 

8.43620 

55 

56 

.84242 

5.34584 

.85967 

6.12630 

.87698 

7.12849 

.89431 

8.46203 

56 

57 

.84270 

5.35743 

.85996 

6.14096 

.87726 

7.14760 

.89460 

8.48800 

57 

58 

.84299 

5.36906 

.86025 

6.15568 

.87755 

7.16681 

.89489 

8.51411 

58 

50 

.84328 

5.38073 

.86054 

6.17046 

.87784 

7.18612 

.89518 

8.54037 

59 

60 

.84357 

5.39245 

.86083 

6.18530 

.87813 

7.20551 

.89547 

8.56677 

60 

267 


TABLE     XVII.— NATURAL  VERSED  SINES  AND  EXTERNAL    SECANTS. 


/ 

84° 

85° 

86° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.89547 

8.50677 

.91284 

10.47371 

.93024 

13.33559 

0 

1 

.89576 

8.59332 

.91313 

10.51199 

.93053 

13.39547 

1 

2 

.89605 

8.62002 

.91342 

10.55052 

.93082 

13.45586 

2 

3 

.89634 

8.64687 

.91371 

10.58932 

.93111 

13.51676 

3 

4 

.89663 

8.67387 

.91400 

10.62837 

.93140 

13.57817 

4 

5 

.89092 

8.70103 

.91429 

10.66769 

.93169 

13.64011 

5 

6 

.897*1 

8.72833 

.91458 

10.70728 

.93198 

13.70258 

6 

7 

.89750 

8  .  75579 

.91487 

10.74714 

.93227 

13.76558 

7 

8 

.89719 

8.78341 

.91516 

10.78727 

.93257 

13.82913 

8 

9 

.89808 

8.81119 

.91545 

10.82768 

.93286 

13.89323 

9 

10 

.89836 

8.83912 

.91574 

10.86837 

.93315 

13.95788 

10 

11 

.89865 

8.86722 

.91603 

10.90934 

.93344 

14.02310 

11 

12 

.89894 

8.89547 

.91032 

10.95060 

.933?'3 

14.08890 

12 

13 

.89923 

8.92389 

.91661 

10.99214 

.93402 

14.15527 

13 

14 

.89952 

8.95248 

.91690 

11.03397 

.93431 

14.22223 

14 

15 

.89981 

8.98123 

.91719 

11.07610 

.93460 

14.28979 

15 

16 

.90010 

9.01015 

.91748 

11.11852 

.93489 

14.35795 

16 

17 

.90039 

9.03923 

.91777 

11.16125 

.93518 

14.42672 

17 

18 

.90068 

9.06849 

.91806 

11.20427 

.93547 

14.49611 

18 

19 

.90097 

9.09792 

.91835 

11.24761 

.93576 

14.56614 

19 

20 

.9C126 

9.12752 

.91804 

11.29125 

.93605 

14.63679 

20 

21 

.90155 

9.15730 

.91893 

11.33521 

.93634 

14.70810 

21 

22 

.90184 

9.18725 

.91922 

11.37948 

.93663 

14.78005 

22 

23 

.90213 

9.21739 

.91951 

11.42408 

.93692 

14.85208 

23 

24 

.90242 

9.24770 

.91980 

11.46900 

.93721 

14.92597 

24 

25 

.90271 

9.27819 

.92009 

11.51424 

.93750 

14.99995 

25 

26 

.90300 

9.30887 

.92038 

11.55982 

.93779 

15.07462 

26 

27 

.90329 

9.33973 

.92067 

11.60572 

.93808 

15.14999 

27 

28 

.90358 

9.37077 

.92096 

11.65197 

.93837 

15.22607 

28 

29 

.90386 

9.40201 

.92125 

11.69856 

.93866 

15.30287 

29 

30 

.90415 

9.43343 

.92154 

11.74550 

.93895 

15.38041 

30 

31 

.90444 

9.46505 

.92183 

11.79278 

.93924 

15.45869 

31 

32 

.90473 

9.49685 

.92212 

11.84042 

.93953 

15.53772 

32 

33 

.90502 

9.52886 

.92241 

11.88841 

.93982 

15.61751 

33 

34 

.90531 

9.56106 

.92270 

11.93677 

.94011 

15.69808 

34 

35 

.90560 

9.59346 

.92299 

11.98549 

.94040 

15.77944 

35 

36 

.90589 

9.62605 

.92328 

12.03458 

.94069 

15.86159 

36 

37 

.90018 

9.65885 

.92357 

12.08040 

.94098 

15.94456 

37 

38 

.90647 

9.69186 

.92386 

12.13388 

.94127 

16.02835 

38 

39 

.90676 

9.72507 

.92415 

12.18411 

.94156 

16.11297 

39 

40 

.90705 

9.75849 

.92444 

12.23472 

.94186 

16.19843 

40 

41 

.90734 

9.79212 

.92473 

12.28572 

.94215 

16.28476 

41 

42 

.90763 

9.82596 

.92502 

12.33712 

.94244 

16.37196 

42 

43 

.90792 

9.86001 

.92531 

12.38891 

.94273 

16.46005 

43 

44 

.90821 

9.89428 

.92560 

12.44112 

.94302 

16.54903 

44 

45 

.90850 

9  92877 

.92539 

12.49373 

.94331 

16.63893 

45- 

46 

.90879 

9.96348 

.92618 

12.54676 

.94360 

16.72975 

46 

47 

.90908 

9.99841 

.92647 

12.60021 

.94389 

16.82152 

47 

48 

.90937 

10.0.3356 

.92676 

12.65408 

.94418 

16.91424 

48 

49 

.90966 

10.06894 

.92705 

12.70838 

.94447 

17.00794 

49 

50 

.90995 

10.10455 

.92734 

12.76312 

.94476 

17.10262 

50 

51 

.91024 

10.14039 

.92763 

12.81829 

.94505 

17.19830 

51 

52 

.91053  J 

10.17646 

.92792 

12.87391 

.94534 

17.29501 

52 

53 

.91082 

10.21277 

.92821 

12.92999 

.94563 

17.39274 

53 

54 

.91111 

10.24932 

.92850 

12.98651 

.94592 

17.49153 

54 

55 

.91140 

10.28610 

.92879 

13  04350 

.94621 

17.59139 

55 

56 

.91169 

10.32313 

.92908 

13.10096 

.94050 

17.69233 

56 

57 

.91197 

10.36040 

.92937 

13.15889 

.94679 

17.79438 

57 

58 

.91226 

10.39792 

.92966 

13.21730 

.94708 

17.89755 

58 

59 

.91255 

10.43569 

.92995 

13.27620 

.94737 

18.00185 

59 

60 

.91284 

10.47371 

.93024 

13.33559 

.94766 

18.10732 

60 

268 


TABLE    XVII.— NATURAL  VERSED  SINES  AND  EXTERNAL  SECANTS. 


/ 

87° 

88° 

89° 

/ 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

Vers. 

Ex.  sec. 

0 

.94766 

18.10732 

.96510 

27.65371 

.98255 

56.29869 

0 

1 

.94795 

18.21397 

.96539 

27.89440 

.98284 

57.26976 

1 

2 

.94825 

18.32182 

.96568 

28.13917 

.98313 

58.27431 

2 

3 

.94854 

18.43088 

.96597 

28.38812 

.98342 

59.31411 

3 

4 

.94883 

18.54119 

.96636 

28.64137 

.9&371 

60.39105 

4 

5 

.94912 

18.65275 

.96655 

28.89903 

.98400 

61.50715 

5 

6 

.94941 

18.76560 

.96684 

29.16120 

.98429 

62.66460 

6 

7 

.94970 

18.87976 

.96714 

29.42802 

.98458 

63.86572 

7 

8 

.94999 

18.99524 

.96743 

29.69960 

.98487 

65.11304 

8 

9 

.95028 

19.11208 

.96772 

29.97607 

.98517 

66.40927 

9 

10 

.95057 

19.23028 

.96801 

30.25758 

.98546 

67.75736 

10 

11 

.95086 

19.34989 

.96830 

30.54425 

.98575 

69.16047 

n 

12 

.95115 

19.47093 

.968i:9 

30.83623 

.98604 

70.62285 

12 

13 

.95144 

19.59341 

.96888 

31.13366 

.98633 

72.14583 

13 

14 

.95173 

19.71737 

.96917 

31.43671 

.98662 

73.73586 

14 

15 

.95202 

19.84283 

.96946 

31.74554 

.98691 

75.39655 

15 

16 

.95231 

19.96982 

.96975 

32.06030 

.98720 

77.13274 

16 

17 

.95260 

20.09838 

.97004 

32.38118 

.98749 

78.94968 

17 

18 

.95289 

20.22852 

.97033 

32.70835 

.98778 

80.85315 

18 

19 

.95318 

20.36027 

.97062 

33.04199 

.98807 

82.84947 

19 

20 

.95347 

20.49368 

.97092 

33.38232 

.98836 

84.94561 

20 

21 

.95377 

20.62876 

.97121 

33.72952 

.98866 

87.14924 

21 

2-2 

.95406 

20.76555 

.97150 

34.08380 

.98895 

89.46886 

22 

23 

.95435 

20.90403 

.97179 

34.44539 

.98924 

91.91387 

23 

2i 

.95464 

21.04440 

.97208 

34.81452 

.98953 

94.49471 

24 

25 

.95493 

21.18653 

.97237 

35.19141 

.98982 

97.22303 

25 

26 

.95522 

21.33050 

.97266 

35.57633 

.99011 

100.1119 

26 

27 

.95551 

21.47635 

.97295 

35.96953 

.99040 

103.1757 

27 

28 

.95580 

21.62413 

.97324 

36.37127 

.99069 

106.4311 

28 

29 

.95609 

21.77386 

.97353 

36.78185 

.99098 

109.8966 

29 

30 

.95638 

21.92559 

.97382 

37.20155 

.99127 

113.5930 

30 

31 

.95667 

22.07935 

.97411 

37.63068 

.09156 

117.5444 

31 

32 

.95696 

22.23520 

.97440 

38.06957 

.99186 

121.7780 

32 

33 

.95725 

22.39316 

.97470 

38.51855 

.99215 

126.3253 

33 

34 

.95754 

22.55329 

.97499 

38.97797 

.99244 

131.2223 

34 

35 

.95783 

22.71563 

.97528 

39.44820 

.99273 

136.5111 

35 

36 

.95812 

22.88022 

.97557 

39.92963 

.99302 

142.2406 

36 

37 

.95842 

23.04712 

.97586 

40.42266 

.99331 

148.4684 

37 

38 

.95871 

23.21637 

.97615 

40.92772 

.99360 

155.2623 

38 

39 

.95900 

23.38802 

.97644 

41.44525 

.99389 

162.7033 

39 

40 

.95929 

23.56212 

.97673 

41.97571 

.99418 

170.8883 

40 

41 

.95958 

23.73873 

.97702 

42.51961 

.99447 

179.9350 

41 

42 

.95987 

23.91790 

.97731 

43.07746 

.99476 

189.9868 

42 

43 

.96016 

24.09969 

.97760 

43.64980 

.99505 

201.2212 

43 

44 

.96045 

24.28414 

.97789 

44.23720 

.99535 

213.8600 

44 

45 

.96074 

24.47134 

.97819 

44.84026 

.99564 

228.1839 

45 

46 

.96103 

24.66132 

.97848 

45.45963 

.99593 

244.5540 

46 

47 

.96132 

24.85417 

.97877 

46.09596 

.99622 

263.4427 

47 

48 

.96161 

25.04994 

.97906 

46.74997 

.99651 

285.4795 

48 

49 

.96190 

25.24869 

.97935 

47.42241 

.99680 

311.5230 

49 

50 

.96219 

25.45051 

.97964 

48.11406 

.99709 

342.7752 

50 

51 

.96248 

25.65546 

.97993 

48.82576 

.99738 

380.9723 

51 

52 

.96277 

25.86360 

.98022 

49  55840 

.99767 

428.7187 

52 

53 

.96307 

26.07503 

.98051 

50.31290 

.99796 

490.1070 

53 

54 

.96336 

26.28981 

.98080 

51.09027 

.89825 

571.9581 

54 

55 

.96365 

26.50804 

.98109 

51.89156 

.99855 

686.5496 

55 

56 

.96394 

26.72978 

.98138 

52.71790 

.99884 

858.4369 

56 

57 

.96423 

26.95513 

.98168 

53.57046 

.99913 

1144.916 

57 

58 

.96452 

27.18417 

.98197 

54.45053 

.99942 

1717.874 

58 

59 

.96481 

27.41700 

.98226 

55.a5946 

.99971 

3436.747 

59 

60 

.96510 

27.65371 

.98255 

56.29869 

1.00000 

Infinite 

60 

269 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


fWfifii    T    Ifidl 

ijt 

»'  '-'  "'Mi       ..;.•         it  &"v  :{ 

m 

ML*  T  P  e  «^ 

~S  te6Q4Q 

Uorf  2.%  61 

REC'D  UD 

NOV  18  b9-yAM 

. 

;  --..   ' 

•  *     '•"" 

* 

LD  21-100m-7,'39(402s) 

